E
r:

 

 

ham. P,
0 .rsxqrsnnfi. 3....
.wm.~umm§.h. ..
. ’15:.Luf53fl9 v.5!
1.4nafifldu
_ 5...».
. s

3.!4I2 1.1,.

ikwm...?.n.fi..

. . JRhnL-tl JEN

u E .. 5 .
.5535):

h... .3
I .P. A...
it 8’..qu
llamas... 11$
15

an , .
.4“ ‘15:».

ten
. . :3! I

35:1. #99..." P
.fiflfiduauhuhfimw

.1: .1 .22....
:niktlii

misffig

$.33... .

44.4... ..
.wn...snu...m.h.
.fi $.13

3

I.» a.
. £32.};
2... 1.1.

..
.7 .393.
a?! ny 22:23.3
: 2:51.33. 1 s .a I...
Kenniazstcal Lalhhflun rat-.33.:
.i ‘14: g”... lug, I [I'll-.53
p. 11.! an...“ h... . 1.4.. 3:5
. . .
. A. .9: .1. . x... .9... :0
in I.t&§
.33).; 118 A {Intact-8.).
34.553.23.51
.29.... .7: titer; .
3': I: a

. {310.1853
li..iz;hl.v at.
m... 2’05!“

tile in ‘1}...
a t! :1? 0..
£551.53!

r. 03 7! In
x r» I... A. 14(5),. I:
a.” (.zI‘ 521...! ‘1 ’ll;
1! it x... 151.:

. x!

P 1 .. 1h)”. 3
5. .4...) u! «(0:01-01:15 .r .v
v .3233. 5:11...” 4...qu i .1...» :13 $3...th
n a... .n is: u ..
P .vttlh... .. {P 1 ) .3

.w' xvii.

an... :
ifi..2uu..55.. V: .

THEBlS

2 . IlllllllllllllllllllllllllllllllHlllllllllllllllllll

(z, " 193 02048 8940
LIBRARY

Michigan State
University

 

 

 

 

This is to certify that the

thesis entitled

AN EXAMINATION OF THE GEOGRAPHICAL MARKET TERRITORIES
OF BASEBALL FRANCHISES

presented by

Daniel R. J. Minadeo
has been accepted towards fulfillment

of the requirements for

M- A- degree in Geography

WWW

Majorw p

Date ’é/g/w

0—7 639 MS U is an Affirmative Action/Equal Opportunity Institution

 

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

DATE DUE

DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11/00 cflflMpfiS—p.“

 

AN EXAMINATION OF THE MARKET TERRITORIES
OF BASEBALL FRANCHISES

By

Daniel R]. Minadeo

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF ARTS
Department of Geography

2000

ABSTRACT

AN EXAMINATION OF THE MARKET TERRITORIES
0F BASEBALL FRANCHISES

By

Daniel R]. Minadeo

Three parties who are interested in the geographical market territories of baseball
franchises are: franchise owners, leagues, and communities including their public officials.
However, the methods that these parties employ in order to determine the trade areas of
franchises are either inefficient or inadequate. Therefore, a potential model is examined to
ascertain if it can provide accurate estimates of the market territories of baseball
fianchises. Data was obtained from six minor league baseball organizations in order to
test the model’s predictions. Log-linear least squares regression and the standardized root
mean square error test statistic were applied to estimate the parameters of the model and
to evaluate the goodness-of-fit of the model. The results indicate that the model is able to
provide accurate predictions of the market territories of baseball franchises, although
competing destinations and outliers can affect the calibration of the model. Suggestions
are made that would allow the model to give better estimations of the trade areas and this
thesis offers an approach with regard to applying the model to other regions not studied in

this work.

To Simona and My Parents
Thank you for your encouragement, patience, and love.

iii

ACKNOWLEDGEMENTS

I would like to thank my advisor, Dr. Bruce Pigozzi, without whose perceptive
comments and constructive criticism this thesis could not have been completed. My
thanks to fellow graduate students, Jim Biles, Scott Crozier, and Paul Rindfleisch, for their
help and advice, and for being there when I needed them to listen to my tales of woe. I
also wish to express a very special thank you to my family for their unending intellectual
and emotional support, for encouraging and allowing me to pursue my educational goals,
and for all the much appreciated care packages. A final, but very important thank you to
my beautiful fiancee, Simona, who has enriched my life without measure and without

whom none of this would have been accomplished.

iv

TABLE OF CONTENTS

LIST OF TABLES ............................................................................... vii
LIST OF FIGURES .............................................................................. viii
LIST OF ABBREVIATIONS .................................................................... x
CHAPTER I
THE IMPORTANCE OF THE GEOGRAPHICAL MARKET TERRITORIES
OF BASEBALL FRANCHISES ................................................................. 1
The Proposed Research ..................................................................... 1
Interested Parties ............................................................................. 3
Franchise Owners ........................................................................ 3
Leagues ................................................................................... 5
Communities and Public Officials ................................................... 8
CHAPTER H
METHODS OF DETERMINING THE TRADE AREAS OF FRANCHISES .......... 13
Problems With Current Methods ......................................................... 13
Franchise Methods ................................................................... 14
League Methods ..................................................................... 16
Methods Used in Economic Impact Analyses .................................... 19
Background of the Gravity Model ........................................................ 22
The Components of the Gravity Model .................................................. 24
The Advantages of the Gravity Model .................................................... 26
Benefits for Owners .................................................................. 27
Benefits for Leagues ................................................................. 28
Benefits for Economic Impact Analyses .......................................... 29
CHAPTER III
METHODOLOGY .................................................................................. 31
Outline of the Methodology ................................................................ 31
The Potential Model ......................................................................... 32
Estimation of the Potential Model ........................................................ 37
Regression Analysis .................................................................. 39
The Standardized Root Mean Square Error ...................................... 41
Residual Analysis ........................................................................... 42
Expansion of the Models ............................................................. 45

CHAPTER IV

RESULTS OF THE EXAMINATION .......................................................... 49
Results of the Models ...................................................................... 49
Examination of the Residuals .............................................................. 52

The Elimination of Distant Observations .......................................... 52
Results of the Models After Elimination ................................................. 57
Influence of Competing Destinations and Outliers ..................................... 68

CHAPTER V

CONCLUSIONS AND FUTURE ANALYSIS ................................................ 89
Improvements to the Model ............................................................... 89

The Inclusion of Demographic Variables ........................................... 90

A Competing Destinations Variable ............................................. ....97
Application of the Model ................................................................. 100
Relevance of this Research ................................................................ 102
BIBLIOGRAPHY ............................................................................... 112

TABLE 1:

TABLE 2:

TABLE 3:

TABLE 4:

TABLE 5:

TABLE 6:

TABLE 7:

TABLE 8:

TABLE 9:

TABLE 10:

TABLE 11:

TABLE 12:

TABLE 13:

TABLE 14:

TABLE 15:

LIST OF TABLES

Franchise Name, Location, League, and Number of Zip Codes... . .. . .. . .........34

Demographic Variables Analyzed and Their Reason For Inclusion ............. 43

Hypothetical Pearson’s Correlation Coefficient Values for Beloit .............. 47

Results of the Transformed Potential Model .................................... ,..SO

Results of the Potential Model ...................................................... 50

Beta Values ............................................................................ 51

Characteristics of the Data Sets

Afier the Elimination of Remote Observations ...................................... 64

Results of the Transformed Potential Model:

Before and After the Elimination of Remote Observations ....................... 65

Results of the Potential Model:

Before and After the Elimination of Remote Observations ...................... 65
Beta Values: After the Elimination of Remote Observations ................... 66
Competitors of the Franchises Under Study ........................................ 69
Locations of the Zip Codes that are

Afl‘ected by Competing Destinations ............................................... 69

Correlation Values of Demographic Variables
and Regression Residuals ............................................................ 91

Correlation Values of Demographic Variables
and SRMSE Residuals ................................................................ 92

The Number of Meaningful Correlation Coefficient Values
for each Demographic Variable ..................................................... 94

vii

FIGURE 1:

FIGURE 2:

FIGURE 3:

FIGURE 4:

FIGURE 5:

FIGURE 6:

FIGURE 7:

FIGURE 8:

FIGURE 9:

FIGURE 10:

FIGUREll:

FIGURE 12:

FIGURE 13:

FIGURE 14:

FIGURE 15:

LIST OF FIGURES

Locations of Franchises that Supplied Data ....................................... 35
West Michigan’s Market Territory
Proportion of Regression Error against LN Dij .................................. 53
West Michigan’s Market Territory
Leverage against LN Dij ............................................................ 54
West Michigan’s Market Territory
Proportion of SRMSE Error against LN Dij ..................................... 56
Market Territory of Beloit .......................................................... 58
Market Territory of Charleston ..................................................... 59
Market Territory of Charlotte ...................................................... 60
Market Territory of Clinton ......................................................... 61
Market Territory of High Desert ................................................... 62
Market Territory of West Michigan .............................................. 63
West Michigan’s Market Territory
Potential Model’s Predicted Attendance Values vs
The Actual Attendance Values ................................................... 67
Zip Codes of Beloit’s Market Territory
that are Influenced by a Competing Destination ................................. 70
Zip Codes of Clinton’s Market Territory
that are Influenced by a Competing Destination ................................. 71
The Zip Code of High Desert’s Market Territory
that is Influenced by Competing Destinations ................................... 72
Zip Codes of West Michigan’s Market Territory

that are Influenced by Competing Destinations ................................. 73

viii

FIGURE 16:

FIGURE 17:

FIGURE 18:

FIGURE 19:

FIGURE 20:

FIGURE 21:

FIGURE 22:

FIGURE 23:

FIGURE 24:

FIGURE 25:

FIGURE 26:

FIGURE 27:

FIGURE 28:

FIGURE 29:

FIGURE 30:

FIGURE 31:

Clinton’s Market Territory
Proportion of Regression Error against Dij
(Afier the Removal of Remote Observations) .................................. 75

West Michigan’s Market Territory
Proportion of SRMSE Error against Dij

(After the Removal of Remote Observations) ................................... 76
Charleston’s Market Territory

Values of the Regression Residuals against Dij

(After the Removal of Remote Observations) .................................. 79
Charleston’s Market Tenitory

Values of the SRMSE Residuals against Dij

(After the Removal of Remote Observations) .................................. 80
Outliers in Charleston’s Market Territory ....................................... 81
Outliers in Beloit’s Market Territory .............................................. 82
Outliers in Charlotte’s Market Territory ......................................... 83
Outliers in Clinton’s Market Territory ........................................... 84
Outliers in High Desert’s Market Territory ...................................... 85
Outliers in West Michigan’s Market Territory .................................. 86
Beloit’s Market Territory vs The BTA ......................................... 105
Charleston’s Market Territory vs The BTA .................................... 106
Charlotte’s Market Territory vs The BTA ..................................... 107
Clinton’s Market Territory vs The BTA ....................................... 108
High Desert’s Market Tenitory vs The BTA .................................. 109
West Michigan’s Market Territory vs The BTA ............................... 110

ix

SMSA

SRMSE

STF 3B

LIST OF ABBREVIATIONS

a coefficient to be estimated; the coefficient of Pi
The Basic Trade Area
a coefficient to be estimated; the coefficient of Dij

Central Business District

a variable representing spatial fiiction between place i and place j; the
amount of distance between the geometric centroid of zip code origins
and the geometric centroid of the zip code destination.

a constant of proportionality to be determined; embedded in this term is

the seating capacity of the stadiums and the number of games where
attendees were surveyed.

a mass variable representing the origin; the population of the zip code
origins

the test statistic of the coefi'rcient of determination statistical measure.
Standard Metropolitan Statistical Area
a constant of proportionality to be estimated

Summary Tape File 3B of the 1990 United States census

the potential of place j to receive flows of movement; the predicted
amount of attendees between the zip code origins and the zip code
destination.

CHAPTER I
THE IMPORTANCE

OF THE GEOGRAPHICAL MARKET TERRITORIES OF
BASEBALL FRANCHISES

The Proposed Research

Baseball franchise owners, baseball leagues, and communities and their public
oflicials all have an interest in knowing the geographical market territories of baseball
franchises. Team owners must understand their fianchise’s market area in order to
maximize revenue (Baade, 1987). Leagues give great importance to maintain an
economically viable association. Recognizing the trade areas of franchises allows leagues
to realize if ballclubs are able to attract the market threshold needed for solvency (Baade
and Sanderson, 1997). Community omcials should acquire knowledge about the market
territories of baseball fi'anchises so that public administrators can make rational decisions
regarding the public subsidization of ballteams (Danielson, 1997).

However, the methods that these three interested parties utilize to obtain
information regarding the geographical market territories of baseball fianchises are either
inefficient or inadequate. In order to learn where attendees reside, interested parties either
conduct surveys; examine information resulting fi'om ticket sales; or they apply the Basic
Trade Area (BTA), which is a little larger than the size of a city’s standard metropolitan
statistical area, or other arbitrary ranges of distance from the stadium (Rosentraub and
Swindell, 1993). Although well designed surveys generally produce fairly accurate
predictions of market territories, it is extremely time consuming and expensive to perform

them. This is also true with regard to obtaining information about a market area from

ticket sales. 0n the other hand, assigning an arbitrary boundary, such as the BTA, to
represent the geographical market territory of baseball organizations is an expeditious
method. But, it is very possible that this latter approach does not correspond with the
interaction behavior of baseball fans. Moreover, applying this approach does not allow
one to realize which areas of the region produce more attendees than others.

In recent years spatial interaction models have been utilized frequently in the
discipline of geography, as well as in the profession of marketing, to estimate the trade
areas of various phenomena (Thompson, 1986; Fotheringham, 1988). It has been
demonstrated that the gravity model, which is an example of a spatial interaction model, is
able to provide reliable predictions of the trade areas of universities (McConnell, 1965;
Kariel, 1968; and Leppel, 1993); state parks (Ellis and Van Doren, 1966; Cheung, 1972);
and recreational trips (Baxter and Ewing, 1981). However, there appears to be no
documentation of the use of gravity models to analyze the market areas of baseball
franchises.

It is likely that a well calibrated spatial interaction model would be a more efficient
method than conducting surveys or examining information derived from ticket sales. It is
also probable that it would provide better predictions of the trade areas of baseball teams
than the utilization of the BTA and other arbitrary ranges. Another advantage of spatial
interaction models is that they are able to estimate the number of spectators that emanate
fi'om different origins. As a result, an operational model would benefit all interested
parties. Therefore, it is the purpose of this thesis to determine if a gravity model is able to

predict accurately the geographical market territory of professional baseball franchises, to

indicate how the model can be improved upon, and to demonstrate how one can apply the

model.

Interested Parties

Three different parties are concerned about the trade areas of baseball
organizations. Owners of fianchises, as well as their front office employees, hope to
maximize revenue. They realize that the amount of income that they can earn is strongly
dependent upon the size and the characteristics of their market territory. Leagues, which
usually consist of a president, other league officials, and all the team owners that
participate in the league desire to create and maintain a profitable association. They
require that all of the teams that partake in the league reside in geographical trade areas
which are able to sustain a ballclub. Public officials, and the communities that they
represent, need also to be concerned. It is believed that baseball fi'anchises can impact the
local economies of principalities that host ballclubs; and of those that do not. The extent

to which teams influence local economies relies heavily upon the origins of the attendees.

Eganchise Owners

Prospective fianchise owners, or owners who are contemplating moving their
balltearn to another area, attempt to locate in a market that can generate enough revenue
for their ballclub to make a profit. Regions with large populations generally offer more
financial benefits than those with smaller populations. This is true because heavily
populated areas often provide more ticket buyers than those with fewer inhabitants

(Baade, 1987). Moreover, if an organization has arrangements that allow it to collect

income fi'om concession sales and souvenir purchases, it is beneficial for the franchise to
be located in a market that can potentially produce a large number of spectators
(Danielson, 1997).

Also important is the fact that proprietors obtain a fair amount of their earnings
fiom advertising within the stadium. Due to the premise that large markets produce high
attendances, companies believe that they will be promoting their products to large
numbers of people. Consequently, owners can increase the asking price for stadium
advertising space, and thus add to their total revenues (Danielson, 1997).

Because large attendances increase the amount of possible revenue, established
baseball organizations attempt to incorporate within their market territory populous areas
that are located at relatively great distances fi'om their stadium. One example of a
fianchise that attempts to add to their trade area is the Baltimore Orioles. Lawrence
Lucchino, the Team President of the Orioles, states:

We embarked on a regionalization campaign... there was a great
opportunity available in areas like Washington; York; Pennsylvania; and
Annapolis. Regionalization became our watchword (Euchner, 1993).

The demographic characteristics of a trade area are arguably just as important as
its size with regard to increasing the amount of income derived fiom ticket sales, food,
beverages, souvenirs, as well as advertising within the stadium. Franchises hope to reside
in a wealthy territory because it is easier to attract attendees who have a large quantity of
recreational funds at their disposal. Such spectators are also more likely to purchase

meals within the stadium and to acquire other stadium merchandise (Danielson, 1997).

Many advertisers target their commodities to people with disposable income.
Owners hope to draw affluent customers to the ballpark so that all types of businesses will
be willing to acquire advertising space within the stadium. As a result, wealthy markets
can add to the demand for in-stadium advertising, thus increasing potential revenue for
baseball organizations (Euchner, 1993).

Due to the notion that afiluent attendees generate more revenue for ballclubs,
already established baseball franchises also direct their marketing endeavors to the
prosperous areas of their market territory. Generally, such attendees reside in the suburbs
of the region. Not only do organizations market towards suburban residents, but they
have also built stadiums within suburbs, or close to the suburbs, in order to make the
stadium more accessible for suburbanites (Euchner, 1993). Franchises that construct
stadiums within central cities commonly locate the stadiums near expressways so that
suburban commuters can easily travel to and from the stadium (Johnson, 1993).

