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Social Networks 33 (2011) 273– 280

Contents lists available at ScienceDirect

Social Networks

journa l h o me page: www.elsev ier .com/ locate /socnet

anking patterns in college football’s BCS selection system: How conference ties,onference tiers, and the design of BCS payouts affect voter decisions

ames Sanders ∗

epartment of Sociology, Po Box 644020, Washington State University, Pullman, WA 99164-4020, USA

r t i c l e i n f o

eywords:ocial structureollege football

a b s t r a c t

Affiliation matrices are used to analyze ranking patterns in the 2007, 2008, 2009 and 2010 USA TodayCollege Football Coaches’ Polls. Results evidence that votes received disproportionately stem from within

CS selection systemoaches’ pollankingoting

conference. As a whole, coaches that share a conference give their own teams between 10.61% and 27.83%more of their votes than other coaches. Also, conferences that receive automatic bids to BCS bowls appearto band together in hopes of minimizing the BCS chances of teams from non-automatic-bid conferences.Non-automatic-bid conferences, however, do not band together to rally around non-automatic-bid teamsvying for a BCS bid. Lastly, ranking discrepancies are greatest when teams are only marginally qualifiedfor BCS bids. Implications for revisions to the BCS selection system are discussed.

Few facets of organized sport generate as much controversy asollege football’s Bowl Championship Series (BCS) selection sys-em. Despite its notoriety, research pertaining to it is limited. Onexception is Eckard (1998), who theorized the NCAA as a cartelhat enforces a competitive imbalance that favors elite teams. Twother studies have linked televised games to improved BCS rank-ngs (Campbell et al., 2007; Paul et al., 2007). Papers printed in lawournals have raised antitrust concerns (Hales, 2003; McClelland,004) and papers in statistics journals have recommended adjust-ents to the BCS formula (Harville, 2003; Stern, 2004). To this

oint, however, systematic analyses of BCS selection system datare absent from academic journals.

This paper analyzes ranking patterns in the USA Today Collegeootball Coaches’ Poll, which makes up one third of the BCS formulaor ranking teams. Literature available on the poll has examinedallots in isolation, focusing on votes cast by individual coachesFalk, 2008). Individual-level frameworks are of limited utility,owever, because the polls rarely consist of coaches who are “good”r “bad” at evaluating talent. Rather, votes are cast under vary-ng contexts—contexts that merit consideration. This paper, then,ocuses on underlying structures of college football that shape vot-ng patterns. Conceptualizing coaches as occupants of unique andistinct space within the larger structure of college football implieshat the structural position of each has implications for voting deci-

ions (cf. Mayhew, 1980). The hypotheses developed and testedere shed new light on the role of structure in the poll.

∗ Tel.: +1 509 592 5216; fax: +1 801 240 3342.E-mail address: jpsanders@wsu.edu

378-8733/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.socnet.2011.08.001

© 2011 Elsevier B.V. All rights reserved.

1. Background

BCS rankings are determined by three components, each ofwhich carries equal weight in the formula (Bowl ChampionshipSeries, 2010a). The first is a composite of six computer-derived sta-tistical rankings. Two human polls, the Harris Interactive CollegeFootball Poll and the USA Today Coaches’ poll, also help determinefinal rankings. The Harris Poll samples former football players, uni-versity administrators, and members of the media. The coaches’ pollis comprised of 59 coaches. Voters submit weekly ballots indicatingtheir ordered picks for the best 25 teams in college football.

The inter-reliability of the six computer models has been ques-tioned (Annis and Craig, 2005; Mease, 2003), but the computersgenerally produce similar rankings (Martinich, 2002). Rankingssubmitted by human participants, however, are less congruent. Thisis partly because coaches cannot systematically evaluate and com-pare dozens of weekly games. Moreover, coaches are not equallyaware of all 120 Division I football teams and must rely on out-side resources such as box scores, the media and other coaches todevelop perceptions about the quality of teams.

The BCS designs polls to be (mostly) representative of Division Ifootball conferences. The Harris Poll, for example, is a “statisticallyreliable representation of all 11 Division I-A conferences and inde-pendent institutions” (Bowl Championship Series, 2010b, p. 1). Thecoaches’ poll, in contrast, permits unequal representation of confer-ences by employing a sample that is only an approximate reflectionof Division I conferences.

