You are close to your rival and everybody hates a winner: a study of rivalry in college football.
Quintanar, Sarah Marx ; Deck, Cary ; Reyes, Javier A. 等
We use a recent survey of college (American) football fans to study
rivalry, where we find the most intense rivalries occur between in-state
teams. Relatedly, within a conference fans are more likely to target
rivalrous feelings toward the winningest teams and, in Bowl Championship
Series conferences, teams who have been conference members for a longer
proportion of time. While the stakes are different from other settings,
such as warring nations, college football teams compete for resources
and often have loyal followings with strong emotional ties. Thus,
examining rivalrous feeling in this setting provides insights into
rivalry more generally besides being of interest in its own right as
college football is a multi-billion dollar industry. (JEL L22, L83)
I. INTRODUCTION
For millions of Americans, Saturdays in the fall are synonymous
with college (American) football. College football has a pageantry all
its own as people gather in groups, sometimes in excess of 100,000, to
cheer for their team and socialize even though many fans have no real
connection to the university. On the field the teams compete to win
games and over the course of a season teams compete to win their
conference title. However, many fans do not view all opponents in the
conference in the same way--games against some opponents are considered
more important irrespective from their impact on conference standings.
For example, the University of Arizona and Arizona State University have
played for the Territorial Cup for over 100 years. (1) Similarly, the
University of Wisconsin and the University of Minnesota compete for Paul
Bunyan's Axe while the University of Alabama and the University of
Tennessee play on "the third Saturday in October." (2) Sanford
and Scott (2014) find that fans are willing to pay higher ticket prices
for rivalry games and these games generate significant television
revenue.
Despite the amateur status of the players, college football is an
$8 billion industry. (3) Several high profile teams are valued at over
$100 million dollars each (Brewer et al. 2011). Team revenue comes from
a variety of sources (television rights, merchandising, fan support,
etc.) and on the field success and profit are connected through these
channels. In addition, teams find themselves repeatedly battling over
the resources needed to compete on the field, namely players and
coaches. In this sense, football rivalries are similar to rivalries
between siblings, firms, or nations. Sibling rivalries form when
children compete for scarce resources (financial, attention, etc.) from
their parents (Garg and Morduch 1998; Morduch 2000). The "cola
wars" between Coke and Pepsi and the "diaper wars"
between Kimberly-Clark and Procter & Gamble arise because these
comparable companies offer slightly differentiated products in the same
markets. Rivalries between warring nations also often involve prolonged
competition over scarce resources (Goertz and Diehl 1993; Klein, Goertz,
and Diehl 2006).
Rivalry is a subjective phenomenon (Kilduff, Elfenbein, and Staw
2010), but it has an identifiable set of antecedents. Geographical
proximity is typically an important determinant of conflict, even in the
context of firm-level rivalries as argued for instance in Yu and Canella
(2007). Identity also plays an important role in the creation of a
rivalry (Menon, Thompson, and Choi 2006). Finally, history and the
outcomes of previous interactions are another key determinant of
rivalries (Kahneman and Miller 1986; Miller and Chen 1996). All three of
these factors are at play in college football. Conferences are typically
comprised of comparable schools in a particular region. Fans identify
with their team by wearing certain clothes and in more extreme cases
with body paint and other adornments. Despite periodic conference
realignment, many teams play each other year after year. Thus, we
believe that in addition to being interesting in its own right,
examining what drives rivalrous feelings in college football can provide
insight into rivalry more generally.
To explore the drivers of rivalrous feelings, we use a unique
dataset drawn from an online survey conducted by Sports Illustrated that
asked Ians about their team and their rival. We believe that our paper
is the first systematic attempt to explain rivalrous feelings in college
football, although sportswriters have attempted to group or classify
rivalries based on various characteristics (see for example Jones 2005).
(4) We consider two different aspects of rivalrous feelings. First, we
examine which teams are the target of rivalrous feelings, a
unidirectional notion. The data suggest the more historic success a
program has had, the more others will harbor rivalrous feelings toward
that program. Second we look at mutual rivalries between two teams, a
bidirectional relationship. Here the data indicate that rivalries tend
to be more intense when the schools are in the same state and have
comparable programs in terms of historic performance.