Since market size and its characteristics afi‘ect the amount of income that a baseball
franchise can earn, the geographical trade area of a ballclub greatly influences the
monetary value of a fi'anchise (Scully, 1989). Therefore, it is clear that franchise owners
must be aware of the traits of the region that their team occupies. Additionally, it is
necessary for prospective proprietors and owners that intend to relocate their teams to

closely examine the possible locations that they may inhabit.

m
Leagues are interested in the geographical market territories of baseball franchises

for reasons pertaining to relocation and expansion. League officials and owners of

—afi_
.-

ballclubs understand that the financial health of all of the teams that make up the league is
important to its economic well being. Therefore, league administrators and owners want
all baseball organizations within a league to locate in economically viable markets.
Leagues expect their franchises to locate in large and wealthy regions for the same reasons
that franchise owners want their own team to occupy such areas (Baade and Sanderson,
1997)

In order to prevent competition between organizations within a region, leagues
grant territorial rights to their franchises. Although there is a limited number of markets
that accommodate more than one ballteam, territorial rights assure baseball organizations
that they alone will occupy the market territory in which they reside. Regions that do
contain more than one team generally have an extraordinarily high population (Markham,
1981). Leagues do not want franchises competing with one another for revenue, because
one team may gain a competitive advantage over the other, which would increase the
possibility that a fi'anchise could become insolvent (Danielson, 1997).

League members have absolute authority regarding team relocation. Franchise
owners who desire to relocate their fi'anchise must receive the approval of a significant
percentage of the other team owners (Johnson and Frey, 1985). The size of the
population and the market characteristics of the proposed area ofien afi‘ect the owners'
decisions (Euchner, 1993). Owners also take into strong consideration the territorial
rights of fi'anchises. Leagues are more willing to allow relocations if the proposed market
lacks a franchise. The likelihood of being allowed to relocate also increases if the ballclub
that is asking permission to move is, at the time, competing with another fianchise within

its current market. This is evident when one examines the five team relocations that

occurred within major league baseball during the 1950's. Major league owners determined
that the proposed locations had the size and prosperity necessary to secure a ballclub.
Furthermore, all of the five teams that were allowed to relocate were sharing a region with
another team. Since the proposed areas were not occupied by another fianchise, there
was relatively little resistance fiom the league (Danielson, 1997).

Baseball owners also have complete control with reference to the addition of new
teams in the league. Similar to decisions regarding relocation, current owners vote upon
which prospective owners will be granted the right to own a fianchise (Johnson, 1993).
The size and characteristics of the potential markets, as well as concerns regarding
territorial rights, are some of the most important subjects that owners consider when
deciding in which markets to expand (Danielson, 1997). In the past decade, the cities of
Denver, Miami, Phoenix, and St. Petersburg successfirlly obtained major league expansion
teams. Baseball promoters fiom these four areas emphasized the potential of attracting
numerous wealthy customers (Euchner, 1993; Danielson, 1997). The city of Bufi‘alo also
attempted to acquire an expansion franchise during this same time period. An important
reason why Buffalo failed to obtain a franchise is because their market is smaller than the
afore-mentioned four regions. Major league owners also rejected Washington D.C.'s
application for an expansion team. This was predominantly due to the perception that the
Baltimore Orioles have included Washington DC. as part of their own market, and
owners do not want two teams competing for these same customers (Danielson, 1997).

The size of the proposed area for an expansion team also is extremely important to
minor league officials and owners of minor league teams. Baseball organizations that are

hosted by small communities are less likely to succeed economically than those that reside

 

in larger principalities. In fact, from 1987-1991, approximately two-thirds of all minor
league franchise relocations took place in regions that had accommodated less than one-
hundred thousand people (Johnson, 1993). As a result, minor league owners are skeptical
that ballclubs in sparsely populated areas can survive, and are, therefore, wary of awarding

a fianchise to a small community.

Communities and Public Ofiicials

Because the demand for fi'anchises is much greater than the supply, owners of
sports fianchises have a better negotiating position than do local officials (Baade, 1987).
The great demand fiom local authorities is mostly attributable to the notion that a sports
fianchise can generate economic development within the host community. The limited
number of franchises is generally due to the fact that leagues have the power to control the
number of teams. Owners use this advantage to request financial assistance fiom state,
county, and local governments. The fact that erecting a major league stadium may cost
two hundred million or more dollars indicates the potential amount of public assistance
nwded in order to build a stadium (Noll and Zimbalist, 1997). The cost of stadium
construction for minor league teams is decidedly less expensive than that of major league
stadiums. Normal construction costs for minor league stadiums are about ten to twelve
million dollars (Johnson, 1993). However, cities that host minor league baseball
fianchises are smaller than those that are home to major league baseball franchises (Chalip
and Johnson, 1996). Therefore, for these communities such an investment is often of

major proportions.

Major and minor league owners also request subsidies from governments for a
number of other amenities. Local authorities often include all or most of the following in a
stadium package: free or subsidized land, favorable leases, tax breaks, improved roads
near the stadium, and police protection surrounding the area (Johnson, 1993; Danielson,
1997). If their demands are not met, many owners will refirse to locate in a particular
area, or will threaten to leave the present locale for another principality that is willing to
meet their demands (Johnson and Frey, 1985; Johnson, 1993).

Many public authorities of cities and suburbs attempt to obtain a baseball team or
to prevent a ballclub from relocating, because they believe that baseball is an export
industry. According to export base theory, businesses are separated into those which
produce goods and services for the export market, and those which provide for the local
market (Tiebout, 1956a). The economic development of regions is undoubtedly
associated with those industries that create products for the export market. This is true
because export industries primarily sell commodities to people who reside outside the
jurisdiction in which the industry is located. Therefore, such businesses obtain money
fi'om other areas and much of this money gets filtered throughout the local economy. The
flow of this money allows residentiary businesses, who only provide for the local market,
to be established within the principality. Not only do residentiary industries subsist due to
the existence of export businesses, but also residentiary activities can expand and increase
in number only if the export activities within a principality can generate additional money
into the local economy (North, 1955).

There appears to be a slight difference between typical export businesses and

baseball organizations as export industries. Typical export businesses ship goods out to

Y»~—_—1

markets, and money flows into the host community. On the other hand, with regard to
baseball organizations, the market travels to the export industry for its goods. Due to this
fact, one can argue that baseball teams contribute to the local economy in more ways than
do typical export businesses. Not only will money flow throughout the local economy
because of the existence of the franchise, but attendees may also purchase goods and
services fi'om residentiary activities outside the ballpark.

However, many academicians maintain that the existence of a franchise does not
contribute to the local economy. They suggest that if most of the attendees are residents
of the host community, a great portion of the leisure money that the fi'anchise obtains is
money that is simply shified away from other recreational activities in the principality to
the baseball organization (Chalip and Johnson, 1996). Since residents may redistribute
some of their income fiom other businesses to the balltearn, it is possible that any
economic development that is created by the fi'anchise will eliminate other forms of
economic activity in the principality (Rosentraub and Swindell, 1993). Baade and Dye
echo this notion:

(the) fundamental issue is the extent to which the stadium causes a net
income in area activity rather than a mere reallocation or redistribution of
the same level of activity (Danielson, 1997).

It is obvious that communities and their public officials need to understand the
geographical market territory of franchises so that accurate regional economic impact
analyses can be performed. The major premise of the concept of export sales is that the
geographical market territory of baseball franchises extends outside city borders. It should

seem obvious that the larger the geographical market territory, the greater the potential

10

economic impact that the host community receives from export sales. On the other hand,
if the market territory of a baseball franchise is relatively small, the potential economic
impact that the city receives will be less. In this instance, most of the spectators are fi'om
the principality that hosts the fianchise. Therefore, a great portion of the money being
spent in and around the stadium may simply be leisure money that is being redistributed
from other recreational activities within the city to the baseball organization and
businesses surrounding the stadium (Baade, 1995).

Assuming that baseball franchises behave like export industries, communities need
also to be concerned with the geographical market territory of franchises in order to
estimate the impact of import substitution. The principal supposition of import
substitution is that due to the existence of the baseball organization, peOple fi'om within
the community will remain in the community in order to attend a baseball game. As a
result of the presence of the baseball franchise, money is retained in the principality, and
can add to the amount of money injected into the local economy. If the ballclub were not
located within the city, the baseball fans from the community would travel to another
principality to attend a baseball game. Therefore, the local economy would lose potential
leisure money, because its own city is now within the trade area of a baseball fianchise in
another city (Baade, 1995). As a result, with regard to the economic impact of import
substitution, it may be in communities' best interests to accommodate a team. On the
other hand, if baseball fianchises do not operate like export industries, there is little
economic reason for a community to attempt to obtain a team.

Clearly, fi'anchise owners, leagues, public oficials and the communities that they

represent have a strong interest in knowing the geographical market territories of baseball

11

teams. Owners realize that the size and the characteristics of the market can greatly
influence the amount of revenue that they collect. Leagues desire viable markets for each
of its franchises, and they also want to avoid competition by granting territorial rights to
their teams. Public ofiicials and communities must recognize that the trade area of a
franchise greatly influences a baseball organization's impact upon local economies. The
following chapter will discuss current methods that are utilized to determine the trade
areas of teams; it will attempt to demonstrate the inefficiency or the inadequacy of each of
these approaches; and it will propose a new method of realizing the market territories of

ballteams.

12

CHAPTER II
METHODS OF DETERMIN G THE TRADE AREAS
OF FRANCHISES

Problems With Current Methods

Existing methods utilized to determine the geographical market territories of
baseball franchises are either extremely time consuming and expensive, or are based on
assumptions with little theoretical or empirical basis; whereas, the application of gravity
models to gain knowledge of trade areas is a relatively efficient and inexpensive process
(Thompson, 1986). Although the theoretical justifications regarding the use of gravity
models have been questioned, gravity models have produced extremely accurate
predictions of the trade areas of various phenomena (Niedercorn and Bechdolt, 1969; and
Haynes and F otheringharn, 1984). Furthermore, it is possible that a gravity model could
provide valuable information pertaining to the market areas of ballteams that other
approaches are unable to furnish. However, before the gravity model and its advantages
are examined, the discussion will first focus upon what information teams, leagues, and
those who perform economic impact analyses hope to obtain fiom examining the
geographical market territory of ballclubs. This section of the discussion will also attempt
to demonstrate that the methods that these three interested parties utilize are either

ineficient, or are not able to fulfill the needs of the interested parties.

13

Franchise Methods

Understanding various aspects of their teams' geographical market territories
allows baseball fianchise owners to increase their profits. For example, recognizing where
most of their attendees originate allows the current owners and their fiont office to direct
their marketing efl‘orts appropriately. Additionally, for the purposes of marketing, owners
should attempt to understand how their teams' trade areas have changed over time.
F urtherrnore, owners who are planning to build a new stadium ought to determine the
location that would draw the most attendees.

For this project, several teams' ofiicials supplied previously collected data
concerning the trade areas of their respective organizations. In order to obtain this
information, teams deemed it necessary to survey their attendees. The use of properly
contrived surveys to determine a market area usually yields reliable estimates
(Fotheringharn, 1986). Geographers, marketing professionals, and transportation
planners, as well as members of other disciplines and professions conduct surveys in order
not only to ascertain the market territories but also to determine the market characteristics
of various enterprises (Fotheringharn, 1986; Harvey, 1987; and Tirnmerrnans, Borges, and
Waerden, 1992). Therefore, assuming that the ballclubs prepared properly designed
surveys, the franchises acquired quality assessments of the origins of their attendees, the
quantity of spectators that emanate from each origin, and several demographic
characteristics of the attendees. As a result, the owners and the front offices of these
ballteams are able to direct their marketing efforts accordingly.

However, surveys are expensive to conduct and the costs of performing surveys

have been rising (Rossi, Wright, and Anderson, 1983). It also takes a great amount of

14

time to collect, categorize, and interpret the data that result from surveys (Babbie, 1990).
For example, one franchise disclosed that it was necessary to conduct three surveys in
order to acquire enough responses which would accurately represent the team's market
territory. Consequently, the organization required nearly three months to merely
accumulate the requested information. The efl‘ort that is needed to employ surveys
decreases the amount of time that employees possess to accomplish other job
requirements. Although gaining knowledge of their team's market territory is very
important regarding the amount of revenue that a fianchise receives, the opportunity costs
and the monetary costs that are encompassed within surveys may influence owners and
their fi'ont oflice officials not to perform them. According to a 1996 survey conducted by
Baade and Sanderson, most minor league baseball franchises acknowledged that they are
not aware of the origins of their attendees (Baade and Sanderson, 1997). Therefore, a
more efficient method of determining the market areas of baseball organizations will not
only save time and money for those franchises that actually attempt to acquire information
about their trade area, but it may also increase the number of ballclubs that might begin to
closely examine their markets.

Because surveys are an inefiicient and an expensive approach to understanding the
trade areas of baseball franchises, they are not able to provide some pertinent information.
For example, to know how a market territory has changed over time, a fianchise would be
required to conduct surveys continually. This may not be fiscally possible for many
ballclubs. Furthermore, it is not possible to conduct the number of surveys needed in
order to realize the best location to construct a stadium. Consequently, another approach

is needed in order to acquire this knowledge.

15

I._.e_agr_re Methods

Leagues wish to maintain economic stability within their respective leagues.
Therefore, they want to know that a proposed region for an expansion fi'anchise can
provide the attendance and income thresholds needed to support a balltearn. Moreover, in
order to prevent instability, leagues do not allow most teams to compete for attendees.
This is accomplished by granting teams territorial rights. These rights do not permit a
team to locate in another fianchise's trade area. Therefore, leagues also attempt to discern
the market boundaries of baseball franchises.

From 1903 to 1952, there were no major league fi'anchises that relocated to
another region. Previous to 1953, a unanimous vote of league owners was required to
permit a team to move from their current home to another city (Danielson, 1997).
However, franchise owners and league officials relaxed rules concerning team relocation.
The new rule allows an owner to move a fianchise with the permission of at least three-
quarters of the other team proprietors. After 1953, mostly due to this modification, seven
teams received approval to relocate (Scully, 1989).

It appears that as franchises were beginning to relocate, Major League Baseball
oficials merely studied certain demographic characteristics when attempting to discern if a
proposed region could sustain a baseball franchise. League administrators only considered
the population, the growth potential, and the income of the market in question. This
procedure only begins to describe the qualities of prospective territories. Consequently,
the Kansas City Athletics and the Milwaukee Braves, two of the organizations that had

moved, later claimed that they were struggling financially due to poor market areas. The

16

owners of these two fianchises were later granted permission to relocate to Oakland and
Atlanta respectively (Miller, 1990). Nevertheless, team owners gave other fianchises to
Kansas City and Milwaukee through expansion. Fay Vincent, a former Commissioner of
Major League Baseball, comments critically on these two cities as well as on other cases:
We moved fiom Kansas City to Oakland and replaced it with a tearrr in
Kansas City. What was the point of that? We moved from Washington
twice and now Washington makes an effort to get a team. We moved
from Milwaukee, we moved fi'om Seattle and in each case the teams were
replaced (Danielson, 1997).

Obviously, Major League Baseball officials would like to prevent firture instability
within the sport. This can be accomplished by determining if a region can supply the
minimum attendance, as well as income, threshold needed in order to support a baseball
fianchise. Therefore, in an effort to acquire this information, owners currently demand
that expansion applicants sell season tickets to area residents (Danielson, 1997). As a
result, league administrators and owners are able to determine immediately if the size of
the potential market is large enough to sustain a ballteam. Moreover, since season ticket
packages are generally expensive, leagues can comprehend if the proposed location will
draw relatively wealthy patrons (Zimbalist, 1992).

In order to obtain this knowledge, prospective owners must spend a great deal of
time and money. Those who desire to acquire a fianchise must market the proposed
ballteam to area residents; and they must be prepared to process ticket orders. Therefore,
potential proprietors may have to invest in an infiastructure such as renting ofices and
buying computers. They also must hire and pay an oflice stafi‘, marketing consultants, and

a public relations department. Furthermore, it is necessary to buy advertising space or

17

commercial time in newspapers and magazines, on billboards, as well as on radio stations
and television networks (Markham 1981; Zimbalist, 1992). Clearly, possible owners, who
are not successfirl in obtaining a team, can sustain substantial monetary and opportunity
costs without reward. Although Major League Baseball‘s arduous demands of
determining the market areas of proposed fianchises are probably quite efi‘ective, it seems
that prospective proprietors would welcome a more practical method so that the costs of
applying for an expansion franchise are diminished.

Leagues also attempt to maintain stability by preventing teams from competing for
attendees. In their attempt to maintain one market area for one team, baseball leagues
grant territorial rights to their franchises. The authorities of Major League Baseball
arbitrarily established a fifty to seventy-five mile range from a ballteam's host city as a
fi'anchise's market area (Danielson, 1997). Minor league baseball ofiicials declared that no
other minor league baseball organization is allowed to locate within a thirty-five mile
radius from another ballclub's stadium (Johnson, 1993). These distances have not been
modified since the dramatic acceleration of the growth of metropolitan areas. As a result,
this method probably does not allow for the inclusion of numerous areas that provide
franchises with attendees (Danielson, 1997). Therefore, another approach is needed to
examine the effect of urban expansion upon the trade areas of teams, so that owners do
not lose potential customers to other baseball organizations that locate near their present
territorial boundary.

Moreover, it is possible that franchises have different market ranges. Some
analysts who examine the markets of baseball teams believe that setting arbitrary

boundaries of the market territories of teams may be disadvantageous to leagues. It is

18

possible that a league would not allow an owner to locate a fi'anchise in an area that is
capable of supporting a ballclub; that is, if the market territory of another ballteam is
relatively small. On the other hand, a league might permit a proprietor to locate in a
region that will not sustain a baseball team; that is, if the trade area of another franchise is
relatively large (Markham, 1981). Consequently, another approach is required in order to

advance the interests of baseball leagues.