Sampling strategies employed by the BCS likely mitigate someunwarranted influence on poll outcomes, but even small degrees ofunequal representation can noticeably alter outcomes (Rogowski,1981). Moreover, it is unlikely that conferences exert pressure

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within v(2a) and v(2b).The final week of college football’s 2010 regular season can serve

as a more true-to-life example of game theory’s predictions. In that

74 J. Sanders / Social Ne

hat is equal in style and magnitude on coaches’ voting deci-ions. Coaches unavoidably exist within a unique niche of a largerocial structure. Their disparate structural locations entail disparatexposure to and impact from events, and thus disparate influencen action (Blau, 1987). Where a coach exists within the structurehapes voting decisions. In this paper, three structural influences onanking patterns are examined: Intra-conference ties, a two-tieredystem of conferences, and increased payments to conferences thatarn multiple BCS bids.

.1. Group solidarity: why intra-conference ties shape rankingatterns

Group solidarity theory teaches that cooperation in competitivenvironments facilitates advancement (Hechter, 1987; Lichbach,995). Although actions to undermine competitors can produce

mmediate payoffs, the long-term costs can be great if competi-ors come to be seen as inferior as a consequence of the actions. Its in actors’ interest, then, to not only best the competition, but alsonsure that the competition is perceived to be tough. The procure-ent of social capital and the ability to capitalize on its rewards

re better facilitated by connection to the esteemed in society, nothose of weaker reputation (Coleman, 1990; Bourdieu, 1986).

Each year, intra-conference teams are in competition with eachther for the conference championship and other rewards. Whenn intra-conference matchup occurs, the winning team undeniablynjures the losing team’s standing, but cooperation for the season’semainder is in the interest of both. Ranking intra-conference teamsoorly to extract revenge for losses indirectly lowers the stand-

ng of one’s own team. Similarly, ranking co-conference membershat one’s own team has bested poorly is akin to shooting oneselfn the foot: it reduces the prestige of victories. Thus, win or lose,oaches are likely to rank conference rivals well for reasons thatxtend beyond mere familiarity and positive perception: doing sondirectly improves the standing of one’s own team. If a coach’seam has earlier bested a team that is highly ranked, the coachan better justify ranking his own team even higher. Conversely,

loss to a highly ranked team is not as damning. Prestige is fur-her increased when conferences are comprised of highly rankedeams. Thus, even teams that do not face off during the season havencentive to rank one another favorably.

The role of conference ties in shaping information flows acrossollege football also bears mentioning. Each season, teams play aajority of their games (eight or nine) against intra-conference

eams, leaving room for only three to four out-of-conference oppo-ents. By consequence, information flows within conferences areuperior to information flows across conferences. The discrepancys exacerbated by coaches’ intense focus on scheduled opponentsn particular, rather than teams in general. Coaches end up inti-

ately and directly aware of the strengths of intra-conferenceivals, but only marginally and indirectly aware of the strengthsf nearly all others. In sum, college football’s conference-basedcheduling structure engenders thorough familiarity with intra-onference teams and cursory familiarity with the remainder,endering coaches more likely to see intra-conference teams ashe embodiment of a quality team. This dynamic may furtherrompt coaches to favor intra-conference teams in the polls. Data

imitations preclude such an analysis here, but future researchould do well to examine whether any observed preferences for

ntra-conference teams are better explained by principles of groupolidarity or structured familiarity.

As conference ties create structural motivations to rank intra-

onference teams favorably, the paper’s first hypothesis, which ishe most conservative hypothesis tested here, is that teams’ votesill come proportionately more from within conference than out of

onference.

33 (2011) 273– 280

This finding would be consistent with group solidarity theoryand suggest that conference-level disparities in representation inpolls can alter ranking outcomes.

1.2. Competitive advantage: why conferences tiers shape rankingpatterns

Six Division I football conferences are guaranteed at least oneBCS bowl bid per season: the Atlantic Coast Conference (ACC), theBig 12 Conference (Big 12), the Big East Conference (Big East), theBig Ten conference (Big Ten), the Pacific-10 Conference (Pac Ten),1

and the Southeastern Conference (SEC). These six compete with thefive other conferences (Conference USA (C-USA), the Mid-AmericanConference (MAC), the Mountain West Conference (MWC), theSunbelt Conference (SUN), and the Western Athletic Conference(WAC)) for four at-large BCS bids, unless others (e.g., Notre Dame)qualify for automatic bids—in which case fewer at-large bids areopen.

The two-tiered system may shape ranking patterns in ways notcurrently accounted for by the BCS. Conceptualizing conferences asisolates assumes that external ties are either nonexistent or incon-sequential. Conferences, however, do not exist in and operate inisolation from one another. Rather, depending on position withinthe larger structure of college football, conferences possess rea-sons to either ally or distance themselves from certain others. Withrespect to the coaches’ poll, whether or not a conference has anautomatic BCS bid is likely a point of bifurcation.