II. MEASURING RIVALRY IN COLLEGE FOOTBALL
In the fall of 2009, Sports Illustrated (SI) conducted a
non-scientific survey called the "College Football Conference
Poll' which asked visitors to its website about their favorite
Football Bowl Subdivision (FBS) college team and its conference. (5,6)
Like all online surveys, these data have some deficiencies, but the SI
data are drawn from a broad audience of people whose feelings were
sufficient to lead them to participate in the survey. Individuals of any
age were allowed to participate and self-report their "favorite
team." The SI survey listed 12 collegiate conferences, including
independents, and their 120 participating member schools. The poll
questions pertain to fan devotion (proportion of respondents who were
ticket holders, number of games attended each season, etc.) and
ascertain opinions regarding the extent and relevance of activities like
tailgating, football traditions, and television viewership.
[FIGURE 1 OMITTED]
The question that provides our main variable of interest was
"Which school is your biggest conference rival?" Participants
were able to select their answer from a list of the other teams who
compete in the same conference. (7) The survey findings include up to
five teams most often listed as a team's rival, as well as the
proportion of total respondents who chose each team as their biggest
rival. Note that the respondents are only allowed to list one other
conference member as their team's biggest rival. Because the survey
only considers within-conference rivalries, our analysis is also
restricted in this way.
We define the percentage of fans of team A who answered team B when
asked "Which school is your biggest conference rival?" as the
degree of rivalrous feelings by A toward B and denote it by rAB. Figure
1 shows the rivalrous feelings in two conferences, the Pac-10 and the
SEC, while the figures for other conferences can be found in the
appendix. In the figure, rAB determines the width of the arrow pointing
from A to B. One can see that every other team in the Pac-10 reported
having some rivalrous feelings toward the University of Southern
California, but only the University of Arizona had rivalrous feelings
toward Arizona State University, at a much greater strength (visible by
the greater width in the arrow directed toward Arizona State).
With [r.sub.AB] we can ask what leads to teams being the target of
rivalrous feelings. For this uni-directional relationship we use a
Concentration Index (CI) to capture the concentration of rivalrous
feeling among other conference members directed toward a team.
Specifically, we use [CI.sub.B] = [[[[summation].sub.A][r.sub.AB]/(n -
1)].sup.2] to measure the concentration of rivalrous feelings directed
toward B by the other n - 1 members of the conference. This measure is
analogous to a firm's component in a Herfindahl-Hirschman Index
(HHI) for market concentration and thus it allows for a comparison
across conferences with different numbers of member schools. As in a
monopoly where the HHI equals 10,000, a team that is the sole focus of
all rivalrous feelings from the other members of its conference would
have a Cl of 10,000.
While the CI measure captures who is the target of rivalrous
feelings, rivalries per se are typically thought of as being mutual or
reciprocal. Therefore, we now introduce two measures of bi-directional
rivalrous feelings. The first captures the intensity of the rivalry
between A and B: [I.sub.AB] = [I.sub.BA] = [([r.sup.2.sub.AB] +
[r.sup.2.sub.BA]).sup.1/2]. This measure is preferable to a simple
average because it accounts for the distribution of rivalrous feelings
between the two schools. For very high and very low levels of intensity
the two teams must have similar feelings toward each other. However, in
the middle there may be rivalries where it is not possible to
distinguish between situations where both parties have moderate
rivalrous feelings and situations where [r.sub.AB] is low while
[r.sub.BA] is high. For instance, imagine a rivalry where both teams
have 50% of fans reporting the other team as a rival, and one rivalry
where team A lists B at 70.71 % and team B lists team A at 0%. In this
case, both rivalry's intensity measure is 70.71, though the
rivalries themselves are quite different as one could be thought of as
mutual while the other is perhaps more of a "big fish versus little
fish" since team A is not concerned with team B. Therefore, we also
consider the lopsidedness of a rivalry with [L.sub.AB] = [L.sub.BA] =
[absolute value of [r.sub.AB] - [r.sub.BA]]. Looking again at Figure 1,
in contrast to the Pac-10 where teams appear to have strong rivalrous
feelings toward a single other team and relationships do not appear to
be lopsided, in the SEC rivalrous feelings are more diffuse and more
relationships are lopsided. For example, the University of Kentucky
considers the University of Tennessee a rival, but the feeling is not
mutual. Louisiana State University (LSU) considers the University of
Alabama a rival, but Alabama considers Auburn University and the
University of Tennessee to be stronger rivals than LSU. The plots in
Figure 1 are technically weighted networks, where the nodes are the
schools and the strength of the links between the nodes are given by the
[r.sub.AB] s. In the Appendix we provide a formal network analysis of
each conference, which is not included herein because it does not
provide substantive insight into rivalry formation beyond the main
analysis presented in the following section.