Methods Used in Economic Impact Analyses

In order to obtain accurate estimates of the economic impact of baseball fi'anchises
upon local economies, it is necessary to know the geographical market territories of
organizations. This is true, because with this knowledge one can understand the amount
of leisure money that enters the community from attendees who reside outside the
principality, which is equivalent to knowing the effect of export sales. One can also
estimate the amount of leisure money that a community loses due to its residents traveling
to another community that hosts a franchise; the equivalent of knowing the impact of
import substitution. With the aid of this information, government oflicials can decide if it
is fiscally wise to subsidize baseball franchises either to obtain, or to retain, a team.

Many analysts who have conducted examinations of the economic impact of
baseball franchises upon regional economies fail to consider the geographical market areas
of teams. Therefore, the phenomena of redistributed spending, export sales, and import
substitution are not considered in these studies (Baade, 1987; Steinhofi‘, 1988; Johnson

and Owen, 1993). On the other hand, some investigators make the effort to perform

19

 

surveys so that they are able to realize the market territories of ballclubs. Noll and

Zimbalist write:
To estimate the exports attributable to a team, local economic impact
studies frequently conduct surveys of those in attendance at games to
ascertain where fans live and then count as tourists attracted by the team all
fans who reside outside the area (Noll and Zimbalist, 1997).

As previously mentioned in this paper, well designed surveys are able to provide very

accurate predictions of the trade areas of baseball organizations, but they are extremely

expensive and time consuming. As a result, in order to save time and money, many

authors of economic impact studies assume that the Basic Trade Area correctly defines the

market territories of ballclubs.

The 129th edition of the Rand McNally Commercial Atlas and Marketing Guide

provides a definition of the Basic Trade Area:
An area surrounding at least one Basic Trading Center. Each Basic
Trading Area is named after one or more cities which are its Basic Trading
Centers. All Basic Trading Area boundaries follow county lines and are
drawn to include the county or counties whose residents make the bulk of
their shopping goods purchases in the area's Basic Trading Center or its
suburbs. Some Basic Trading Areas have two or more Basic Trading
Centers, generally because residents may conveniently shop at either one.

The 129th edition of the Rand McNally Commercial Atlas and Marketing Guide gives the

definition of Basic Trading Centers as follows:

20

A city which serves as a center for shopping goods purchases for the
surrounding area... Basic Trading Centers also serve their surroundings
with various specialized services, such as medical care, entertainment,
higher education, and a daily newspaper.
It should be mentioned that the Basic Trade Area of a city is larger than the Standard
Metropolitan Statistical Area (SMSA) defined by the Bureau of Census. This is the case
because the BTA includes rural communities that depend upon large urban centers for
recreational activities. Rosentraub and Swindell write, "it is common to use the BTA, not
SMSA, as the geographical area of reference in calculating attendance at games and
spending." (Rosentraub and Swindell, 1993).

Clearly, this a rough estimate of the influence that baseball fi'anchises have upon
the surrounding area. It is possible that a baseball franchise does not serve an entire
metropolitan area, and thus any calculations of export sales may be overestimated. As a
result, the baseball organization will not have the economic impact that is projected upon
the host community. Conversely, the range of a franchise may be larger than the estimate
of the BTA. If this is the case, projections of the economic impact of export sales will be
underestimated.

The utilization of the Basic Trade Area may also cause poor assessments of the
efi‘ect of import substitution upon communities that do not host ballteams. This may be
true because if the BTA incorporates an area that does not supply attendees to ballgames,
then the projection of the economic influence of import substitution upon this community
-will be exaggerated. On the other hand, the BTA may not encompass a principality in

which its residents do attend games. Therefore, authors who apply this method would

21

probably conclude falsely that the baseball organization does not impact the local economy
of this community.

Furthermore, employing the BTA does not allow one to determine the quantity of
spectators who originate fiom different areas of a market territory. Without this
knowledge, those who conduct economic impact studies cannot be certain of what
proportion of money a host community receives is derived fiom export sales. Also, one is
not able to ascertain the quantity of money that a principality loses to the community that
hosts the ballclub. As a result, another method must be utilized in order to assist
investigators who attempt to determine the economic impact of baseball organizations

upon local economies.

Background of the Gravity Model

Applying a gravity model to predict the geographical market territories of baseball
fianchises may have numerous advantages over the previously mentioned methods.
However, before these benefits are discussed, the background of the model, as well as the
components of the model, will be addressed.

The gravity model is based upon the normative theory of economic geography.
The foundation of this theory is that people behave in similar fashions. Therefore, it is
possible to use scientific approaches and models in order to examine the phenomena that
occur within the discipline of economic geography. The gravity model, which is a
modification of Newton's law of gravitation, is one of the original spatial interaction
models to be employed in the discipline of geography (Haynes and Fotheringharn, 1984).

Instead of using the model to predict gravitational pull in the cosmos, social scientists

22

(such as Isbell, 1944; Stewart, 1947; and Carrothers, 1956) began to utilize this
mathematical formulation in order to forecast human spatial interaction (Desta, 1988).
Using a model that was created from the laws of physics has caused some uncertainty
whether the model should be applied toward human spatial phenomena, because there is
little theoretical basis that explains why humans should behave like objects in outer space
(Niedercorn and Bechdolt, 1969). However, Alan Geoffrey Wilson in 1970 resolved this
dilemma by demonstrating that the model can be derived fi'om entropy maximization
methodology (Desta, 1988).

Since its creation, the model has been expanded so that there currently exists an
entire family of gravity models (Wilson, 1971). The advent of the other models has
allowed the gravity concept to be used frequently to describe different types of spatial
interaction patterns (Haynes and Fotheringharn, 1984). For example, several forms of the
gravity model have been used to determine the market areas of such activities as state
parks (Ellis and Van Doren, 1966); recreational trips (Baxter and Ewing, 1981);
secondary schools (Pacione, 1989); and universities (McConnell, 1965; Kariel, 1968;
Leppel, 1993). Academicians, as well as marketing professionals, have illustrated that

gravity models are able to provide reliable estimates of trade areas (Pooler, 1994).

23

The Components of the Gravity Model

The formula for the traditional gravity model is as follows:

T..- = karts") I D," (m)
where:
T3 = the predicted spatial interaction between place i and place j
P; = a mass variable representing place i, the origin
Pj = a mass variable representing place j, the destination
Dij = a variable representing spatial fiiction, or deterrence, between
place i and placej
k = a constant of proportionality to be estimated
a,b,c = coefficients to be estimated

(Wilson, 1971)

This formula attempts to predict spatial interaction patterns by assuming that the amount
of spatial movement that occurs between an origin and a destination is directly
proportional to the mass of the origin multiplied by the mass of the destination, and
inversely proportional to the spatial fiiction between an origin and a destination (Kariel,
1968). It must be made clear that the gravity model is applicable only to the aggregate
population, not to individuals (F otheringham, 1988). However, social scientists ofien
assume that if the aggregate population behaves in a certain manner, it is likely that a
typical individual will behave in the same way (Greenwood and Sweetland, 1972).
Applying this notion, the model is able to produce relatively accurate estimations of the
likelihood of an individual participating in the activity that is being examined (Kariel,
1968)

In order to comprehend how the traditional gravity model is able to provide
reliable predictions of spatial interaction behavior, it is necessary to understand the

variables which compose the formula. The origin mass variable represents a characteristic,

24

or characteristics, of origins which demonstrates the origins’ capability to send to
destinations the units that one is investigating. Some examples that are often used as the
origin mass variable characteristics are: the population of an origin, the origin's population
density, and the median household income of the area (Haynes and Fotheringharn, 1984).
The population of zip code origins is employed in this thesis in order to predict the spatial
interaction patterns of baseball game attendees (this will be discussed in greater detail in
Chapter III). The destination mass variable ofien depicts the allure of places (Niedercorn
and Bechdolt, 1969). For example, the number of square feet of a supermarket or a retail
outlet is often applied in examinations of the trade areas of these destinations
(F otheringham, 1988). The seating capacity of baseball stadiums is used as the destination
mass variable in this thesis (this will also be expounded upon in Chapter III).
Consequently, as the values of the mass variables increase, the greater the likelihood that
interaction occurs between the origins and the destinations. However, the mass variables
may not equally contribute to the explanation of the interaction behavior between places.
Therefore, coefficients, or parameters, are incorporated into the mass variables as
exponents. The coefficients allow one to determine which of the two mass variables have
a greater impact upon spatial interaction (Johnston, 1978). The higher the value of an
exponent, the greater the effect that a particular mass variable has upon interaction
behavior (Haynes and F otheringharn, 1984).

Also included within the traditional gravity model is a variable that delineates
spatial fiiction. Spatial fiiction negatively affects the magnitude of spatial movement that
occurs among places (Batty and Mackie, 1972). This is true because as spatial fiiction

expands, people have less knowledge of places, the financial expenditures that are needed

25

to interact increase, and psychological impediments toward interaction grows (Leppel,
1993). Generally distance between places, or the time that is needed to travel between
places, is employed as the spatial fiiction variable in most examinations. Distance in miles
is used in this thesis (this will be discussed in greater detail in Chapter III). The variable is
also modified by a parameter to determine the influence of spatial fiiction upon spatial
movement. High parameter values indicate that the spatial fiiction variable is a strong
deterrent with regard to the interaction between places (Haynes and Fotheringham,
1984).

The constant that is incorporated within the model is a coefficient of
proportionality (Johnston, 1978). The variables that compose the model are usually
measured in difi‘erent units. Therefore, the constant is needed in order to balance the

entire formula (Haynes and Fotheringham, 1984).

The Advantages of the Gravity Model

Spatial interaction models have been previously used to calculate the number of
people that may attend an event (F otheringharn, 1996). However, there is no evidence
that a spatial interaction model has been employed to determine the geographical market
territories of baseball franchises. The use of a gravity model may produce more accurate
estimates of the trade areas of baseball organizations than the use of the BTA, or other
arbitrary delineations. The model is also a more efiicient method than performing surveys
or obtaining information from ticket sales (Thompson, 1986). If a well calibrated gravity
model is able to accurately predict the trade areas of ballclubs, it would benefit all

interested parties.

26

Benefits for Owners

A well calibrated gravity model, which is a model which has been fitted by a
goodness-of-fit test in order to ascertain reliable parameter estimates, would be able to
provide information that is pertinent to the interests of prospective owners. For example,
the model would be advantageous to those who are applying for an expansion fi'anchise.
A gravity model would be able to approximate the number of people who would attend a
game, as well as the number of wealthy attendees who would travel to the stadium.
Therefore, it would no longer be necessary for leagues to require that potential owners sell
season tickets in order to demonstrate that a region could financially support a ballclub.
Clearly, this would ease the burden of those applying for an expansion fianchise.

An operational model also would be able to help direct marketing efi'orts of
established franchises because it can divide a market territory into difi‘erent sections
(Thompson, 1986). Therefore, the model can predict which areas of a market territory
would send the most attendees. Moreover, the model can assess if a team's trade area
incorporates communities with large populations that are located at relatively great
distances from the stadium.

However, the trade areas of baseball organizations are dynamic. This is true
because teams' market territories are afi‘ected by demographic changes that occur in the
areas where fi'anchises reside (Danielson, 1997). Nevertheless, an operational gravity
model would be able to efficiently demonstrate how market areas have transformed during
a certain time period, and it could predict how trade areas will vary in the firture. It

would, therefore, aid firture marketing endeavors.

27

A functional gravity model would assist prospective owners, as well as current
owners, who are attempting to decide upon a location for a stadium. Not only would a
gravity model allow one to determine which location will draw the largest number of
attendees, it can also reveal the location that will draw the largest possible number of
afiluent attendees.

It is true that surveys can provide some of the information that a gravity model
provides, but they are extremely time consuming. It is also true that surveys cannot

collect some of the information which gravity models are able to furnish relatively

expeditiously.

Benefits for Leagues

Applying a gravity model to determine the market areas of teams may also benefit
leagues. Instead of granting territorial rights by arbitrarily employing ranges of distance, a
working model can ascertain the market boundaries of ballclubs. The model may disclose
that teams have diflerent market boundary ranges. Therefore, the model could indicate
that there are locational opportunities for leagues to place teams, or it may reveal that a
ballteam’s market territory already encompasses an area that is attempting to obtain a
ballclub. The current method that leagues use to allot territorial rights might be too static,
and it is possible that the current approach does not allow league officials to have the
flexibility needed to make wise decisions regarding the placement of franchises. As a

result, the model could assist leagues in finding the best regions to locate ballteams.

28

Benefits for Economic Impact Analyses

Due to the fact that a gravity model is able to separate a market territory into
several segments, analysts can better estimate the economic impact that a baseball
fianchise has upon the local econonries of the region that hosts the ballclub. This is the
case because applying an effective gravity model would allow one to efiiciently and
accurately estimate the economic effects of export sales and import substitution.

This is beneficial for communities that are contemplating providing public subsidies
to retain a baseball franchise. Interested parties can realize the number of residents, as
well as residents of other principalities, that attend ballgames. Therefore, elected ofiicials
will be able to determine the proportion of money that the local economy receives as a
result of export sales or redistributed spending. Public officials that encounter this
situation must also understand the economic impact of import substitution. With the use
of the model, public authorities could project how many people from their principality
would attend games if the team were to move to another city within the region. As a
result, government officials would comprehend the amount of money that would leave the
community.

An operational model would help communities that do not host ballclubs as well.
Since city administrators could discern the spatial behavioral patterns of attendees, they
would be able to determine the amount of money that the community would acquire due
to export sales, if it were to become host to a baseball fianchise. They could also
ascertain how much money they are presently losing to another community where the

ballteam resides.

29

If a gravity model is able to provide reliable predictions of the geographical market
territories of baseball franchises, it would no longer be necessary for investigators to
conduct surveys in order to acquire this information. Moreover, it would provide a better
alternative than the application of the BTA.

The use of a well calibrated gravity model may be advantageous to all interested
parties. Franchise owners and their fi'ont ofices could make logical and eficient
locational decisions, create strategic marketing plans, and study the changes that occur to
their trade areas over a period of time. Moreover, the burden of applying for an expansion
fianchise would be lessened. The gravity model may also assist leagues in making
insightfirl decisions regarding the location of teams. Finally, the model would benefit
entire communities who want to determine if it is economically wise to ofi'er public
subsidies to team owners.

However, gravity models are sometimes limited in their explanatory power of trade
areas. Often other variables must be considered in order to accurately explain a market
territory. Therefore, it is the purpose of this thesis to determine how well a gravity model
predicts the geographical market territory of baseball fianchises and to evaluate other
variables that may add to the explanatory power of the model. The following chapter will

outline the methodology of this examination.

30

CHAPTER HI
METHODOLOGY

Outline of the Methodology

In order to test a gravity model's predictive ability with regard to the geographical
market territories of baseball fianchises, actual data was obtained from six Single A minor
league baseball franchises. Single A baseball fi'anchises are considered to be the lowest
level of the hierarchy of professional baseball franchises that play a full season. (This will
be discussed in greater detail in Chapter V). Due to the nature of the data, the potential
model, which is discussed in this chapter, was employed to predict the geographical
market territories of the six fi'anchises. In order to ensure that the results of the model
were valid, two different goodness-of-fit tests, the coefiicient of determination (R2) and
the standardized root mean square error (SRMSE), were applied to the results of the
potential model. Therefore, this section of the thesis will present a reasonable description
of the potential model and its capability of producing accurate predictions of the trade
areas of baseball franchises.

Past research has stated that the demographic characteristics of a region’s
population influences a fianchise’s market territory (Euchner, 1993; Stix, 1993: and
Danielson, 1997). Therefore, demographic data was collected to determine if other
variables can add to the predictive power of the potential model. A detailed account of
the selection of the demographic variables is provided later in this chapter. In order to
discern if a relationship exists between the demographic variables and the regression

residuals, Pearson's correlation coefiicient test statistic was employed. Pearson's

31

correlation coefficient test statistic was also utilized to ascertain if a relationship exists
between the demographic variables and the SRMSE residuals. Variables that are
correlated with either the regression residuals, or the SRMSE residuals, should be
incorporated into the model appropriately. This too will be expounded upon later in this
chapter. Therefore, this section of the analysis should allow one to realize other variables
that are able to add to the explanatory power of the potential model, and also in what form

they should be included in the model.

The Potential Model

The potential model is a derivation of the traditional gravity model (Isard, 1960).
Therefore, it, too, is based upon the normative theory of economic geography and
Newton's law of gravitation (please refer to Chapter II). This model has been used
extensively to predict or to examine the market areas of several difi‘erent types of
phenomena (McConnell, 1965; Kariel, 1968; Cheung, 1972; Pacione, 1989; and Talen and
Anselin, 1998). Unlike the traditional gravity model, the potential model estimates the
amount of movement between one area and all other areas of interest (Haynes and
Fotheringham, 1984). Therefore, one can examine the unidirectional spatial interaction
between multiple origins and a single destination (Niedercorn and Bechdolt, 1969).
Because this is the same type of phenomenon that I am analyzing, I employed the potential
model in order to predict the geographical market territories of minor league baseball
fianchises.