The issuance of automatic bids engenders and reifies inequal-ities within college football (Eckard, 1998). BCS conferences tendto enjoy greater revenues, fanbases, media coverage, prestige, andrecruiting advantages (Dumond et al., 2008; Campbell et al., 2007).Advantages are threatened, however, anytime a team from a non-automatic-bid conference earns a BCS bid. Thus, automatic-bidconferences possess structurally induced reasons to keep non-automatic-bid conferences out: doing so maintains advantage.Conversely, non-automatic-bid conferences benefit when theirteams “bust the system”: their presence in BCS bowls disrupts thestatus quo that renders them disadvantaged.

Insights from cooperative game theory, which focuses on possi-bilities for agreement and collaboration among game players, alsosuggest that conferences will group together by conference typein the polls. By definition, a cooperative game consist of a finiteset of players represented as N = {1, 2, . . ., n}, possible subsets(e.g., alliances) of N represented as S, and the valued outcome ofeach S represented as v(S) (Brandenburger, 2007). In games, play-ers seek to maximize v(S) (Branzei et al., 2008; Camerer, 2003).Applied to the coaches’ poll, automatic-bid conferences will favora v(S) that furthers the status quo, and non-automatic-bid confer-ences will favor a v(S) that weakens it. To illustrate the pattern,Fig. 1 presents an extensive form graph of the coaches’ poll whenanalyzed from the perspective of cooperative game theory. A ‘+’ rep-resents advancement of the status quo and a ‘−’ represents injuryto the status quo. When ranking teams, each conference is expectedto make choices that lead to the best available v(S) (i.e., a v(S) con-taining one or more ‘+’ signs for automatic-bid conferences but av(S) containing one or more ‘−’ signs for non-automatic-bid confer-ences). Thus, automatic-bid conferences will cluster within v(1a)and v(1b) of Fig. 1 and non-automatic-bid conferences will cluster

week, three undefeated teams were in contention for the number

1 As of July 2011, the Pac Ten is now the Pac 12.

J. Sanders / Social Networks

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Fig. 1. Extensive form graph of coaches’ poll.

ne ranking: Auburn of the SEC, Oregon of the Pac Ten, and TCU ofhe MWC. Initially, S = 1, but S = 2 at the point where conferencesecide whether or not to give a number one ranking to a team fromn automatic-bid conference. From there, three conferences are inosition to further improve their standing with respect to the statusuo by choosing to vote for an intra-conference team. The result ofll decisions is five v(S): v(SEC) = ‘+ +’, v(Pac Ten) = ‘+ +’, v(ACC, Bigast, Big Ten and Big 12) = ‘+’, v(C-USA, MAC, SUN and WAC) = ‘−’,nd v(MWC) = ‘− −’. This is illustrated in Fig. 2.

As the structure of college football pits two tiers of conferencesgainst one another for access to limited resources, the second andhird hypotheses tested here are that automatic-bid conferences willand together to give comparatively low rankings to non-automatic-id schools in contention for a bid and non-automatic-bid conferencesill band together to give comparatively high rankings to their schools

n contention for a bid. At first glance, it may seem that if one hypoth-sis is correct, the other must be too. It is possible, however, for

utomatic-bid conferences to act in concert to maintain the statusuo without non-automatic-bid conferences acting in concert toisrupt it. Hence, two hypotheses are needed.

ig. 2. Extensive form graph of selecting auburn of SEC, Oregon of Pac Ten, or TCUf MWC in 2010.

33 (2011) 273– 280 275

1.3. Economic voting: why increased payments shape rankingpatterns

The literature on economic voting theory is detailed andnuanced, but one simple finding is relevant here: net of candidatepopularity and other voting functions, economic considerationsinfluence about one-third of the vote (Lewis-Beck and Paldam,2000). Accordingly, candidates who are regarded as a means to eco-nomic stability and prosperity posses an advantage because theyhave the fortune of being regarded as strong on a critical issuefor voters (Evans, 2004). Applied to the coaches’ poll, economicvoting theory suggests that ranking decisions will be especiallydisparate when conferences are trying to procure a second BCSbid. A second bid entitles a conference to millions of dollars morethan it would receive otherwise. All members benefit becauseconference revenue sharing plans redistribute monies awarded toBCS bound teams. In 2008, for example, the Big Ten and Big 12each sent two teams to BCS bowls. Though Minnesota and Bay-lor (the poorest performing teams in the respective conferences)both lost every conference game, they each received a $2 mil-lion revenue-sharing payment that equaled the amount receivedby conference champions (Easterbrook, 2007). Consequently, anyteam that can secure a second BCS bid is viewed by co-conferencemembers as “good for the economy.” Moreover, economic consid-erations in voting decisions are thought to be of greatest magnitudewhen (a) voters feel directly capable of influencing outcomes and(b) significant money is at stake (Lewis-Beck and Paldam, 2000).The coaches’ poll, comprised of a mere 60 people who deter-mine the fate of tens of millions of dollars, is a match on bothaccounts.