III. ANALYSIS AND RESULTS
We consider the two types of rivalrous relations, uni-directional
and bi-directional, in separate subsections. However, we first ask
whether or not the respondents simply responded to the question of
interest randomly. First, we note that the strongest identified
rivalries correspond to common fan and sportscaster perceptions of the
strongest rivalries implying that survey responses were not random.
Second, we conducted a simulation exercise to look at the likelihood
that team A's rivalrous feeling toward its greatest rival, i.e.,
[r.sub.AB*] where B* = [argmax.sub.B][r.sub.AB], is as large as what we
observe. For every single team, our simulation gives a p value <
.0001 for testing the responses is random. (8)
A. The Uni-directional Target of Rivalrous Feelings
Table 1 lists the team with the largest CIB for each conference.
These teams are the ones that are the recipient of the most rivalrous
feelings in the conference. The column labeled Overall Ranking gives the
team's Cl ranking taken over all 117 teams in the 11 conferences.
Thus Boise State is the team with the greatest concentration of (with-in
conference) rivalrous feelings directed toward it in college football.
The Cl for every team in the 11 conferences is available in an online
appendix (Table SI).
To explore what drives rivalrous feeling, we provide the ordinary
least squares (OLS) analysis in Table 2. In addition to conducting the
analysis on the whole sample, we also estimated separately for the BCS
or "power" conferences, which had automatic berths into the
most lucrative post season bowl games known as the Bowl Championship
Series. (9) The results show that the most dominant determinant is a
team's historical winning percentage. These results based on past
performance are robust as using a 20-year window for long-term success
or a 5-year window for recent success do not substantially alter the
findings. Finally, as the length of time a team has been in the
conference increases so does the amount of rivalrous feelings directed
toward it. These findings are consistent with previous studies of
rivalry in other contexts (Kahneman and Miller 1986; Miller and Chen
1996).
An additional implication of the results from Table 2 is that
rivalries can be dynamic. As winning histories change over time, our
data suggest that this may alter the beliefs of fans about their main
rivals. Hence, while rivalries are certainly durable in the short run,
one cannot rule out the possibility that they may change in the long run
(as winning histories change).
B. Bi-directional Rivalries
Table 3 provides the most intense rivalry, as determined by the two
teams with the highest IAB, in the conference. The most intense rivalry
is between Central Michigan University and Western Michigan University.
Out of the power conferences, the most intense rivalry is between the
University of Arizona and Arizona State University. The intensity of all
nonzero rivalries between any two teams in a conference is given in an
online appendix (Table S2).
To determine the factors that lead to a more intense rivalry, we
conducted the analysis reported in Table 4. The data include all nonzero
rival pairs which existed in the data. (10) This allows us to
investigate what makes a rivalry stronger, conditional on the fact that
some feeling of rivalry exists. As discussed in the introduction, one
would expect geographic proximity and history of interaction to affect
the intensity of a rivalry. Thus, we collected information about the
driving Distance in miles between the two schools using Google Maps and
use this as a control variable in the analysis. The regression in Table
4 also includes a dummy variable for the two schools being in the Same
State and another dummy variable for the two schools being in Bordering
States. History between the schools is captured by the number of Games
Played against each other and by Relative Strength, where Relative
Strength = [[[(Win Percentage of A over B - 50).sup.2] + [(Win
Percentage of B over A- 50).sup.2]].sup.1/2]. (11)
Jones (2005) argues that college rivalries are more intensive if
the funding status between schools is different: where one school is
publicly funded and the other is privately funded so the dummy variable
Status takes a value 1 for this case and a value of 0 if the status of
the schools are the same (both public or both private). On the one hand,
this has an intuitive appeal as funding type may serve to form an
identity. However, if rivalry is based on resource competition then one
would expect schools with similar funding structures to have a greater
rivalry because they are competing for the same resources off the field.