The equation of the potential model that is utilized in this thesis is given on the

following page:

32

Tj = k* X (ZPib/ Dif) (E2)

where

Tj = the potential of place j to receive spatial flows of movement
Pi = a mass variable representing place i, the origin

Dij = a variable representing spatial fiiction, or deterrence, between

place i and placej
k = a constant of proportionality to be determined; embedded in this
term is the seating capacity of the stadium and the number of
games where attendees were surveyed
b,c = coefficients to be estimated
By examining the formula of the traditional gravity model (please refer to Chapter II), one
can understand how the potential model is derived. As previously mentioned, the
traditional gravity model attempts to predict the spatial interaction flows between many

origins and many destinations. In order to predict the amount of movement to only one

destination, the formula of the traditional gravity model must be modified. Therefore, only
the orgin mass variable, Pi is divided by the spatial fiiction variable, Dij. Since there is
only one destination, the destination mass variable, Pj is now embedded in the constant k.

which is used to multiply the quotient of Pi and Dij, Consequently, one who employs this

model attempts to understand a destination's potential of receiving flows of movement
from the surrounding area.

To test the explanatory power of the potential model it is necessary to obtain
actual data from baseball franchises. The following studies all utilized actual spatial
movement data in order to investigate the capability of a gravity model to produce

accurate estimates of interaction: McConnell, 1965; Ellis and Van Doren, 1966; Kariel,

33

 

 

1968; and McAllister and Klett, 1976. Therefore, I requested the number of tickets sold
per zip code fiom over one-hundred minor league ballclubs. The use of zip codes as the
unit of study is acceptable since it has been used in other geographic studies (Pacione,
1989; Leppel, 1993). Six Single A organizations responded with 1997 sample data that
they had collected. Table 1 shows the franchises that responded with information, the
host city and state of the organization, the league in which the franchise participates, and
the number of zip codes from which the sampled attendees originate. Figure 1, on page

35, displays the locations of these franchises.

 

 

 

 

 

 

 

TABLE 1
Franchise Nam Location Lea nd Number of Zi es
FRANCHISE LOCATION LEAGUE ZIP CODES
Beloit Snappers Beloit, WI Midwest 78
Charleston RiverDogs Charleston, SC South Atlantic 50
Charlotte Rangers Port Charlotte, FL Florida State 24
Clinton LumberKings Clinton, IA Midwest 142
High Desert Mavericks Adelanto, CA California 40
West Michigan Whitecaps Comstock Park, MI Midwest 178

 

 

 

 

 

 

As one can realize, the six data sets that were applied for this thesis are rather diverse. Six
different states and four different leagues are represented, and the number of zip code
origins in each data set ranges from twenty-four to one-hundred seventy-eight.

The size of the population of each zip code under study was utilized as the origin
mass variable, Pi. The populations of the zip codes were obtained from the Summary
Tape File 3B (STF 3B) of the 1990 United States census. The STF 3B contains one-
hundred percent counts for total persons in each zip code in the United States. The

literature is well documented with reference to using population as a mass variable within

34

Fr

 

 

 

FIGURE“: Location of Franchises
that Supplied Data

 

Scale = 1:88.843.451

 

35

 

 

gravity models. McConnell, 1965 and Kariel, 1968 both employed population as the
origin mass variable in order to test the predictive ability of a potential model with regard
to the origins of enrolled university students. Cheung, 1972 utilized population as a mass
variable in order to explain recreational park visitation patterns. Haynes and
Fotheringham, 1984 also applied population as the push variable in an attraction
constrained gravity model which was used to predict attendance at conventions.

The Pythagorean distances, or the straight-line distances, between the geometric
centroids of the zip code origins and the geometric centroids of the zip codes that contain
the stadium were used to represent the deterrence variable, Dij, in the potential model.
The distances were obtained from ZipFind, http://link-usa.com, which is an Internet
company. Distance is often employed as the spatial fiiction variable in spatial interaction
models, and it is excellent for estimating intraurban spatial movement (Ewing, 1980;
Ottensmann, 1997). Pacione, 1989 utilized straight-line distance in order to study
accessibility to secondary schools. However, it is also necessary to calculate the distance
traveled by attendees who reside in the zip code that contains the stadiurrr, or the
intrazonal separation within the host zip code. This was accomplished by dividing the
distance value of the zip code nearest to the stadium in half. Thrill, 1995 applies this
method when attempting to model store choices.

As a result, the potential model employed in this thesis assumes that the number of

people that attend baseball games, Tj, is directly proportional to the population of the zip
code origin, Pi, and is inversely proportional to the distance between the centroids of the

zip code origins and the centroid of the zip code that hosts the stadium, Dij.

36

Estimation of the Potential Model
The potential model predicts attendance values for each zip code of a franchise's
market territory. In order to test the explanatory power of the model for each of the six
franchises, a loglinear least-squares regression analysis was applied. This is the
conventional approach of calculating the parameters of a gravity model (McAllister and
Klett, 1976). For example, both McConnell, 1965 and Kariel, 1968 employed loglinear
least-squares regression to test their potential models. This method is able to demonstrate

causal relationships between the dependent variable and the independent variables. That
is, with regard to this thesis, one can understand the contribution of both P; and Dij with

reference to explaining the variance of the actual number of attendees. Additionally, a
researcher using ordinary least squares regression analysis is capable of testing the
significance of estimated parameters, subject to specific assumptions (Thompson, 1986).

However, it must be noted that regression analysis is an imperfect method.
Therefore, another goodness-of-fit test, the standardized root mean square error
(SRMSE), was also applied to test the predictive ability of the potential model. Before the
SRMSE statistical test is discussed, some of the problems that are associated with
regression analysis will be addressed.

First, one must be cautious of creating an uninterpretable equation. For example,
if there is multicollinearity among the independent variables of the regression equation,
that is, when two or more variables are strongly correlated, the results will most likely be

uninterpretable (McAllister and Klett, 1976; and Thompson, 1986).

37

 

Another problem is that the coeficient of determination should not be used to
assess a model's results across different data sets. That is, an investigator should not make
any conclusions by comparing a model's R2 values of two difl‘erent sets of data. This is
due to the fact that the variance of the actual data values influences the value of the test
statistic (Knudsen and Fotheringham, 1986).

Since the loglinear least-squares regression is a function of the observed data, the
resulting parameter values may be inaccurate. This is because the analysis gives difi’erent
weights to the observations. That is, each observation of the data is not treated equally.
Therefore, it is possible that outliers are given too much weight by the analysis, thus
causing inaccurate parameter values (Batty and Mackie, 1972).

To obtain coefficient values and to test the goodness-of-fit of the potential model,
the standardized root mean square error (SRMSE) was also applied to each of the six data
sets. This goodness-of-fit test employs a series of iterations in order to determine the
explanatory power of the model and to obtain the parameter values. The SRMSE
statistical test is also included in the methodology, because it is considered to be the best
test statistic to determine if there is a statistically significant difference between actual and
expected spatial interaction flows (Knudsen and Fotheringham, 1986). Knudsen and
Fotheringham, 1986 studied several goodness-of-fit examinations that are able to be
employed to assess the results of aggregate spatial interaction models. Both, the SRMSE
and the R2 test statistics were examined in their study. Knudsen and F otheringharn
concluded that the SRMSE test statistic is superior to the other goodness-of-fit tests that
were studied. The major determinant that led to this conclusion is that by applying the

SRMSE test statistic, the goodness-of-fit of difi‘erent data sets can be compared using

38

 

metric properties. In other words, suppose an analyst applies the SRMSE test statistic to
a model's predictions of two different data sets: Data Set #1 and Data Set #2. Ifthe error
value, the test statistic value, is two times larger for Data Set #1 than for Data Set #2, then
one is able to infer that the model is twice as accurate for Data Set #2 as it is for Data Set
#1. Knudsen and Fotheringharn also concluded that this line of reasoning cannot be made
using the coefficient of determination. Another advantage of the SRMSE test statistic
with regard to the R2 goodness-of-fit test is that the SRMSE test weighs each observation
equally, unlike the coefficient of determination. Therefore, outliers are less likely to cause
inaccurate parameter estimates (Knudsen and Fotheringham, 1986).

Because the optimum value of goodness-of-fit tests is usually found with difi‘erent
parameter values, the use of two tests results in two different sets of test statistics and
parameter values for each of the six data sets. As a result, there are six sets of multiple
squared R test statistics and six sets of SRMSE statistical tests. From both of these
analyses, one should have a fairly accurate idea of how well the potential model predicts

the geographical market territory of Single A baseball franchises.

Regression Analysis

In order to use least-squares regression analysis as a method to estimate the
parameters, and to test the goodness-of-fit of the model, it is necessary to transform the
variables of the model (Johnston, 1978). This is due to the fact that the potential model
(EZ) is multiplicative with exponents requiring estimation. Regression equations should
have an additive, or linear, relationship between the dependent variable and the

independent variables. If this relationship is not additive, the results of the regression

39

 

analysis will most likely be erroneous (Clark and Hosking, 1986). Since transformations
are able to make nonlinear functions intrinsically linear, Talen and Anselin, 1998,
transformed a potential model which was utilized to estimate origin-destination flows of

playgrounds (Thompson, 1986). The logarithmic form of the potential model is given as:
*
lnTj = lnk + (Z bll’lPr - clnDij) (E3)

To estimate the coefficients (b and c) of the independent variables (Pi and Dij), and

to test the explanatory power of the model, the dependent variable (Tj) and the

independent variables were transformed and ordinary least-squares regression was applied

in the statistical computer program Systat. The estimation of the population coefficient b

allows one to realize the slope of the relationship between Tj and Pi, with Dij held
constant. In like manner, one can also understand the slope of the relationship between Tj

and Dij, with P; held constant, by estimating the distance coeficient c (Johnson, 1978).

To examine the statistical significance of the estimated coefiicient values, the student's t

test was employed, using a one-tailed test and an alpha level of 0.05.

The coeficient of determination allows one to realize the total contribution of Pi
and Dij, that is the variables' combined contribution as well as each variable's separate
contribution, with regard to accounting for the proportion of the variance of Tj (Johnston,

1978). The coefiicient of determination ranges from O to 1. A value of zero signifies that
there is not a relationship between the dependent variable and the independent variables.

On the other hand, a value of one demonstrates that there is complete correspondence

40

between the dependent variable and the independent variables (Knudsen and
Fotheringham, 1986). The F-ratio, applying an alpha level of 0.05, was utilized to

determine if the value of the coeficient of determination is statistically significant.

The Standardized Root Mean Square Error

Because it is irrelevant to the calculations of the SRMSE test statistic that the
potential model has a multiplicative form, there is no need to transform the model in order
to conduct this goodness-of-fit examination. The formula of the standardized root mean

square error is as follows:

SRMSE = {2a,}. - i512 /n} / (gay n) (124)

where:
tij = an element of the observed flows
n = the number of observations

= an element of the predicted flows

The objective of the SRMSE goodness-of-fit test is to educe parameter values that
rnininrize the value of the SRMSE test statistic, which is also referred to as simply the
error value (Desta, 1988). With regard to this project, the error is the average difference
between the actual attendance values and the number of attendees that the potential model
has predicted. In order to obtain the lowest error value possible, an analyst inputs starting
values for every parameter value to be calculated, and then runs the SRMSE goodness-of-
fit test which conducts a series of iterations to find the parameter values which minimizes

the error value. For this project the starting values were set equal to one, which is the

41

normal practice. This was conducted in Microsoft Excel’s Solver option. The lower limit
of the SRMSE test statistic is zero, which denotes completely accurate model predictions
of the observed data. Conversely, large error values signify poor model predictions.
However, there is no upper limit of this test statistic. Theoretically, the value of the error

can continue towards infinity (Knudsen and Fotheringham, 1986).

Residual Analysis

Gravity models cannot firlly explain a market territory. In order to build a better
model, the residuals must be examined. The investigation of residuals assists in
recognizing other elements that affect spatial interaction. As a result, one can improve a
model's predictive powers (Baxter and Ewing, 1981).

Residuals are the differences between the actual number of trip flows and a model's
predicted number of trip flows (Ewing, 1980). Regarding this project, positive residuals
indicate zip codes that provide more attendees than would be expected given the values of

Pi and Dij. Therefore, zip codes with positive residuals show that the potential model is

underpredicting the number of attendees who actually attend baseball games. On the other
hand, residuals with negative values denote zip codes fi'om which fewer attendees travel to
the stadium than the potential model predicts. In this case, the model is overpredicting the
number of attendees that originate from these zip codes. Therefore, after examining the
influence of population and distance, the patterns of residuals may provide information
that would suggest firture improvements to the model.

In an attempt to add to the explanatory power of the potential model, the SRMSE

residuals are correlated with selected demographic variables. These demographic

42

variables were also correlated with the regression residuals of the transformed potential
model. This procedure allows one to ascertain if other variables can contribute to the
explanatory power of the models. Furthermore, the investigation of the regression
residuals also reveals if the assumptions of the coefficient of determination goodness-of-fit
test have been met. However, before the methodology of this operation is discussed, the
selection of the demographic variables will be addressed.

Demographic data at the zip code level was collected in order to examine the
residuals. This information was acquired from the Summary Tape File 38 (STF 3B) of the
1990 United States Census which contains sample data weighted to represent the total
population of the zip code. Table 2 illustrates which demographic variables were

examined and a summary of the reason for their inclusion.

 

 

 

 

 

 

 

 

 

 

 

TABLE 2
Demographic Variables Anm and Their Reason For Inclusion

Demographic Variables Vernacular Reason

For Inclusion
Median Household Income Income Baseball
% of Family Households Families Baseball
% of Males Males Baseball
% of Minorities Minority groups Baseball
% of People 16 and Over Employed Professional- Baseball
in Professional Positions Managerial Positions
% of Home Owners Home Owners Retail Sales
% of Multiple Person Households Multiple Retail Sales

Person Households

% of People 15 and Over Married Marital Status Retail Sales
% of People 18 and Over with Some Education Recreational
College Education Activities
% of People with Ages of 25-59 Age Recreational

Activities

 

 

 

 

 

43

The above variables have been chosen for various reasons. Five of the above variables are
said to directly influence the market characteristics of sports and baseball. Income is
included because affluent markets offer more potential customers than areas with less
wealthy residents (Danielson, 1997). Danielson, 1997 adds that since the middle of the
twentieth century sports have been marketed toward families. However, males have been
more likely to attend games than females (Danielson, 1997). According to a study
conducted by Sager and Culbert, 1992 African-Americans are less inclined to attend
baseball games than Caucasians (Stix, 1993). Since Hispanics and Asians have
increasingly become interested in baseball, 1 have included all minority groups with regard
to this variable (Sands and Gammons, 1993). The lower middle class has traditionally
supplied most of the attendees of ballgames. However, in recent years baseball fianchises
have increased ticket prices (Danielson, 1997). As a result, baseball fi'anchises are
marketing towards people with employment in professional or managerial positions
(Euchner, 1993). The following list illustrates which categories from the STF 3B file tape
1 utilized in order to determine the percentage of people who are employed in professional
or managerial positions within each zip code: Executive, Administrative, and Managerial
Occupations; Professional Specialty Occupations; Technicians and Related Support
Occupations.

Researchers have used the ensuing five variables to describe the market areas of
other phenomena, not including baseball franchises. These five variables are: home
owners, marital status, multiple person households, age, and education. Because this is
an exploratory exercise, I have included these five variables in the examination in order to

determine if they also affect the geographical market territory of baseball fianchises. Both

home owners and marital status affect the patronage of grocery stores (F otheringham,
1988). Multiple person households also affect retail sales (Thompson, 1986). McAllister
and Klett, 1976 report that participation for recreational activities varies greatly by age.
Similarly, Mueller and Guerirr, 1961 found that age and education assist in explaining park
visitation patterns (Cheung, 1972). The age range of 25-59 was chosen for this thesis
because data collected fiom baseball franchises suggest that this age range contributes
approximately sixty to eighty percent of the total number of sample attendees.
Information obtained from baseball organizations also indicates that people with at least
some college education account for almost seventy-five percent of the total number of
attendees sampled.

It should be mentioned that the total population of each zip code was used to
create the percentages for the variables of age, gender, and race. Furthermore, in order to
create percentages for family households, home owners, and multiple person households,
it is necessary to obtain the total number of households within each zip code. The STF 3B
tape file also consists of one-hundred percent counts of total housing units within each zip

code of the United States.

Expansion of the Models

Because other variables may be able to add to the models’ predictive ability, it is
necessary to discern if it is possible to expand the models. As previously mentioned, this
can be accomplished by examining the residuals apropos of the demographic variables. To
determine if there is a statistical relationship between the demographic variables and the

residuals, Pearson's correlation coefficient was employed. This statistical test is able to

45

demonstrate the correlation between two variables. The range of values for Pearson’s
correlation coefficient varies from -1 to 1, where a value of 1 indicates a perfect positive
correlation between two variables. Conversely, a value of -1 denotes a complete negative
correlation between two variables. A value of 0 indicates absolutely no correlation
between two variables. Therefore, extreme values generally demonstrate that a correlation
with the observed sign occurs in the population (Johnston, 1978). As a result,
demographic variables that have a statistical relationship with the residuals should be
incorporated into the model in order to add to its explanatory power.

Because the regression residuals result fiom a transformed potential model, the
values of the residuals are in a transformed form. Therefore, if the demographic variables
have a statistical relationship with the regression residuals, then the demograch variables
should be incorporated into the potential model in a multiplicative form. On the other
hand, the SRMSE residuals are absolute because one does not need to transform the
potential model in order to conduct the standardized root mean square error goodness-of-
fit test. Consequently, demographic variables that have a statistical relationship with the
SRMSE residuals ought to be included into the potential model in an additive form.

Each fianchise data set has two sets of correlations: the demographic variables
against the regression residuals, and the demographic variables against the SRMSE
residuals. To determine if the demographic variables have a significant correlation with
the regression residuals or the SRMSE residuals, Pearson correlation coeficient values of
0.3 and -0.3 were used as guides. Therefore, if a demographic variable has a correlation
value of above 0.299, or below —0.299, it was concluded that it should be incorporated

into the appropriate model.

An example using hypothetical Pearson correlation coemcient values should assist
to clarify the above methodology. Suppose the Beloit data set has the following Pearson
correlation coefficient values (please see Table 3). In this hypothetical example, only the
income variable has a significant Pearson correlation coefficient value with the regression
residuals. Therefore, income should be included into the transformed potential model in a
multiplicative form. On the other hand with regard to the SRMSE residuals, income and
age have significant Pearson correlation coefficient values. As a result, they ought to be
incorporated into the potential model in an additive form.

This chapter has described the methodology employed in order to determine if the
potential model is able to accurately predict the geographical market territories of Single

A minor league baseball franchises. In order to ensure that the predictive results of the

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 3

Hymthetical Pearson's Correlation Coefficient Values fpr Beloit
DEMOGRAPHIC VARIABLES RESIDUALS ERROR TERMS
Median Household Income 0.302 0.324
% of Family Households 0.242 0.225
% of Males 0.211 0.223
% of Minorities -0.023 -0. 124
% of People 16 and Over 0.233 0.226
Employed in Professional Positions
% of Home Owners 0.228 0.224
% of Multiple Person Households 0.283 0.292
% of People 15 and Over Married 0.238 0.221
% of People 18 and Over with 0.183 0.142
Some College Education
% of People with Ages of 25-59 0.293 0.372

 

 

 

 

potential model were accurate, two difl’erent goodness-of-fit tests were applied to the

model. To determine what other variables may add to the explanatory power of the

47

model, and in what form they should be incorporated into the model, the regression
residuals and the SRMSE residuals were correlated against specific demographic

variables. The following chapter will show the results of the examination.

48

CHAPTER IV
RESULTS OF THE EXAMINATION

This chapter begins with an analysis of the models’ predictions regarding the six
market territories under investigation. The discourse then illustrates how zip codes
located at great distances fi'om the stadium adversely afiect the results of the models.
Reasons for eliminating these observations, as well as an explanation of how these zip
codes were removed fiom the data sets, are discussed. The models are then reexamined
without these observations. The chapter concludes by demonstrating that competing

destinations and outliers impair the models’ estimations.

Results of the Models

The transformed potential model and the potential model were applied to each of
the six data sets. The results are tested using the coefficient of determination and the
standardized root mean square error respectively. Table 4 displays the results of the
regression analysis, and Table 5 shows the SRMSE test statistics.

An alpha level of 0.05 was employed to test the statistical significance of R2.
Since, for each of the six fianchises, the values of R2 are significantly difl’erent from zero,
there is a less than five percent probability that the results have occurred by chance. The
transformed potential model performs well with regard to the trade areas of Charleston,
Charlotte, and West Michigan. However, this model produces less accurate estimations of
the trade areas of Beloit, Clinton, and High Desert, which have R2 values below 0.5. The

distance coefficients (c) for all of the franchises are statistically significant, and four of the

49

six fianchises have statistically significant population coeficients (b). High Desert's and

Charlotte's population coefficients are not statistically significant.

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 4
Results of the Transformed Potential Model

Franchise R2 Distance Coefficient Population Coefficient
Beloit 0.491 -0. 743 0. 178
Charleston 0.743 -0.993 0.546
Charlotte 0.654 -0.833 not significant
Clinton 0.49 -0.994 0.305
High Desert 0.465 -1.052 not significant
West Michigan 0.784 -1.7 0.451

TABLE 5

Results of the Potential Model

 

 

 

 

 

 

 

 

 

Franchise SRMSE Distance Coefficient Population Coefficient
Beloit 1.538 0.462 0.367
Charleston 1 .323 0.333 0.543
Charlotte 0.976 0.61 0.358
Clinton 0.88 1.357 0.761
High Desert 1.317 1.304 0.688
West Michigan 0.974 0.896 0.691

 

 

 

 

 

Standardized partial regression coeficients, or beta values, indicate the change
measured in standard deviations in the dependent variable associated with a one standard
deviation change of an independent variable, with the effects of all other independent
variables held constant (Johnston, 1978). Therefore, through the examination of the beta

values, it is possible to determine which variable contributes more to the model's

predictive ability. Table 6 lists the statistically significant beta values of Dij and P; for all

50

six fianchises. It is clear that Dij is the more powerful of the two variables for each of the

market territories.

 

 

 

 

 

 

 

TABLE 6
Beta Values

Franchise Beta Value for Dy Beta Value for Pi
Beloit -0.718 0.174
Charleston -0.789 0.348
Charlotte -0.871 not significant
Clinton -0.787 0.367
High Desert -0.669 not significant
West Michigan -0.831 0.283

 

 

 

 

 

The potential model, which was tested with the standardized root mean square
error, generated fairly accurate predictions for each of the six fianchises. The value of the
SRMSE test statistic ranges between zero and infinity, where a value of zero denotes
completely accurate model predictions of the observed data. The test statistic values for
the six franchises varied from 0.88 to 1.538. The trade areas in which the potential model

provides its best predictions are Clinton, West Michigan, and Charlotte.

It appears that Dij and Pi capture much of the variation in the trade areas of
baseball franchises. Moreover, in all of the examinations, the dependent variable and the

independent variables have the expected relationships. Dij has an inverse relationship with

T3, and P; has a positive relationship with Tj.

51

Examination of the Residuals
By examining the residuals, one can discern that zip codes which are located at
relatively great distances from the franchises' stadiums impair the models' estimates of the
trade areas. The following section not only illustrates that this is true, but it also provides
reasons for eliminating these observations as well as an explanation of how these zip codes

were removed from the data sets.

The Elimination of Distant Obsemtions

Figure 2, on page 53, applies to the model tested with the coefiicient of
determination statistical measure. This figure shows the proportion of error regarding the
model's predictions of attendees against the logarithm of distance for the West Michigan
trade area. In order to obtain the proportion of error in the number of attendees, in their
antilog form the regression residuals were divided by the actual number of attendees. This
graph depicts that as distance increases from West Michigan's stadium, the magnitude of
the error of the model's predictions becomes larger. In other words, the model does not
accurately predict the number of attendees that originate fi'om distant zip codes. This is
also true for the market territories of the other five franchises.

Figure 3, on page 54, exhibits the relationship between leverage and the logarithm
of distance for West Michigan's trade area. Leverage values demonstrate the weight that
each observation has upon the results of the R2 statistical test. Therefore, an observation
that has a high leverage value contributes more to the R2 analysis than an observation with
a small leverage value. Through the examination of Figure 3, one can realize that

observations that are near to West Michigan’s stadium have high leverage values. More

52

 

Proportion of Error in the Number of Attendees

FIGURE #2: West Michigan’s Market Territory
Proportion of Regression Error against LN Dij

 

 

 

 

 

O l l l l l C

9 - Q.
8 P ._
7 - _
6 - _
5 r O _.
4 - O _
3 - _.

o

2 _
1 . . _
0 : ,- J

0 1 2 3 4 5 6

LNDistanee

53

FIGURE #3: West Michigan’s Market Territory

 

 

 

 

 

Leverage against LN Dij
0.08 o I l l 1 l
0.07 —
O
0.06 — O
0.05 —
0
g, 0.04 — 0 o O
r: o 0 O
0 % O
E. 0.03 — o g 00 8
0% O 0 £3
0.02 - ‘9 0 <2, 9°00
a0 (g 09%
0.01 —
0.00 ' ' ' i ' '

importantly, zip codes that are located at great distances fiom the ballpark have high
leverage values as well. This is also the case with regard to the trade areas of the other
five fianchises. Therefore, Figures 2 and 3 reveal that the model estimated with the R2
test statistic provides poor predictions for remote zip codes, and that these zip codes
heavily influence the model's estimates of the market territories. As a result, these
observations adversely affect the performance of the model.

The model tested with the SRMSE goodness-of-fit test also has difiiculty in
accurately estimating the number of attendees that originate from distant zip codes.
Figure 4, on page 56, displays the proportion of error regarding this model's predictions of
attendees against the logarithm of distance for West Michigan's market territory. To
acquire the proportion of error in the number of attendees, the SRMSE residuals were
divided by the actual attendance values. This figure exhibits that as distance increases
from West Michigan's ballpark, the magnitude of the error of the potential model's
predictions enlarges. In fact, the model greatly overpredicts the number of attendees that
originate from remote zip codes. This phenomenon can also be observed for the trade
areas of the other five fianchises. Therefore, the zip codes that are located at relatively
great distances from the franchises' stadiums are impairing the predictive ability of the
potential model. However, because the SRMSE statistical measure weighs each
observation equally when calculating its test statistic and parameter values, distant
observations probably do not affect the results generated by the standardized root mean
square error as much as they influence the results produced by the R2 statistical measure.

Observations that are located at great distances fiom the franchises' ballparks do

not provide many attendees to the fi'anchises. It is argued that these attendees, who reside

55

 

Proportion of Error in the Number of Attendees

FIGURE #4:

.10

West Michigan’s Market Territory
Proportion of' SRMSE Error against LN Dij

 

 

 

 

l l l 1

 

.4

2 3 4 5 6

LN Distance

in the remote zip codes, are most likely business travelers, people who are visiting fiiends
and family, or tourists. Consequently, the distant zip codes do not appear to be an integral
part of the franchises' normal market territories. In order to improve upon the models'
predictive powers, especially for the local market, the remote zip codes were eliminated
from the data sets and the models were again applied to all six market territories under
examination. Therefore, all zip codes that are located beyond the point of distance where
the models' predictions begin to worsen were removed fi'om the data sets. As a result,
with regard to West Michigan’s trade area, all zip codes located beyond 50.6 miles from
the stadium (3 .9 on a logarithmic scale) were eliminated fi'om the data set. Referring back
to figures 2 and 4 allows one to discern that at this point of distance the models’
predictions begin to worsen.

The elimination of distant observations should allow the models to provide better
parameter estimates, which in turn would permit the models to firrnish more accurate
predictions of the market territories. Precedence for eliminating observations in order to
improve a spatial interaction model's predictions can be found in Kariel, 1968 and Pooler,

1992.

Results of the Models After Elimination
The number of zip codes that remain in each of the data sets, as well as the ranges
of each franchises' market territory are presented in Table 7, on page 64. Figures 5-10 on

pages 58-63 show the actual trade areas of all six fi'anchises.

57

FIGURE #5: Market Tenitory of Beloit

LEGEND
= 55+ Attendees Q = Location of the Stadium
= 21-54
= 10-20
= 1-9

= No attendance
Seale = 1:1,449,380

 

58

 

FIGURE #6: Market Territory of Charleston

 

 

 

 

Legend
- = 301+ Attendees O = Location Of the Stadium
- = 151-300
- = 93-150
1:] = 1-92
[:3 = No attendance Scale = 131,449,380

 

 

59

 

FIGURE #7: Market Tenitory of Charlotte

 

257E

 

 

 

,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(£2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Legend
- = 41+ Attendees

- = 13-40

- =9-12

=1-a

[:3 = No attendance

 

O

= Location of the Stadium

Stale = 1:1,499,380

 

 

 

 

FIGURE #8: Market Territory of Clinton

- = 301+ Attendees
- = 101-300

- = 33-100

=1-32

E: =‘No attendant»

Legend
0

= Location of the Stadium

61

Stale = 1:1.199,38O

 

 

FIGURE #9: Market Territory of High Desert

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

*1
1: .
p.
a" i
75.: v;
' p
r-- f
’7 1
'1‘ “
-.':.' 1,
.. 1
.‘e f" '
a" '. ..
1 .. 1_
":Yr ’ l t
.‘.‘
.9. . .' '
r' .
rm .j_ J ".
ea- : -
-..‘~‘ . -
‘43:“! .
5.
egg-
” «.5
. 14
u
s
e

 

 

 

 

 

 

Legend

- = 95+ Attendees
- = 65-94

- = 37-64

,1. = 1-36

1:1 = No attendance

= Location of the Stadium

Scale = 1:3,000,000

 

62

 

 

 

FIGURE #10: Market Territory of West Michigan

Legend
- = 200+ Attendees O = Location of the Stadium
- = 100-199
- = 54-99

=1-53

 

:1 = No attendance Scale = 121,099,380

63

TABLE 7
Characteristics of the Data Sets After the Elimination of Remote Observations

 

 

 

 

 

 

 

 

 

Franchise # of Zip Codes Range of Market Territory
Beloit 28 41. 8 miles
Charleston 30 38.9 miles
Charlotte 17 21.7 miles
Clinton 62 49.2 miles
High Desert 12 31.3 miles
West Michigan 102 50.6 miles

 

 

 

After the elimination of the distant observations, both models were applied to each
of the six market territories. This procedure allowed the transformed potential model to
produce considerably better estimates for the market territories of Clinton and High
Desert. The removal of observations also enabled the potential model to provide much
improved estimates for five of the six market territories. However, the transformed
potential model and the potential model generated worse predictions with regard to
Charlotte's trade area. Table 8 and Table 9 on page 65, display the goodness-of-fit results,
as well as the parameter estimates, for both of the models before and after the elimination
of distant observations.

Relative to its predictions of the other four market territories after the removal of
remote zip codes, the model tested with the R2 test statistic does not successfirlly estimate
the trade areas of Beloit and Charlotte. Nonetheless, the distance coeficient for each of

the data sets are statistically significant, and five of the population coefiicients have
significant values. However, Pi appears to be unable to explain the variation within the

High Desert trade area.

TABLE 8
Results of the Transformed Potential Model:
Before and After the Elimination of Remote Observations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Franchise R2 Distance Population
Coefficient Coefficient
Beloit (b)* 0.491 -0.743 0.178
Beloit (a)* 0.474 -0.706 0.571
Charleston (b) 0.743 -0.993 0.546
Charleston (a) 0.735 -0.469 0.933
Charlotte (b) 0.654 -0.833 not significant
Charlotte Q1) 0.356 -0.721 not significant
Clinton (b) 0.49 -0.994 0.305
Clinton (a) 0.615 -1.636 0.566
High Desert (b) 0.465 -1.052 not significant
High Desert (3) 0.702 -2.343 0.002
West Michigan (b) 0.784 -1.7 0.451
West Michigan (a) 0.793 -1.71 0.742
TABLE 9

Results of the Potential Model:
Before and After the Elimination of Remote Observations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Franchise SRMSE Distance Population
Coefficient Coefficient
Beloit (b)* 1.538 0.462 0.367
Beloit (a)* 0.907 0.569 0.41
Charleston (b) 1.323 0.333 0.543
Charleston (a) 0.93 0.139 0.524
Charlotte (b) 0.976 0.61 0.358
Charlotte (a) 1.024 -0.025 0.246
Clinton (b) 0.88 1.357 0.761
Clinton (a) 0.606 1.312 0.758
High Desert (b) 1.317 1.304 0.688
High Desert (a) 0.54 0.681 0.564
West Michigan (b) 0.974 0.896 0.691
West Michigan (6) 0.698 0.808 0.679

 

*note for both tables: (b)

(a)

the results of the examination before the removal

of distant zip codes.

the results of the examination after the removal of

distant zip codes

65

 

With the exception of the market territory of the Charleston fianchise, Dij explains
more of the variation within the trade areas than does Pi (however, the explanatory power
of Dij and P; are almost equal for Beloit’s market area). This can be understood by

examining Table 10, which displays the statistically significant beta values of Dij and Pi

after the elimination of distant zip codes.

TABLE 10
Beta Values:
After the Elimination of Remote Observations

 

 

 

 

 

 

 

 

 

 

 

Franchise Beta Value for 3.1 Beta Value for Pi
Beloit -0.443 0.44
Charleston -0.28 0.693
Charlotte -0.598 not significant
Clinton -0.658 0.514
High Desert -0.503 0.193
West Michigan -0.612 0.444

 

Similar to the analysis with the inclusion of the distant observations, the potential
model generates accurate predictions for more of the market territories than does the
transformed potential model. The SRMSE values reveal that the potential model
successfully predicts the market territories of: Beloit, Charleston, Clinton, High Desert,
and West Michigan. Examining Figure 11, on page 67, confirms this notion. This figure
depicts the model’s predicted attendance values against the actual attendance values for
West Michigan’s market territory. As one can realize, for most of the observations, the
potential model gives reasonable predictions with regard to the number of attendees that

originate fiom each of the zip codes. Graphs of the same nature show that the model also

FIGURE #11: West Michigan’s Market Territory

Potential Model’s Predicted~Attendance Values
vs
The Actual Attendance Values

 

 

 

 

 

700 l I l l l
600 — 9-
500 — —
g 400 '- O O —‘
< 300 - O O —
200 — g -

O Q ((3) 0
<9

100 — O -

OiZOL l J l l

0 100 200 300 400- 500 600

Predicted-

67

provides reliable estimations for the trade areas of Beloit, Charleston, Clinton, and High
Desert.
However, the results of the SRMSE statistical measure demonstrate that the

potential model is unable to provide an accurate estimate of the Charlotte trade area. In
fact, with regard to the Charlotte franchise, Dij does not account for the number of people

that attend their games (please refer to Table 9).

Influence of Competing Destinations and Outliers

Because the distant observations have been eliminated fi'om the trade areas, it is
now possible to realize that competing destinations are influencing the models' estimates
for the following franchises: Beloit, Clinton, High Desert, and West Michigan. The
removal of remote zip codes also facilitates the examination of the residuals within the
cores of the trade areas for all six fianchises. One can now recognize outliers within the
heart of the trade areas, which in most of the market territories are either located within
the central city, or are suburban zip codes that are located near to the periphery of the city.
The succeeding discourse will focus upon these two issues.