The survey was conducted mid-season in 2009, but robustness tests
including a dummy if the teams played in 2009 prior to the survey do not
change the results. The relative strength measure includes the history
of play for 30 years from the 1979 to 2008 seasons.
The analysis presented in Table 4 reveals that being located in the
same state has a dramatic effect on rivalry intensity. While the number
of games played also has a statistically significant effect, it is not
large in magnitude. The effect of the two schools being in the same
state is comparable to the two schools having played each other for over
100 additional years. Relative strength does not appear to matter
overall, but is an important factor in the BCS conferences where the
stakes are arguably higher. Status is never positive and significant
suggesting status does provide identity. In fact, when one controls for
the schools being in the same state, status is negative and significant
meaning that schools with the same funding structure have greater
rivalries as they are competing for the same dollars.
One can also use our data to predict if a rivalry exists between
schools. To do this, we rely upon a probit model and use data on every
pair of schools in the same conference. Using the same control variables
as the regression in Table 4 we find that rivalries are most likely to
occur between schools located in the same state who have played often
with the other factors not having a significant effect. The results are
suppressed for brevity.
The above analysis looks at the intensity and existence of a
rivalry, but it does not capture the similarity in rivalrous feelings
between two schools. To investigate similarity in feelings, Table 5
considers the factors influencing lopsidedness, [L.sub.AB]. The results
show that lopsidedness is impacted by similar characteristics as rivalry
strength, as was seen in Table 4. One surprising finding is that
lopsidedness is not impacted by relative strength for BCS schools. It is
also interesting that being in the same state increases the lopsidedness
of a rivalry. This suggests that frequently one of the in-state schools
is really focused on another in-state school but the other school's
attention is split between the in-state school and an out-of state
school. Perhaps this occurs due to the fact that the state identity
causes a competition for scarce resources which is more relevant for the
weaker team. For example, the weaker team may have negligible odds to
reach the conference championship, but some faith for beating their
in-state rival if they put forth an additional effort (along with a bit
of luck). Meanwhile, the stronger team might feasibly be able to compete
outside of the state for the conference championship itself. The most
extreme example is in the appendix where Oklahoma State is almost
exclusively focused on Oklahoma, but Oklahoma is far more rivalrous
toward Texas than Oklahoma State. In fact, the Oklahoma-Oklahoma State
rivalry is the most lopsided in our sample.
IV. CONCLUSIONS
College football evokes very strong feelings among fans. One topic
that is discussed frequently is rivalry, and heated debates often erupt
regarding which ones are the most intense. This paper provides a
systematic answer to questions that often form the heart of such
discussions.
Using recent survey data we find the most intense bi-directional
rivalry within a conference is between Central Michigan and Western
Michigan. Of course, this does not mean that the feelings are stronger
here than in the second-place rivalry between Arizona and Arizona State,
only that the fan base's feelings between those two are more
aligned. In general, bi-directional rivalries are strongest between
schools from the same state but if one school tends to win more often,
then the winner's fan base loses interest.
The team considered a rival by the most of its conference foes is
Boise State. This is likely due to the sustained success that Boise
State has experienced. More generally, the more games a teams has won,
the more the fan base of other schools will consider it a rival. Fans
also tend to direct rivalrous feelings to those teams their favorite
school has played the longest. There is the possibility of endogeneity
in that schools may opt to be in conferences in order to play their
rival; however, that does not appear to be the case. Since the 2009
survey, 27 teams have switched conferences. In other analyses, we
investigated whether or not the concentration of rivalrous feelings or
the intensity of a team's rivalries impacted the decision to switch
conferences, but found no evidence to suggest these relationships matter
in an economically significant way. Instead, it seems that the movers
have gone to more highly ranked conferences with higher earning
potential independent of what it means for existing rivalries. (12)
Overall, our results correspond with more general findings in the
rivalry literature. Schools battle over resources, as do companies
competing for customers in similar markets and warring nations (Goertz
and Diehl 1993; Klein, Goertz, and Diehl 2006). Geographical proximity
was found to be the most important indicator as well as the outcomes of
previous interactions (similar to Miller and Chen 1996; Yu and Canella
2007, for example). Though rivalries are not impacted by being a public
versus private school, identity itself matters outright for BCS schools
in that schools which share the same funding source have stronger
rivalries. Similarly, identity in college football is important in
revenue considerations for both ticket prices and memorabilia sales for
rivalry games (Sanford and Scott 2014).