Beloit, Clinton, High Desert, and West Michigan compete with other ballteams for
attendees in specific areas of their respective market territories. Table 11, on page 69,
reveals the competitors of these four fianchises. These competitors provide alternatives,
especially for the residents of certain zip codes. As a result, the zip codes that are
influenced by competing destinations send fewer than the predicted number of attendees to
the franchises that are examined in this project. Therefore, the competing destinations are

forcing the models to overpredict the zip codes in which the franchises must compete for

68

attendees. Figures 12-15, on pages 70-73, shows the relative location of the competitors
of the fi'anchises under investigation, as well as the zip codes that the models overpredict
due to the existence of the competing destinations. It should be mentioned that in order to
denote zip codes that are affected by competing destinations, both models must have
overpredicted zip codes that are located relatively close to a competing fianchise. The
locations of these zip codes relative to the stadiums of the franchises that under study are

listed in Table 12.

TABLE 11
Competitors of the Franchises Under Study

 

Franchise Under Study Competitors

Beloit Snappers Rockford Cubbies

Clinton LumberKings Quad City Bandits

High Desert Mavericks Rancho Cucamonga Quakes
San Bernadino Stampede
West Michigan Whitecaps Lansing Lugnuts

 

 

 

 

 

 

 

 

 

 

 

 

 

Michigan Battle Cats
TABLE 12
Locations of the Zip Codes that are Affected by Competing Destinations
Franchise Location of the Affected
Zip Codes from the
Host Zip Code

Beloit 3.1-20.6 miles
Clinton 18.2-45.3 miles
High Desert 27.4 miles"
West Michigan 27455 miles

 

 

 

 

*note: Only one zip code is afi‘ected by High Desert’s competitors.

69

 

 

 

FIGURE #12: Zip Codes of Beloit’s Market Tenitory

that are Influenced by a Competing Destination

 

 

N

A

 

 

 

 

 

 

 

 

 

Illilnr

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 1 I l— l
/
Legend

-.- Zip code. that are 0 = Stadium location of fl

influenced by the Beloit

competing destination

. = Stadium location of

[:3 = Zip codes that are not Rockford

influenced by the

competing destination

Scale = 1:1,549,380

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

70

 

 

FIGURE #13: Zip Codes of Clinton’s Market Territory
that are Influenced by a Competing Destination

N

A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6 “6E

 

 

 

 

 

 

 

 

 

 

 

 

l 1 l f 1
Legend
= Zip codes that are . = Stadium location of
influenced by the Clinton
competing destination
. O = Stadium location of
1:) = Zip codes that are not Quad City
influenced by the
competing destination

Scale = 111,549,380

 

 

71

 

 

FIGURE #14: The Zip Code of High Desert’s Market Territory
that is Influenced by Competing Destinations

it

 

 

 

 

 

 

 

 

 

 

Legend

 

= Zip code that is O = Stadium location of ‘
influenced by the High Desert
competing destinations
= Stadium location of
C} = Zip codes that are not Rancho Cucamonga
influenced by the

competing destinations . = Stadium location of
San Bernadino

 

Scale = 1:1,549.380

 

 

 

72

 

 

 

 

FIGURE #15: Zip Codes of West Michigan’s Market Territory
that are Influenced by Competing Destinations A

K

 

 

L—J—‘L—l—L Lj L in

i ”‘1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o},

 

 

 

 

 

 

 

 

 

 

per

 

 

 

 

 

 

 

 

Legend A
= Zip codes that are . = Stadium location of

 

 

 

 

 

 

 

 

 

influenced by the West Michigan
competing destinations , ,
. = Stadium location of r.
:1 = Zip codes that are not Lansrng
influenced by the . .
competing destinations . = Stadium location of
Michigan

 

Scale = 1:1,549,3801

 

 

73

 

 

The zip codes that are affected by competing destinations have the greatest
proportion of error with regard to the models' predictions. Figure 16, on page 75, which
pertains to Clinton's market territory after the elimination of distant zip codes, exhibits the

proportion of error apropos of the transformed potential model's estimations of attendees

against Dij. Like the analysis before the removal of remote observations, the accuracy of

this model decreases as Dij increases. However, the zip codes that are afl’ected by the

Quad City franchise have the greatest magnitude of error in the number of people that
attend Clinton's games. The affected zip codes are located between 18.2-45.3 miles from
Clinton's stadium (again, to denote these zip codes, both models must have overpredicted
observations that are located relatively close to the competing fi'anchise). Studying Figure
16, it is possible to estimate that within this range of distance there are many zip codes
that have extremely large proportions of error in the number of attendees. The
observations that have large magnitudes of error are those that are affected by Quad City.
This model also generated similar patterns of the proportion of error in the number of
people that attend games for the market territories of Beloit, High Desert, and West
Michigan.

The potential model has difficulty in accurately predicting the number of attendees
that originate fiom zip codes that are influenced by competing destinations as well. This
can be realized through the examination of Figure 17, on page 76, which shows the
proportion of error pertaining to the potential model's estimations of attendees for West

Michigan's market territory against Dij. Similar to the examination of the residuals before

remote observations were eliminated, this model greatly overpredicts the remanent distant

74

FIGURE #16: Clinton’s Market Territory
Proportion of Regression Error against Dij

(After the Removal of Remote Observations)

Proportion of Error in the Number of Attendees

 

 

 

 

0.7 | l l l
o

0.6 0 -
o

0.5 o a

0.4 o o —

o
0.3 0 o 00 o 00 '-
o 03, 0 o
0.2 00 000 O 0 080 00 O ‘-
08 ' 8’ 00 o
0.1 ° . -
00 l l J I
0 10 20 30 40 50'

75

Proportion of Error in the Number of Attendees

FIGURE #17:

West Michigan’s Market Territory
Proportion of SRMSE Error against Dij
(After the Removal of Remote Observations)

 

 

 

 

10 l r 1 I l
O IQWW o 0 0000000 0 "'
O
o 8 QJO o O O
8 ChocJo
-10 _ 063,0 80 g 0 _
O
-20 ‘- —
O
-30 .. ._
O
-40 l l l l l .
0 10 20 30 4O 50 60

Distance

76

zip codes. However, the zip codes that are influenced by the Lansing and the Michigan
fianchises have the largest magnitudes of error with regard to the number of people that
attend the games of West Michigan. The observations that are affected by these two
franchises are located between 27-45.5 miles fi'om West Michigan's ballpark (again, to
denote these zip codes, both models must have overpredicted observations that are
located relatively close to the competing fi'anchises). Through the investigation of Figure
17, one is able to recognize that as distance nears 30 miles, the proportion of error in the
number of attendees becomes eminently greater for many observations. This is due to the
fact that the fianchises of Lansing and Michigan are afi‘ecting several zip codes beyond this
point of distance. The affected zip codes have the highest proportions of error in the
number of people that attend games. The potential model produced resembling
configurations of the magnitude of error in the number of attendees for the market
territories of Beloit, Clinton, and High Desert, as well. As a result, zip codes that are
influenced by competing destinations contaminate the predictive ability of both models.

As previously mentioned, remote observations had been eliminated fiom the data
sets because they did not appear to be an integral part of the franchises' market territories.
However, the examination of the residuals after the removal of the distant zip codes
suggests that many of the eliminated observations may also have been influenced by
competitors of the franchises under study. This may explain why the proportion of error
in the models' predictions before the elimination of distant zip codes became larger as
distance increased from the fianchises' stadiums.

Although the magnitude of the models' error is not as great for zip codes that are

located near to the stadiums as they are for distant zip codes, there is evidence that the

77

models have difiiculty in accurately estimating the number of attendees that originate from
various zip codes within the cores of the trade areas as well. This is clear when examining
the values of the residuals for each of the observations. Unlike the proportion of error
values which demonstrate the magnitude of the error of the models' predictions in the
number of attendees, the values of the residuals indicate the difi‘erence between the actual
number of attendees and the models' estimated number of attendees in real numbers. This
measure of examining the residuals is equally as important as the former approach because
it reveals outliers within the data sets. Most of these outliers are either central city zip
codes, or they are suburban zip codes that are located near to the city.

Figure 18 on page 79 displays, for Charleston’s market territory, the values of the

regression residuals against Dij; and Figure 19 on page 80 exhibits the values of the

SRMSE residuals against Dij. One can observe that almost all of the outliers are located

within ten miles of Charleston's stadium. The outliers are those observations that are
either greatly overpredicted or underpredicted. The observations that the models
overpredicted are located within the city of Charleston. On the other hand, the
underpredicted observations are suburban zip codes that are on the periphery of the city.
Figure 20 on page 81 depicts the zip codes within the cores of the trade areas that both
models poorly predict for Charleston's trade area. Examining the values of the regression
residuals and the values of the SRMSE residuals for the other five fi'anchises revealed
similar patterns of outliers within the cores of these market territories as well. Figures 21-
25 on pages 82-86 show the zip codes within the heart of the trade areas that both models

badly estimate for the other five franchises.

78

 

Regression Residual Values

FIGURE #18:

Charleston’s Market Territory

Values of the Regression Residuals against Dij
(After the Removal of Remote Observations)

 

 

 

 

400 l l l
300 - ° -
200 - "
O
100 - ‘
O o O
0 ”'0 o @OQD 000 O 0 0(9—
O O
-100 - o r
O
-200 ' ‘ '
0 1 0 20 30 40
Distance

79

 

SRMSE Residual Values

FIGURE #19:

Charleston’s Market Territory
Values of the SRMSE Residuals against Dij
(After the Removal of Remote Observations)

 

 

 

 

400 1 I I
300 — O a
200 - '-
o
100 — o -
O o O O
0 _° 0 (190‘?) 000 O O o 06>—
o o o o
-100 - o -:
o
o
_200 l l l
0 1 O 20 30 40
Distance

 

 

n’s Market Territory

URE #20: Outliers in Charlesto

FIG

 

 

 

 

 

 

FIGURE #21: Outliers in Beloit’s Market Territory

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3
a
r ’ .
' :l
13
a I i
__ W H l 1
"J
4] —l
«1 r __
I L I Lg
Legend
[:1 = Zip codes that . = Stadium location of
are extremely Beloit E
underpredicted __
L
Scale = 1:1,549,380

 

 

82

 

 

 

FIGURE #22: Outliers in Chariotte’s Market Territory

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g 1"
VV
r—I‘
M
Legend
[:3 -.- Zip code that . = Stadium location of
is extremely 9113110119
underpredicted

Scale =1:1,149,380

 

 

83

 

FIGURE #23: Outliers in Clinton’s Market Territory

Legend

= Zip codes that . = Stadium location of
are extremely Clinton
underpredicted

Scale = 1:1,549,380

 

 

 

it

FIGURE #24: Outliers in High Desert’s Market Territory

 

 

 

Legend

 

              

 

 

 

= Stadium location of
High Desert

- =Zipcodethat

Scale = 1:1,549,380

overpredicted

[:3 = Zip codes that

are extremely
underpredicted

is extremely

 

 

85

 

FIGURE #25: Outliers in West Michigan’s Market Territory

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

k

 

 

 

 

 

J6 I

 

 

- = Zip codes that
are extremely
overpredicted

E3 = Zip codes that
are extremely
underpredicted

Legend
0

= Stadium location of
Western Michigan

Scale = 121,549,380

 

 

 

This chapter has described the results of the methodology that was addressed in
Chapter III. Both models were applied to each of the six data sets and were tested with
the R2 and the SRMSE goodness-of-fit test statistics. The models performed adequately,
but it was discovered that zip codes that are located at great distances fi'om the stadium
afi‘ect the results of the models. Therefore, such zip codes are removed from the data sets
and the models are reexamined. Although the models performed rather accurately,
outliers and competing destinations affect the models' parameter estimates. Therefore,
improvements need to be made to the models for two reasons. First, both models vastly
overpredict or underpredict certain zip codes that are located within the cores of the
market territories. Secondly, competing destinations affect the models' estimates of the
trade areas.

Since the models have difficulty in accurately estimating the number of attendees
that originate from certain central city zip codes and suburban zip codes, it appears that
some type of measure needs to be incorporated into the models in order to account for
difi‘erent levels of affluence. In Chapter III, ten variables were selected to examine if they
might be able to add to the models’ explanatory power. These variables were chosen
because they are said to directly influence the market characteristics of baseball fianchises,
or they describe the market areas of other phenomena. The addition of demographic
variables could allow the models to provide more reliable estimates of central city and
suburban zip codes. Furthermore, a variable that accounts for competing destinations
should permit the models to produce better predictions of zip codes that are within the

market territory of another franchise.

87

The succeeding chapter reveals that adding particular demographic variables into
the models would improve the models' predictions for some of the market territories. The
potential benefit, as well as the problems of incorporating a variable that accounts for
competing destinations, is also discussed. This thesis concludes with suggestions for a
researcher who would like to apply one of the models to an area, and who has no prior

knowledge of the origins of a franchises' attendees.

88

 

CHAPTER V
CONCLUSIONS AND FUTURE ANALYSIS

Improvements to the Model

In order to find a better method of determining the market territories of baseball
franchises, this thesis has proposed a methodology to ascertain whether a spatial
interaction model is able to predict accurately the origins of attendees. Only six Single A
minor league baseball fi'anchises responded to more than one-hundred requests for data,
thus any conclusions may not be resolute. Nevertheless, a potential model and a
transformed potential model were tested upon the actual trade areas of these six
fianchises. The transformed potential model gave accurate predictions for four of these
franchises’ market territories, and the potential model produced sound estimations for five
trade areas. Neither model was able to effectively capture the variation within Charlotte’s
trade area.

Through the examination of the residuals, one can distinguish outliers for all six of
the trade areas. This chapter demonstrates if additional variables are added into the
model, the model should be able to provide relatively accurate predictions for all
observations. The chapter also suggests how the model can be applied to a region that is
not studied in this thesis, and it concludes with a discussion of the general relevance of this

work.

89

T_h_e Inclmn of Demogtgaphic Variables

In order to discover other variables that may be incorporated into the models, and
thus allow for better predictions of the market territories, ten demographic variables were
correlated with the residuals. Five of these variables are believed to affect the market
areas of baseball franchises. The other five variables are said to characterize the trade
areas of different activities. Please refer to Table 2 on page 43 to review these ten
variables and the reasons for their inclusion in this analysis.

Demographic variables that have significant Pearson correlation coeflicient values
with the regression residuals must be added to the transformed potential model in a
multiplicative form. Conversely, variables that are significant with the SRMSE residuals
need to be incorporated into the potential model in an additive form. Table 13, on page
91, reveals the hypothesized demographic variables that have correlation coefficients of at
least 0.3 or -0.3, against the regression residuals for each of the six franchises. Table 14,
on page 92, displays the same information with reference to the SRMSE residuals.

It should be noted that a positive Pearson correlation coefficient value signifies
that the model underpredicts zip codes which have a large proportion of its households, or
its residents, that meet the criteria of a certain demographic variable. For example, the
percentage of family households in a region is said to directly impact the number of people
who attend baseball games. Therefore, if the families variable has a large positive
coefficient, then the appropriate model underpredicts zip codes that contain many family
households. A positive Pearson correlation coefficient value also indicates that the model
overpredicts observations which have a small percentage of homes, or inhabitants, that

satisfy the criteria of a selected demographic variable. Therefore, if the family variable has

 

 

a large positive coefficient, then the pertinent model overpredicts observations that consist

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

of few families.
TABLE 13
Correlation Values of Demographic Variables
and Regession Residuals
Variables Beloit Charleston Charlotte Clinton High West
Desert Michigan ,

Income 0.55
Families 0.302 0.308
Males
M.G. -0.598
P.M.P. 0.398 -0.31
H.O. 0.364 0.331 0.363
MPH. 0.385 0.379
M.S. 0.746
Education
Age 0.665 0.348
*notes: M.G. = minority groups

P.M.P. = professional and managerial positions

H.O. = home owners

M.P.H. = multiple person households

M.S. = marital status

91

TABLE 14

Correlation Values of Demographic Variables

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MW
Variables Beloit Charleston Charlotte Clinton High West
Desert Michigan

Income 0.479 -0.476 0.38
Families
Males
MG. -0.409 -0.326
P.M.P. 0.526
H0. 0.345 0.345 0.501
M.P.H.
M.S. 0.366 0.319 0.309
Education 0.446 -0.354
Age 0.508
*notes: MG. = minority groups

P.M.P. = professional and managerial positions

H.O. = home owners

MPH. = multiple person households

M.S. = marital status

Conversely, a negative value denotes that the model overpredicts zip codes which

have a large number of people that fit the criteria of a particular demographic variable.

That is, if the minority groups variable has a large negative coefiicient, then the relevant
model overpredicts zip codes that consist of a large number of minorities. A negative

Pearson correlation coefficient value also signifies that the model underpredicts

92

 

observations which have a small proportion of its residents that meet the criteria of a
certain demographic variable. Therefore, if the minority groups variable has a large
negative coeflicient, then the appropriate model underpredicts observations that contain a
small number of minorities.

After examining Tables 13 and 14, it is obvious that the incorporation of
demographic variables would allow for better estimations of certain trade areas more than
others. There are many demographic variables that are able to add to the models
explanatory power with reference to Charleston's market territory. On the other hand,
with regard to Beloit's trade area, the results demonstrate that none of these variables can
contribute to the models' predictive ability. Assuming that there is a small amount of
collinearity among the variables, the addition of one to three variables would probably be
sumcient to allow the models to produce better estimates of the trade areas for the other
four fianchises.

Table 15 shows the number of meaningful correlation coefficient values that each
demographic variable has with the regression residuals as well as the SRMSE residuals.
This table reveals that the home owners variable can add to the explanation of the
variation of more trade areas than can any of the other variables. This is true because this
variable has significant correlation coefficient values for three sets of regression residuals,
and three sets of SRMSE residuals. The income and the marital status variables have
significant values for one set of regression residuals and three sets of SRMSE residuals.
Therefore, other than the home owners variable, these two variables are able to explain the

variation of more market territories than the other variables that are examined.