ABBREVIATIONS
BCS: Bowl Championship Series
CI: Concentration Index
FBS: Football Bowl Subdivision
HHI: Herfindahl-Hirschman Index
OLS: Ordinary Least Squares
SI: Sports Illustrated
doi: 10.1111/ecin.12215
APPENDIX
NETWORK ANALYSIS OF EACH CONFERENCE
Mathematically, each conference network can be represented in a
square matrix, R, where the row A, column B entry is given by
[r.sub.AB]. This matrix, which is plotted in Figure 1 for the Pac-10 and
SEC, is often referred to as the weighted proximity matrix. (13) Figure
A1 shows the network graphs for the other conferences. In this appendix
we are interested in studying the structure and pattern of the rivalries
across conferences. We use a clustering coefficient measure in order to
assess which conferences present a more tightly knitted network through
the rivalries reported in the data. In particular we chose to compute
the clustering coefficient for each conference. In the context of the
rivalry networks, this measure can be interpreted as the overall
probability for the conference to have adjacent teams reporting each
other as rivals and also report a third (same) team as rival (i.e., a
complete triangle pattern). The higher the clustering coefficient, the
higher is the existence of these mutual and adjacent rivalries, thus
revealing the existence of a tightly connected conference. Given that
the link between teams in conference, [r.sub.AB], denotes the degree of
rivalrous feelings by A toward B, we can compute the binary and the
weighted clustering coefficient following Fagiolo (2007). Doing so
further extends the analysis to take the degree of rivalrous feelings
that form the complete triangles (weighted clustering) and not just the
mere reporting of a team as a rival (binary approach).
The idea is to see which conferences present a more tightly knitted
and balanced structure, taking into consideration the degree (level) of
the rivalries reported. A more clustered conference would correspond to
one where more rivalry triangles are reported thus suggesting that there
is a lower number of dominant pair-rivalries, i.e., a more balanced
rivalry network. Given that the number of teams in each network can
vary, we need to provide a benchmark for each conference to be able to
make comparisons across conferences. To do so, we build a fully
connected and balanced network for each conference where the weighted
proximity matrix presents 0's in the diagonal of the matrix and all
other cells are equal to 1/(1 - n). These assumptions result in a
weighted clustering coefficient for these benchmark networks equal to
1/(1 - n). Using this clustering as a reference in each conference, we
can use the ratio of the computed clustering coefficient using the
actual data to this benchmark to assess how close to a fully connected
and balance network each conference is, given the number of teams that
form the conference. The closer the ratio is to 1 the more the
conference in question resembles a balanced rivalry network.
[FIGURE A1 OMITTED]
Table A1 shows the weighted and binary clustering coefficients by
conference. The results indicate that the linkages forming rivalry
triads are more prevalent in the Big East, Big 12, and Pac-10
conferences, but these are not very strong (rivalrous) triads. In fact
the more rivlarous triads (which approximate more the tightly connected
and balanced rival networks) are present in the USA and the WAC
conferences. These conferences should be perceived as the ones where the
rivalrous feelings reported depict more prevalent triads which form
clustered sub-sets of teams (cliques) while for the other conferences
the rivalry pattern is that of rivalrous pairs.
Intuitively, the presence of clusters points toward the existence
of strong rivalries among a group of teams, a dominant group defined by
mutual rivalries among the cluster. On the other hand, the conferences
with no prevalent triads suggest a rivalry pattern with no clear
dominant sets of teams, a more balanced distribution of rivalrous
feelings among all teams in the conference.
TABLE A1
Clustering Coefficients by Conference
Conference Weighted Network Binary Network
ACC .42867 .48512
Big Ten .34297 .54641
Big 12 .48672 .63586
Big East .49181 .68413
MAC .5856 .25762
MW .56252 .51867
Pac-10 .30915 .6252
SEC .32727 .56507
Sun Belt .53619 .37647
USA 1.02412 .58553
WAC .93787 .58022
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SUPPORTING INFORMATION
Additional Supporting Information may be found in the online
version of this article:
Table S1. Uni-directional Rivalry Measures (Concentration Index)
for All Teams
Table S2. All Rivalries: Intensity and Lopsidedness
Table S3. Conference Changes from 2009 to 2012
Table S4. Team Abbreviations Explained
(1.) Considered the best rivalry trophy in college football by
http://sports.yahoo.com/news/top-25-greatest-collegefootball-rivalry-trophies-time-163400769-ncaaf.html
(2.) Scheduling issues sometimes lead this game to be played on a
different weekend, but even so it is typically referred to by this
moniker.
(3.) According to a January 29, 2011 PBS interview with Andrew
Zimbalist available at http://www.pbs.org/wgbh/
pages/frontline/money-and-march-madness/interviews/
andrew-zimbalist.html.
(4.) In fact, the economics literature on rivalries in sporting
competitions is rather limited. Osborne (2008), where rivalries are
modeled as a habitual good, and Amegashie and Kutsoati (2005), who argue
that rivalries lead to greater effort in boxing rematches, are the only
theory papers to our knowledge. Empirically there are a few studies that
have used rivalries to explain game day fan attendance (Leonard 2005;
Owen and Weatherston 2004; Price and Sen 2003). Sanford and Scott (2014)
investigate factors in secondary market ticket prices for the SEC and
find that rival games increase those prices. In an interesting paper
Beck (2003) examines whether soccer is relevant for understanding
Britain's relationship with Germany.
(5.) The survey itself was available on http://sports
illustrated.cnn.com/2009/football/ncaa/10/26/collegefootball-survey/index.html until early 2014 when SI seemingly removed it from their website.
Anyone could answer the questions by first picking the conference of
"their favorite team" and then selecting their "favorite
team." The set of possible answers to the remaining questions were
limited based upon the conference chosen and indicated favorite team.
The survey was first available on October 26, 2009. Our belief is that
the survey was available for 1 week because participants were told the
results would be presented in 1 week.
(6.) College football teams are divided into the FBS and Football
Championship Subdivision (FCS), both classified as Division I. FBS teams
(formerly known as Division I-A) hold post-season bowl games, as opposed
to the tournament structure within the FCS.
(7.) The survey lumped "Independents," teams that do not
have conference affiliations, together as if they were a conference.
These independent teams include Notre Dame, Army, and Navy and
constituted the 12th conference. We exclude these independent teams.
(8.) If respondents are randomly selecting a rival, then one would
expect the fraction of people picking any given team in a conference of
size n to be 1 /(n - 1). Of course, there will be variance in the number
of people actually picking any particular potential rival so even if
people are picking randomly there will be an apparent main rival as we
have defined it. The question is, does the frequency with which people
picked the observed main rival exceed what could reasonably be expected
from random chance? To address this, we simulate survey responses.
Unfortunately, we do not know how many people completed the survey for
each team. For each simulation, 100 "respondents" for a team
randomly select a rival from n - 1 possible choices and the resulting
[r.sub.AB*] is recorded. This process is repeated 10,000 times to
determine an empirical distribution for [r.sub.AB*] in a conference with
n schools under the maintained assumption of random behavior. We believe
that 100 respondents per team is a conservative estimate of the number
people who responded to the survey in which case our test is
conservative since extreme values for [r.sub.AB*] are more likely to
occur when there are fewer respondents. The observed [r.sub.AB*] can be
compared to this empirical distribution to determine the p value, which
is taken to be the fraction of simulated values of [r.sub.AB*] that are
more extreme than the observed value. For every single team, the
rivalrous feeling toward its biggest rival is greater than any value in
our simulation for the appropriate conference size.
(9.) In 2005 the four major BCS bowls paid $117.2 million dollars
to its participants (Hagen 2005). The BCS was replaced with a four-team
tournament where the participants are selected by a committee in 2014.