93

 

TABLE 15

The Number of Meaningtul Correlation Coefficient Vflpes
for each Demographic Variable

 

 

 

 

 

 

 

 

 

 

 

 

Variables Regression Residuals SRMSE Residuals
Income 1 3
Families 2 0
Males 0 0
Minority Groups 1 2
Professional-Managerial 2 1
Positions

Home Owners 3 3
Multiple Person Households 2 0
Marital Status 1 3
Education 0 2
Age 2 1

 

 

 

Interestingly, of these three variables, only income has been said to influence the market
characteristics of baseball (please refer to Table 2 on page 43).

All of the demographic variables have the expected relationship with the residuals,
with the exception of the two sets of correlation tests that pertain to Charlotte's market
territory. The professional positions variable has a negative relationship with the
regression residuals (please refer to Table 13). The income and education variables have
negative correlation values against the SRMSE residuals (please see Table 14). Therefore,
the models overpredict zip codes that have large values of these three variables, and they
underpredict observations that contain few people that meet the criteria of these variables.
On the other hand, the home owners variable has a positive correlation value with the
SRMSE residuals. Consequently, the potential model underpredicts observations that
contain a large number of home owners, and it overpredicts zip codes that have a small

quantity of residents who own homes.

94

 

These results suggest that residents who own homes in and around Port Charlotte,
FL, do not have relatively large amounts of income, are not employed in professional or
managerial positions, nor did they attend college. These circumstances probably
contradict the suppositions of most people. As a result, the tests of correlation reveal that
Charlotte's market territory is an anomaly with regard to the trade areas of the other five
fi'anchises under investigation.

However, this set of conditions may be describing elderly residents. Most senior
citizens are not employed, thus they receive a limited income. Moreover, they were raised
during a period of time when attending a university was not the norm. Nevertheless, it is
very possible that they have earned enough income in their lifetimes to have bought a
home. The reason that the age variable did not capture this phenomenon is because this
variable represents the percentage of people that are 25-59 years old who reside within a
zip code. Therefore, this variable, as it is presently specified, is not able to isolate the
impact that elderly residents may have upon this market territory.

As previously mentioned, the models do 'not predict Charlotte's market territory
very well. Therefore, it is possible that Dij and Pt do not adequately explain the variation

in trade areas in which senior citizens make up most of the attendees. Including a variable
that represents elderly residents might allow the models to produce better forecasts of
Charlotte's market territory.

If there are certain subareas of a market territory that have a high proportion of
Afiican-Americans, an argument could be made to add a variable that accounts for this
particular minority group. Of the six fianchises, the trade areas of West Michigan,

Charleston, and High Desert have zip codes with relatively high percentages of minorities.

95

 

Two of these market territories, Charleston and West Michigan, show a relationship
between the minority groups variable and the residuals.

The Charleston and High Desert market territories consist of many zip codes that
have a high percentage of minority groups that are located throughout their trade areas.
However, only in the trade area of Charleston could the minority groups variable add to
the models predictive powers (please refer to Tables 13 and 14). This may be due to the
fact that the minorities that reside in Charleston's market territory are Afiican-Americans,
while Hispanics and Asians makeup most of the minorities that inhabit High Desert's trade
area. In Chapter HI it was stated that Afiican—Americans are not inclined to attend
baseball games, and that Hispanics and Asians have become more interested in baseball.
Therefore, if a trade area being examined contains subareas that are heavily populated by
Afiican-Americans, it is advisable to add a variable to account for this minority group.

West Michigan’s market territory provides more evidence to incorporate a variable
that accounts for Afiican—Americans as opposed to all minority groups. In West
Michigan's trade area, the only observations that consist of a large number of minorities
are zip codes located within the cities of Grand Rapids and Muskegon. These
observations contain relatively large numbers of Afiican-Americans. The correlation test
of the SRMSE residuals reveal that there is a negative relationship between the minority
groups variable and the residuals for this market territory (please see Table 14). Because
most of the minorities that reside in this region are Afiican-Americans, the minority
groups variable basically describes the percentage of Afiican-Americans in each of the zip

codes. This may explain why this variable has significant correlation coeficient values.

Although it was found that the home owners, the income, and the marital status
variables would contribute to the explanatory power for more of the market territories, it
appears that in certain circumstances it would be appropriate to add other variables into
the models. For instance, for Charlotte’s trade area, incorporating a variable that accounts
for the percentage of elderly residents within all zip codes would likely allow the models
to provide a better estimation of that market area. Moreover, adding the percentage of
Afiican-Americans that reside in each of the zip codes would probably contribute to the
models’ explanatory power for Charleston’s and West Michigan’s market territories.
However, none of the ten variables would increase the predictive ability of the models for
all six of the trade areas. Therefore, there is not one set of variables that is able to
elucidate upon all the trade areas of baseball fi'anchises. Instead, each market territory has
its own characteristics; and, thus, different sets of variables should be incorporated into
the models to obtain accurate estimates. However, it is not necessary to thoroughly
investigate every market territory of every baseball franchise. Employing the analog
approach allows one to apply the results of this thesis to other regions. This will be

discussed later in this chapter.

A Competing Destinations Variable

In four of the franchises under study, competitors afi’ected the results of the
models. In order to obtain more precise predictions, a variable that accounts for
competing destinations should be included into the model. Obviously, this only needs to
be accomplished in cases where a competitor is infiinging upon the market territory that is

being investigated. Incorporating a variable that represents the amount of distance

97

between an observation and the nearest competing destination should allow the models to
provide accurate estimates of the number of attendees that originate from zip codes that
are a part of another market territory.

This task is more difiicult than it may appear and will only be discussed here. This
is true because a hierarchy exists in the sport of baseball. Professional baseball teams, that
is, those fianchises who pay salaries to players for their abilities, are separated into two
categories: the major leagues and the minor leagues. In 1997, the average attendance for
a major league game was 28,229 (wwwsportslinecom). On the other hand, in 1997 the
average attendance for minor league teams that played a full season ranged from 2,552 to
5,680 (www.minorleaguebaseball.com). This attendance figure is dependent upon the
level of minor league baseball, which will be discussed shortly.

The major reason for the large discrepancy in attendance levels between major
league baseball and minor league baseball is due to the fact that there is a higher caliber of
play in the major leagues. Because many minor league franchises are owned by a major
league franchise, the role of the minor league team is to develop young players for the
major league ballclub. Judging by attendance levels, fans would rather attend games that
offer the highest caliber of play. Therefore, it should seem obvious that major league
franchises have much larger catchment areas than minor league fianchises.

The hierarchical structure is even more complex than simply the major and the
minor leagues. There are three levels that constitute the minor leagues: Triple A, Double
A, and Single A. Near the top of the hierarchy, just below the major leagues, is Triple A
baseball. The primary reason that it derives this status is due to the fact that when players

are needed major league teams normally call up players fiom this level. Therefore, Triple

98

A teams consist of the most talented ballplayers who play in the minor leagues. Double A
baseball and Single A baseball are the next two tiers of the hierarchical structure within
minor league baseball. Their position in the hierarchy is based on the same reason given
for Triple A baseball, modified accordingly (Johnson, 1993). As mentioned earlier, the
franchises that were examined in this study are Single A baseball teams.

Based on attendance figures, the difference between each of the classes within the
hierarchy of the baseball industry is not uniform. The difference between major league
baseball and Triple A baseball is much greater than the disparity between the other levels
of the baseball industry. A major league franchise probably has a much larger
geographical market territory than do minor league baseball teams. Moreover, it is quite
possible that Triple A baseball teams have larger trade areas than the trade areas of
Double A and Single A fi'anchises. This may also be true with reference to Double A and
Single A baseball fi'anchises.

Therefore, franchises of different levels of the hierarchy most likely have different
powers of attraction. This poses challenges for incorporating a competing destinations
variable into the models. For example, suppose a major league franchise and a Triple A
fianchise encroach upon the market territory of a Single A ballteam. For one zip code
within the trade area of the Single A franchise, the major league ballclub is located forty
miles from this zip code, and the Triple A fi'anchise is positioned twenty miles fi'om this
observation. In order to account for competing destinations, it was previously suggested
to add a variable that represents the distance between an observation and the nearest
competing destination. However, in this example, is the Triple A fi'anchise more attractive

to the potential attendees that reside in this zip code than is the major league fianchise

99

 

 

merely because it is closer? Attendance levels suggest that the major league franchise
would entice more people to attend its games. As a result, in order to add a variable into
the models that would completely capture the effect of competing destinations upon a
franchise's market territory, further research must be conducted to determine the
differences in the powers of attraction for franchises within different levels of the baseball

hierarchy.

Application of the Model

As stated earlier, it appears that all fi'anchises do not have identical market
characteristics. Therefore, applying a uniform model would not effectively predict the
market territory for all franchises. The addition of certain demographic variables would
add to the models' predictive abilities for some trade areas, but not for all trade areas.
Furthermore, not all market territories are afi‘ected by competing destinations. However,
by employing the analog method it is possible to apply the results of this thesis to other
trade areas.

The basic assumption of this approach is that if one has reliable information about
the characteristics of a trade area, then it is possible to apply this knowledge to analogous
regions (Thompson, 1986). In order to employ one of the models with no prior
knowledge of a trade area, correct parameter values must be inserted so that the model

provides accurate estimates of the origins of the attendees. To achieve this, a researcher
must consider whether Dij or P; should have more influence with regard to a model's

predictions. This can be accomplished by examining the market characteristics of the six

fianchises that were investigated in this thesis.

100

According to the beta values, Pi is a stronger predictor of attendees than is Dij for

only one franchise, Charleston (please refer to Table 10 on page 66). This is probably due
to the fact that of the six stadiums, only Charleston's stadium is located in the central
business district (CBD). Therefore, many zip codes that are located relatively close to the
ballpark are within the central city. Through the examination of Figure 6 on page 59, one
can realize that zip codes that are located within the central city send relatively few
attendees to the fianchise. These zip codes are surrounded by suburban zip codes that
submit a larger number of patrons. Studying the zip codes that are located in the central
city reveals that the demographic characteristics of the residents are those that would
indicate that the residents are not likely to attend games. That is, these zip codes contain:
few people with high incomes, a small number of married couples, few people that are
between the ages of 25-59, etc. (please refer to Tables 13 and 14 on pages 89-90).
Moreover, zip codes located in Charleston's central city consist of a large number of
minorities, more specifically Afiican-Americans. Therefore, it appears that the
demographic characteristics of those who reside in central city zip codes are negating the
predictive power of Dij.

Consequently, it appears that the location of the stadium seems to be an important

factor in determining whether Di,- or Pt should have a higher parameter value when

applying one of the models to another area. In the case that the stadium is not located in

the CBD of the major city in the region, as are the stadiums of the other five franchises,

there is no evidence to suggest that D,- should not have more influence in forecasting the

market territory than does Pi. Conversely, if the ballpark is located downtown, and the

101

 

residents who live near to the stadium have demographic characteristics similar to those in
the Charleston trade area, it may be wise to input the parameter values so that Pi has more
influence. However, with only six data sets, this conclusion is not resolute.

Although it seems that P, should be stronger than Dij when the above conditions

are met, this does not resolve the problem of determining the values of b and c. A
researcher could either use the appropriate parameter values (for example, if the stadium
of the fi’anchise is located downtown, then the researcher should use the parameter values
that were calculated for the Charleston fianchise) that were computed by regression
analysis, or by the SRMSE statistical measure. Because the R2 test, unlike the SRMSE
examination, weighs certain observations more than others when calculating its test
statistic value and its parameter values, the coefiicient of determination examination is
more likely to be influenced by outliers and competing destinations than the standardized
root mean square error. Therefore, it may be wise for an investigator to utilize the
parameter values that were estimated by the SRMSE test statistic.

Although it may be sensible to use the parameter values that were computed by the
SRMSE statistical measure, it is not necessary. This is the case because other variables
will be added to the model to account for outliers and competing destinations. In order to
incorporate proper variables into the model, one should study the market characteristics of
the six franchises examined in this thesis. For example, if the region that is under
investigation is located in the sun belt, studying the market characteristics of Charlotte
would probably be appropriate. It appears that for tearns situated in the sun belt the
proper variable to incorporate into the model is one that accounts for elderly residents.

Suppose the stadium of another franchise is located in the CBD, and the demographic

102

 

characteristics of central city residents are similar to those of Charleston's city inhabitants.
It would then be prudent for an investigator to add a number of demographic variables
into a model. However, it is necessary to be aware of multicollinearity between the
variables and it is best if the model is parsimonious. Thompson, 1986 suggests using one
variable for every twenty observations.

In some circumstances, it appears that one should not add other demographic
variables into the model. For instance, if the area that is being studied is similar to that of
Beloit's market territory, it appears that the addition of demographic variables will not
contribute to the model's predictive powers. Instead, it is necessary to add a variable that
accounts for competing destinations. Again, firrther research needs to be conducted in
order to determine the difi‘erence in the strength of attractiveness for franchises within
different levels of the baseball hierarchy.

It should be mentioned that the addition of demographic variables is a subjective
process. This is the case because no two trade areas are exactly alike. Therefore, the
analog method provides options to an investigator who is applying one of the models for
another franchise. For example, assume that the region that a researcher is examining is
similar to that of West Michigan. The tests of correlation demonstrated that five variables
would add to the explanatory power of the models with reference to West Michigan's
trade area: families, multiple person households, income, marital status, and minority
groups. As stated earlier in this chapter, a variable that represents the proportion of
Afiican-Americans that reside in zip codes would capture more of the variation within
trade areas than the current variable that delineates all minority groups. Therefore, if the

region that is being examined does not contain a large number of Afiican-Americans, but

103

in every other manner is similar to West Michigan's market territory, then this variable
should not be incorporated into the model. As a result, there is not a uniform model that
efl’ectively portrays the market territories of analogous regions. Instead, the analog
method firrnishes ideas to researchers who must use their own discretion when deciding

what other variables should be added to the model.

Relevance of this Research

This thesis has demonstrated that three parties are interested in the geographical
market territories of baseball franchises. However, the methods utilized by franchises,
leagues, and economic impact analyzers are either ineficient or inadequate. Gaining
knowledge of a market territory through the use of surveys or by selling season tickets are
cumbersome and costly approaches. The application of arbitrary measures is a deficient
method of estimating the market territories of baseball franchises. Through the
examination of Figures 26-31 on pages 105-110, one can realize that a city's Basic Trade
Area does not effectively portray the trade areas of the six fianchises under investigation.
Therefore, estimates of the economic impacts of export sales and import substitution may
be erroneous. Another unsatisfactory measure of depicting franchises' trade areas is the
minor leagues' arbitrary designation for granting ballclubs territorial rights. As previously
mentioned, no minor league baseball franchise is able to locate their team within thirty-five
miles of another team's stadium. Referring to Table 7 on page 64, it is clear that the
ranges of some fianchises' trade areas are less than thirty-five miles, while others are larger
than this distance. Assuming that all minor league teams have different market ranges, it is

possible that leagues are not allowing proprietors to locate a franchise in a region that is

104

 

FIGURE #26: Beloit’s Market Territory
vs
The BTA

Legend
- = 55+ Attendees O = Location of the Stadium

- =21'54 _
- =10-20 of Janesville—Beloit, WI
. =1_9

= The Basic Trade Area

1: = No attendance
Scale = 121,449,380

 

105

 

FIGURE #27: Charleston’s Market Territory
vs

The BTA A

 

 

 

 

 

Legend
- = 301+ Attendees O = Location of the Stadium
- = 151-300 _ = The Basic Trade Area
- = 934 50 of Chadeston. SC
= 1-92
1:1 = No attendance Sale = 1:1,449,380

 

106

 

FIGURE #28: Charlotte’s Market Territory
vs
The BTA

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. j _
ix"l
E M
Legend ,
- = 41+ Attendees O = Location of the Stadium
- =13.40 — =TheBasicTradeArea
of Fort Myers. FL

- = 9-12

. A}. = 1.8

[:3 = No attendance Scale = 121,499,380

 

 

107

 

 

FIGURE #29: Clinton’s Market Territory
vs
The BTA

Legend

- = 301+ Attendees o = Location of the Stadium
- = '°"3°° — = The Basic Trade Area
- = 33-100 of Clinton, lA-Steliing, IL
=1-32

[:1 = No attendance
Scale = 1:1,199,380

 

108

 

 

FIGURE #30: High Desert’s Market Territory

V8

The BTA

 

 

 

 

 
 
  

native-.3.- 03“”-

' ' 'zl'flif; " V-Jn
‘5‘.

1: I ,3:
as, 95kt:

7' . 4f- 0‘-

 
  

  

 

«ur--

 

 

 

  
  

 

 

 

 

- = 95+ Attendees O = Location of the Stadium '
- = 65-94 — = The Basic Trade Area
- = 37-64 of Los Angeles, CA

= 1-35

1:] = No attendance Scale = 1:3.000.000

 

 

 

109

 

 

 

FIGURE #31: West Michigan’s Market Territory
vs
The BTA

Legend
- = 200+ Attendees Q = Location of the Stadium

- = 100-199 — = The Basic Trade Area

of Grand Rapids, MI
- = 54-99

1: =1-53

l: = No attendance

 

110

capable of supporting a baseball team. On the other hand, leagues may be permitting
owners to locate in an area that is not able to support a ballclub. Therefore, a better
method is needed in order to allow for eflicient and effective predictions of the trade areas
of baseball fianchises.

This thesis reveals that using population and distance as the variables within a
potential model -and with the incorporation of pertinent demographic variables; and when
appropriate, the addition of a variable that accounts for competing destinations- the model
should be able to accurately predict the market territories of all baseball franchises.
Therefore, the model provides a better tool of estimating a team's market territory than
does the application of applying arbitrary measures. As a result, the potential model
would improve measurements of the effects of export sales and import substitution upon
local economies, and leagues could place teams in more advantageous locations.
Moreover, the model would provide franchise owners with a more efficient method of

learning about their trade areas, which should result in a more profitable operation.