Prior to that the BCS conferences were ACC, Big East, Big Ten, Big 12,
Pac-10, and the SEC. Groza (2010) provides a degree of formalism to
judging the quality of a conference by using three measures: number of
BCS bowl appearances, average attendance at home games, and the Sagarin
Computer Ratings, which provide a measure of recent on-field success
that considers both win percentage and the opponent's level of
competitiveness. He finds that the six most highly rated conferences are
SEC. Big 12, ACC, PAC 12, Big Ten, and the Big East,
respectively--exactly the set of BCS conferences.
(10.) As a robustness check, we also conducted the analysis
including all pairs of schools within a conference, even when no
rivalrous feeling was reported. The main results are consistent between
the two analyses, but including non-rivalrous pairs reduced the
magnitude of coefficients relative to those reported in Table 4.
(11.) Note that this is similar to lA's win percentage -501,
but because longer histories of play may have resulted in ties between
teams, we choose our measure as opposed to this simplified version. The
dynamics of ties do not significantly impact results, but for accuracy
we utilize the measure which does account for ties.
(12.) Success on the field impacts a team directly as well as the
decision to switch conferences. Athletic success has been linked to
increases in donations by male donors (Meer and Rosen 2009), increases
in the number of applicants to the school, and finishing a football
season ranked in the top 20 leads to higher average SAT scores among
applicants (Pope and Pope 2009). Indirectly, this success may increase
the likelihood of a higher conference's desire to add a new team,
which provides monetary incentives as mentioned before, but also some
indirect benefits. For example, Groza (2010) finds that teams which
change conferences have an increase in home attendance even controlling
for the level of competition. In fact, only two teams move to a lower
ranked conference: Nebraska and Colorado. However, both teams remained
in BCS conferences.
(13.) An alternative approach is to use the adjacency matrix where
the A, B entry equals to 1 if [r.sub.AB] > 0 and is 0 otherwise. Like
R, this matrix is a directed binary network, since it is not symmetric.
SARAH MARX QUINTANAR, CARY DECK, JAVIER A. REYES and SUDIPTA
SARANGI *
* We would like to thank the co-editor Jeff Borland and two
anonymous referees for their many useful suggestions. Also, we would
like to thank Ram Devireddy, Doug McMillin, Jeryl Mumpower, Rob
O'Connor, and seminar participants at Louisiana State University
and Texas Christian University for useful suggestions. Any opinion,
findings, and conclusions or recommendations expressed in this material
are those of the authors and do not necessarily reflect the views of the
National Science Foundation.
Quintanar: Department of Economics and Finance, University of
Arkansas at Little Rock, Little Rock, AR 72204. Phone (501) 569-8874,
Fax (501) 569-8871, E-mail smquintanar@ualr.edu
Deck: Department of Economics, University of Arkansas,
Fayetteville, AR 72701 and Economic Science Institute, Chapman
University, Orange, CA 92866. Phone (479) 575-6226, Fax (479) 575-3241,
E-mail cdeck@walton.uark.edu
Reyes: Department of Economics, University of Arkansas,
Fayetteville, AR 72701. Phone (479) 575-6079, Fax (479) 575-3241, E-mail
reyes@uark.edu
Sarangi: Department of Economics, Louisiana State University, Baton
Rouge, LA 70803; National Science Foundation, Arlington, VA 22230;
Virginia Tech, Blacksburg, VA 24061. Phone (225) 578-7193, Fax (225)
578-3807, E-mail sarangi@lsu.edu
TABLE 1
Target of Most Rivalrous Feelings by
Conference
Concentration Overall
Conference Team Index [CI.sub.B] Ranking
ACC North Carolina 528.16 9
Big 12 Oklahoma 516.53 11
Texas 516.53 11
Big East West Virginia 2413.62 3
Big Ten Michigan 667.19 7
CUSA Houston 718.24 6
MAC Central Michigan 306.54 19
MW BYU 2428.03 2
Pac-10 Oregon 277.78 22
SEC Tennessee 417.64 14
Sun Belt Middle Tennessee 871.73 4
WAC Boise State 3266.12 1
TABLE 2
Explaining Concentration of Rivalrous Feelings
Directed toward a Team
All BCS
Conferences Conferences
Proportion of Time in 138.99 168.89 **
Conference Since Its (91.04) (52.10)
Founding
30 Year Historical Winning 1643.37 ** 1039.87 ***
Percentage (1979-2008) (577.87) (229.79)
Public University -96.53 44.73
(127.24) (55.69)
Constant -840.92 -611.30 **
(295.04) (173.28)
N 117 65
Note: All regressions include conference dummies. OLS
coefficients are listed with robust standard errors clustered by
conference. Column II includes only the ACC, Big East, Big
Ten, Big 12, Pac-10, and SEC. N is all schools in the sample
data. Results are not qualitatively different if a historical
winning percentage of 20 years is used. If a 5-year history
is used then the BCS regression is different: only Public is
significant and is positive. Results are also consistent if two
controls are included: one for 1 year and one for 30.
*, **, and *** denote statistical significance at 10%, 5%,
and 1% levels, respectively.
TABLE 3
The Most Intense Rivalry by Conference
Rivalrous Overall
Teams Feelings Intensity Ranking
A [r.sub.AB] [I.sub.AB] = of Rivalry
B [r.sub.BA] [I.sub.BA] Intensity
ACC Miami (FL) 88.9% 131.65 11
Florida State 97.1%
Big 12 Oklahoma 97.4% 133.64 9
Texas 91.5%
Big East Pitt 96.7% 138.39 4
West Virginia 99.0%
Big Ten Michigan 96.0% 137.33 5
Ohio State 98.2%
CUSA Houston 57.3% 110.94 22
Rice 95%
MAC Central Michigan 100% 138.83 1
Western Michigan 96.3%
MW BYU 97.2% 138.67 3
Utah 98.9%
Pac-10 Arizona 98.0% 138.73 2
Arizona State 98.2%
SEC Alabama 80.2% 123.95 16
Auburn 94.5%
Sun Belt UL Lafayette 84.6% 130.99 12
UL Monroe 100%
WAC Idaho 99.4% 107.33 26
Boise 40.5%
TABLE 4
OLS Estimates for Rivalry Intensity
Rivals in BCS
All Rivals Conferences
I II III IV
Distance -.01 * -.02
(.01) (.02)
Same State 46.26 *** 47.68 ***
(8.89) (11.19)
Border States 4.56 ** 4.59 *
(1.88) (2.06)
Relative -.15 -.13 -.33 *** -.29 **
Strength (.09) (.09) (.06) (.08)
(Past 30
Years)
Status -2.56 -8.80 * -4.63 -10.43 *
(4.57) (4.20) (4.77) (4.27)
Games Played .58 *** 39 *** 48 *** 37 **
(.07) (.09) (.06) (.id
Constant 7.48 .32 23.14 6.21
(5.84) (4.73) (11.40) (4.54)
N 346 346 214 214
Note: All regressions include conference dummies. OLS
coefficients are listed with robust standard errors clustered
by conference. There are no substantial changes if relative
strength for the previous 20 years or previous 5 years is
used instead of the previous 30 years, except that 5-year
win history is not statistically significant in any specification.
Games Played is always the total number of games the two
teams have played, as it is meant to capture the length of their
history.
*, **, and *** denote statistical significance at 10%, 5%,
and 1% levels, respectively.
TABLE 5
Estimates for Rivalry Lonsidedness
Rivals in BCS
All Rivals Conferences
I II III IV
Distance -.01 ** -.01
(.002) (.01)
Same State 16.39 ** 23.34 **
(6.44) (8.90)
Border States 2.07 1.77
(1.42) (2.17)
Relative .02 .03 -.03 -.01
Strength (.05) (.05) (.05) (.05)
(Past 30
Years)
Status -.13 -2.31 -.79 -3.72
(2.23) (2.38) (2.23) (2.57)
Games Played .22 ** .15 * .23 ** .15
(.07) (.07) (.09) (.08)
Constant 4.53 1.67 6.32 1.62
(3.52) (3.28) (6.89) (4.52)
N 346 346 214 214
Note: All regressions include conference dummies. OLS
coefficients are listed with robust standard errors clustered
by conference. Results are qualitatively identical if relative
strength for the previous 20 years or previous 5 years is used
instead of the previous 30 years.
*, **, and *** denote statistical significance at 10%, 5%,
and 1 % levels, respectively.