111

 

BIBLIOGRAPHY

112

BIBLIOGRAPHY

Associated Press. 1998. “Padres get a new home in 2002.” [Online] Available
http://www.CNNSI.com, November 4, 1998.

Attendance. 1997. [Online] Available http://www.sportsline.com, October 20, 1997.

Baade, Robert, A. 1987. “Is There an Economic Rationale for Subsidizing Sports
Stadiums?” Heartland Policy Study. Chicago: The Heartland Institute.

Baade, Robert, A. 1995. “Stadiums, Professional Sports, and City Economies: An
Analysis of the United States Experience.” lhe Stadium and the City, edited by
John Bale and Olof Moen. Keele: Keele University Press. 311-322.

Baade, Robert A. and Allen R. Sanderson. 1997. “Minor League Teams and
Communities.” Sports, Jobs, and T ares. eds. Roger G. N011 and Andrew
Zimbalist. Washington DC: The Brookings Institution. 324-354.

Babbie, Earl. 1990. Survey Research Methods. Belmont, California: Wadsworth
Publishing Company.

Bainr, Dean V. 1994. Yhe Sports Stadium as a Municipal Investment. Westport:
Greenwood Press.

Bamekov, Timothy and Douglas Hart. 1993. “The Changing Nature of US. Urban
Policy Evaluation: The Case of the Urban Development Action Grant.” Urban
Studies 30 (9): 1469-1483.

Bamekov, Timothy and Daniel Rich. 1989. “Privatism and the Limits of Economic
Development Policy.” Urban A flairs Quarterly 25 (December): 212-238.

Batty, M. and S. Mackie. 1972. “The calibration of the gravity, entrepy, and related
models of spatial interaction.” Environment and Planning 4: 205-233.

Baxter, M.J. and GO. Ewing. 1979. “Calibration of Production-Constrained Trip
Distribution Models and the Effect of Intervening Opportunities.” Journal of
Regional Science 19 (3): 319-329.

Baxter, M.J. and GO. Ewing. 1980. “Models of Recreational Trip Distribution.”
Regional Studies 15 (5): 327-344.

Beny, Robert C., William B. Gould IV, and Paul D. Staudohar. 1986. Labor Relations
in Professional Sports. Dover: Auburn House Publishing Company.

113

Bovaird, Tony. 1993. “Analyzing Urban Economic Development.” Urban Studies 30
(4/5): 631-658.

Brooks, Christine M. 1994. Sports Marketing. Englewood Cliffs: Prentice Hall.

California League. [Online] Available http://www.minorleaguebaseball.com/leagues/cal/,
February 8. 1998.

Carolina League. [Online] Available http://www.minorleaguebaseball.com/leagues/car/,
February 8, 1998.

Chalip, Laurence, and Arthur Johnson. 1996. “Sports Policy in the United States.”
National Sports Policies, edited by Laurence Chalip, Arthur Johnson, and Lisa
Stachura. Westport: Greenwood Press. 404-430.

Cheung, Hyrn K. 1972. “A Day-Use Park Visitation Model.” Journal of Leisure
Research. 4 (Spring): 139-156.

Christaller, Walter. 1966. Central Places in Southern Germany. Trans. C.W. Baskin.
Englewood Cliffs, NJ: Prentice-Hall.

Clark, W.A.V. and PL. Hosking. 1986. Statistical Methods for Geographers. New
York: John Wiley and Sons.

“Council cleans way for Stadium.” 1995. fire Detroit Free Press, December 5.

Danielson, Michael N. 1997. Home Team: Professional Sports and the American
Metropolis. Princeton: Princeton University Press.

Department of Commerce. U. S. Census Bureau. Social and Economic Characteristics of
the Population. Washington DC: Department of Commerce, 1990.

Desta, Engdawork. 1988. “Spatial Structure and Spatial Interaction.” Diss. Michigan
State University.

Dicken, Peter and Peter E. Lloyd. 1990. Location in Space. New York: Harper Collins.

Diplock, G. and S. Openshaw. 1996. “Using Simple Genetic Algorithms to Calibrate
Spatial Interaction Models.” Geographical Analysis 28 (3): 262-279.

Donnely, Harrison. 1988. “High Stakes of Sports Econonrics.” Editorial Research
Reports 8 (April): 170-183.

114

Ellis, Jack B. and Carlton S. Van Doren. 1966. “A Comparative Evaluation of Gravity
and System Theory Models for Statewide Recreational Traffic Flows.” Journal of
Regional Science 6 (2): 57-70.

Euchner, Charles C. 1993. Playing the Field. Baltimore: The Johns Hopkins University
Press.

Ewing, Gordon 0. 1980. “Progress and Problems in the Development of Recreational
Trip Distribution Models.” Leisure Sciences 3 (1): 1-24.

Fainstein, SS. and NI. Fainstein. 1983. “Economic Change, National Policy and the
System of Cities.” Restructuring the City: the Political Economy of Urban
Development. eds. S.S. Fainstein, N.I. Fainstein, R.C. Hill, D.R Judd, and MP.
Smith. New York: Longrnan. 1-26.

Florida State League [Online] Available http://www.minorleaguebaseball.com/leagues/fsV,
February 8, 1998.

F otheringharn, A. Stewart. 1981. “Spatial Structure and Distance-Decay Parameters.”
Annals of the Association of American Geographers. 71 (3): 425-436.

F otheringham, AS. 1988. “Market share analysis techniques: a review and illustration of
current U. S. practice.” Store Location and Techniques of Market Analysis. Neil
Wrigley. London: Routledge. 120-159.

Fotheringhanr, AS. and R. Trew. 1993. “Chain image and store-choice modeling: the
effects of income and race.” Environment and Planning A 25 (February): 179-
196.

F otheringham, A. Stewart. Rev. of Gravity Models of Spatial Interaction Behavior. By
Ashish Sen and Tony E. Smith. 1995. New York: Springer.

Greenwood, Michael J. and Douglas Sweetland. 1972. “The Determinants of Migration
Between Standard Metropolitan Statistical Areas.” Demography 9 (4): 665-681.

Hansen, Mark. 1995. “Positive Feedback Model of Multiple-Airport Systems.” Joumal
of Transportation Engineering 21 (6): 453-460.

Hartman, L.M. and David Seckler. 1967. “Toward the Application of Dynamic Growth
Theory to Regions.” Journal of Regional Science, Vol. 7 as reprinted in Regional
Economics: Theory and Practice eds. D.L. McKee, R.D. Dean, and W.H. Leahy.
New York: The Free Press, 81-89.

Harvey, Greig. 1987. “Airport Choice in a Multiple Airport Region.” Transportation
Research Part A: General 21 (6): 439-449.

115

Haynes, Kingsley E. and A. Stewart Fotheringham. 1984. Gravity and Spatial
Interaction Models. Beverly Hills: Sage Publications. Vol. 2 of Scientific
Geography Series.

Hill, Edward W., Harold L. Wolrnan, and Coit Cook Ford 111. 1995. “Can Suburbs
Survive Without Their Central Cities?” Urban Affairs Review 31 (2): 147-174.

Hufi‘, David L. 1961. “A Note on the Limitations of Intraurban Gravity Models.” Land
Economics 38 (February): 64-66.

Huff, David L. 1962. “A Probabilistic Analysis of Shopping Center Trade Areas.” Land
Economics 39: 81-90.

Huff, David L. 1964. “Defining and Estimating a Trading Area.” Journal of Marketing
28 (July): 34-38.

Isard, Walter. 1960. Methods of Regional Analysis: An Introductions to Regional
Science. New York: John Wiley and Sons, Inc.

Johnson, Arthur T. 1985. “The Sports Franchise Relocation Issue and Public Policy
Responses.” Government and Sport, edited by Arthur T. Johnson and J arnes H.
Frey. Totowa: Rowrnan And Allanheld. 219-247.

Johnson, Arthur T. 1986. “Economic and Policy Implications of Hosting Sports
Franchises: Lessons from Baltimore.” Urban Aflairs Quarterly 21 (March): 411-
434.

Johnson, Arthur T. 1993. “Introduction: The Politics of Development and the Stadium
Issue.” Minor League Baseball and Local Economic Development, edited by
Arthur T. Johnson. Urbana: University of Illinois Press. 1-8.

Johnson, Arthur T. 1993. “PART I: The Business of Minor League Baseball, the Major
Leagues, and Community Ownership of Stadiums.” Minor League Baseball and
Local Economic Development, edited by Arthur T. Johnson. Urbana: University
of Illinois Press. 9-35.

Johnson, Arthur T. 1993. “PART IV: The Use of Stadiums for Downtown
Redevelopment.” Minor League Baseball and Local Economic Development,
edited by Arthur T. Johnson. Urbana: University of Illinois Press. 173-178.

Johnson, Arthur T. 1993. “Harrisburg, Pennsylvania.” Minor League Baseball and Local

Economic Development, edited by Arthur T. Johnson. Urbana: University of
Illinois Press. 179-187.

116

Johnson, Arthur and James H. Frey. 1985. Government and Sport. Totowa, New Jersey:
Rowman and Allanheld.

Johnson, Arthur T. and C. James Owen. 1993. “South Bend, Indiana.” Minor League
Baseball and Local Economic Development, edited by Arthur T. Johnson.
Urbana: University of Illinois Press. 188-199.

Johnston, RJ. 1978. Multivariate Statistical Analysis in Geography. New York: John
Wiley and Sons.

Kanaroglou, Pavlos S. and Mark R. Ferguson. 1996. “Discrete Spatial Choice Models
for Aggregate Destinations.” Journal of Regional Science 36 (2): 271-290.

Kaplan, Marshall. 1990. “Infrastructure Policy: Respective Studies, Uneven Responses,
Next Steps.” Urban Aflairs Quarterly 25 (March): 371-388.

Kariel, Herbert G. 1968. “Student Enrollment and Spatial Interaction.” Annals of
Regional Science 2: 114-125.

Knudsen, Daniel C. and A. Stewart Fotheringharn. 1986. “Matrix Comparison,
Goodness-of—Fit, and Spatial Interaction Modeling.” International Regional
Science Review 10 (2): 127-147.

Leagues. [Online] Available http://wwwminorleaguebaseball.com/standings.html,
February 5, 1998.

Leppel, Karen, 1993. “Logit Estimation of a Gravity Model of the College Enrollment
Decision.” Research in Higher Education. 34(3): 387-398.

Markham, Jesse W. 1981. Baseball Economics and Public Policy. Lexington,
Massachusetts: Lexington Books.

McAllister, Donald M. and Frank R. Klett. 1976. “A Modified Gravity Model of
Regional Recreation Activity with an Application to Ski Trips.” Journal of Leisure
Science 8(1): 21-34.

McConnell, Harold. 1965. “Spatial Variability of College Enrollment as a Function of
Migration Potential.” The Professional Geographer 17 (6): 29-37.

Midwest League. [Online] Available http://www.minorleaguebaseball.com/leagues/mid/,
February 8, 1998.

Miller, James Edward. 1990. The Baseball Business. Chapel Hill: The University of
North Carolina Press.

117

Niedercorn, J.H. and RV. Bechdolt. 1969. “An Economic Derivation of the ‘Gravity
Law’ of Spatial Interaction.” Journal of Regional Science 9 (2): 273-282.

Noll, Roger G. and Andrew Zimbalist. 1997. “The Economic Impact of Sports Teams
and Facilities.” Sports, Jobs, and Taxes. eds. Roger G. Noll and Andrew
Zimbalist. Washington DC: The Brookings Institution. 55-91.

North, Douglass C. 1955. “Location Theory and Regional Economic Growth.” Journal
of Political Economy, Vol. 63 as reprinted in Regional Development and
Planning: A Reader. eds. John Friedmann and William Alonso. Cambridge, MA:
The MIT Press. 240-255.

North, Douglass C. 1956. “A Reply.” Journal of Political Economy, Vol. 64 as reprinted
in Regional Development and Planning: A Reader. eds. John Friedmann and
William Alonso. Cambridge, MA: The MIT Press. 261-264.

Ottensmann, J .R. 1997. “Partially Constrained Gravity Models for Predicting Spatial
Interactions with Elastic Demand.” Environment and Planning A 29: 975-988.

Pacione, Michael. 1989. “Access to Urban Services-the Case of Secondary Schools in
Glasgow.” Scottish Geographical Magazine 105 (1): 12-18.

Pagano, Michael A. 1988. “Fiscal Disruptions and City Responses.” Urban Affairs
Quarterly 24 (September): 188-137.

Pooler, J. 1992. “Spatial uncertainty and spatial dominance in interaction modeling: a
theoretical perspective on spatial competition.” Environment and Planning A 24
(July): 995-1008.

Pooler, Jim. 1994. “An Extended Family of Spatial Interaction Models.” Progress in
Humcm Geography. 18 (1): 17-39.

Quirk, James and Rodney D. Fort. 1992. Pay Dirt. Princeton: Princeton University
Press.

Rand McNally. Commercial Atlas and Marketing Guide. 1998. 129'h ed., Rand McNally
and Company. United States of America.

Riposa, Gerry. 1996. “From Enterprise Zones to Empowerment Zones.” American
Behavioral Scientist 39 (5): 536-551.

Rosentraub, Mark S. 1997. “Stadiums and Urban Space.” Sports, Jobs, and Taxes,

edited by Roger G. N011 and Andrew Zimbalist. Washington DC: The
Brookings Institution. 178-207.

118

Rosentraub, Mark and David Swindell. 1993. “Fort Wayne, Indiana.” Minor League
Baseball and Local Economic Development, edited by Arthur T. Johnson. Urban:
University of Illinois Press. 35-54.

Rubin, Irene S. and Herbert J. Rubin. 1987. “Economic Development Incentives: The
Poor (Cities) Pay More.” Urban A flairs Quarterly 23 (September): 37-62.

Sands, Jack and Peter Gammons. 1993. Coming Apart at the Seams. New York:
Macmillan Publishing Company.

Schneider, Mark and Fabio Fernandez. 1989. “The Emerging Suburban Service
Economy.” Urban Affairs Quarterly 24 (June): 537-555.

Scully, Gerald W. 1989. The Business of Major League Baseball. Chicago: The
University of Chicago Press.

Scully, Gerald W. 1995. The Market Structure of Sports. Chicago: The University of
Chicago Press.

Sen, Ashish and Zbigniew Matuszewski. 1991. “Properties of Maximum Likelihood
Estimates of Gravity Model Parameters.” Journal of Regional Science 31 (4):
469-486.

Senior, Martyn L. 1979. “From gravity modeling to entropy maximizing: a pedagogic
guide.” Progress in Human Geography 3 (June): 175-210.

Sheehan, Richard G. 1996. Keeping Score. South Bend: Diamond Communications,
Inc..

Smith, Stephen L]. 1980. “Intervening Opportunities and Travel to Urban Recreation
Centers.” Journal of Leisure Research 12 (4): 296-308.

South Atlantic League. [Online] Available
http://www.minorleaguebaseball.com/leagues/sall, February 8, 1998.

Steinhoff, Stephen, and The Nathalie P. Voorhees Center for Neighborhood and
Community Improvement. 1988. A New Sports Stadium: Can it Bring Economic
Benefits to Residents of the Near West Side? Chicago: The University of Illinois
at Chicago.

Stix, Gary. 1993. “Blackballing the Inner City.” Scientific American. 269 (September):
152.

Stokes, Robert. 1995. “Baseball and Economic Development.” APA Journal. (Autumn):
521-522.

119

Summary Tape File 38. 1990. Computer Software. Department of Commerce. US.
Census Bureau.

Talen, E. and L. Anselin. 1998. “Assessing Spatial Equity: an Evaluation of Measures of
Accessibility to Public Playgrounds.” Environment and Planning A 30: 595-613.

The Baseball Encyclopedia. 1990. New York: Macmillan Publishing Company.
Thompson, John. 1986. Site Selection. New York: Lobhar-Friedman Books.

Thrill, JG 1995. “Modeling store choices with cross-sectional and pooled cross-
sectional data: a comparison.” Environment and Planning A. 27 (August):
1303-1315.

Tiebout, Charles M. 1956a. “Exports and Regional Economic Growth.” Journal of
Political Economy, Vol. 64 as reprinted in Regional Development and Planning:
A Reader. eds. John Friedmann and William Alonso. Cambridge, MA: The MIT
Press. 256-260.

Tiebout, Charles M. 1956b. “Rejoinder.” Journal of Political Economy, Vol. 64 as
reprinted in Regional Development and Planning: A Reader. eds. John Friedman
and William Alonso. Cambridge, MA: The MIT Press. 265.

Tirnmerrnans, Harry, Aloys Borgers, and Peter van der Waerden. 1992. “Choice
Experiments versus Revealed Choice Models: A Before-After Study of Consumer
Spatial Shopping Behavior.” Professional Geographer 44 (4): 406-416.

“Twins not heading south just yet.” 1997 . USA Today Baseball Weekly, November 26-
December 2.

White, Paul. 1998. “New parks no guarantee to success.” [Online] Available
http://www.USAToday.com, December 4, 1998.

Whitt, J. Allen. 1987. “Mozart in the Metropolis: The Arts Coalition and the Urban
Growth Machine.” Urban A flairs Quarterly 23 (September): 15-36.

Wilson, AG. 1971. “A Family of Spatial Interaction Models, and Associated
Developments.” Environment and Planning 3: 1-32.

Wilson, A. G. and MJ . Kirkby. 1980. Mathematics for Geographers and Planners.
Oxford: Clarendon Press.

Wolrnan, Harold L., Coit Cook Ford III, and Edward Hill. 1994. “Evaluating the Success
of Urban Success Stories.” Urban Studies 31 (6): 83 5-850.

120

Zimbalist, Andrew. 1992. Baseball andBilIions. New York: BasicBooks.

121

     

HICHIG N S R E U IV 18

lllllllllllllll“