Because receiving two BCS bids increases a conference’s eco-nomic windfall, economic voting theory suggests that conferenceswill strive to obtain multiple bids. To be eligible for at large bids,teams must be ranked 14th or better. In some cases, however, the“second best” teams from automatic-bid conferences possess onlymarginal qualifications. In such cases, conferences will need to votefor that team even more disproportionately than usual in orderto have a fighting chance of procuring a second bid. Accordingly,the fourth hypothesis tested here is that ranking disparities will beexaggerated when automatic-bid conferences hope to procure a secondautomatic bid for marginal teams.

1.4. Statement of problem

The BCS selection system may currently fail to consider impor-tant structural impacts on ranking outcomes. In particular, thematter of whether rankings are shaped by conference ties, a two-tiered system of conferences, and the design of BCS payouts meritsdeeper consideration. The hypotheses developed within the paperare now tested. Consistent with the hypotheses’ claims, the testsproduce clear evidence that structural properties shape rankingoutcomes in ways currently unaccounted for by the BCS.

2. Data and method

Data are from the 2007, 2008, 2009, and 2010 coaches’ polls.A combined 238 ballots were cast in those years (only 59 coacheswere polled in 2009 and 2010). Ballots are collapsed by conferenceso that college football conferences act the unit of analysis. Individ-ual ballots are published only once in a season. The week ballots arereleased, however, is a critical one: the final week of the season—or

the week BCS bowl bids are handed out. It represents conferences’final chance to rank teams into positions that either improve orweaken the likelihood of BCS bids. As a note, some of the analysespresented here pool together ballots from all the years.

276 J. Sanders / Social Networks 33 (2011) 273– 280

Table 1Descriptive statistics of conferences.

Conference Conference type Conference size Percent of league Number of voters Percent of coaches polled Percent of poll Degree of representation

ACC Automatic 12 10.00 24 50.00 10.08 +0.08Big East Automatic 8 6.67 16 50.00 6.72 +0.05Big Ten Automatic 11 9.17 26 59.09 10.92 +1.75Big 12 Automatic 12 10.00 25 52.08 10.50 +0.50C-USA Non-automatic 12 10.00 24 50.00 10.08 +0.08MAC Non-automatic 13 10.83 24 46.15 10.08 −0.75MWC Non-automatic 9 7.50 16 44.44 6.72 −0.78Pac Ten Automatic 10 8.33 20 50.00 8.40 +0.07SEC Automatic 12 10.00 26 54.16 10.92 +0.92SUN Non-automatic 8 6.67 16 50.00 6.72 +0.05WAC Non-automatic 9 7.50 16 44.44 6.72 −0.78

Mean – 10.55 8.79 21.18 50.03 8.90 +0.11

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SD – 1.81 1.51 4.40

ote: Data are pooled from 2007 to 2010 seasons.

.1. Dependent variable

Ranking is the dependent variable. It represents the rankingsiven by coaches (at the conference level). The scale that coachesse to rank teams runs from 25 (25th best) to one (absolute best). Forome analyses, rankings are reverse-coded (i.e., one indicates 25thest and 25 indicates absolute best). The reverse-coded measureroduces an intuitive conceptualization of rankings: Each coachas 325 votes ((25(25 + 1))/2) to distribute; the best team receives5 votes; the second best receives 24 and so on down to the 25thest team, which receives only one vote. When analyses examinehe reverse-coded measure, the term votes is used for the sake oflarity.

.2. Independent variables

Conference is the primary independent variable. There are 11onferences in Division I football. Several conference-level vari-bles are also considered in analyses. First is conference type, whichifferentiates between conferences that receive automatic BCS bidsnd those that do not. Second, conference size is the number of teamsn a conference. Third, percent of league indicates what percent ofivision I football plays in the conference. Fourth, number of voters

s the total number of coaches from the conference that participatedn the poll. Fifth, percent of coaches polled represents the percent ofoaches that were polled. Sixth, percent of poll indicates how muchf the poll was comprised of voters from the conference. Lastly,egree of representation is the degree to which the conference over-r underrepresented in the poll. It is calculated by subtracting theercent of league variable from the percent of poll variable. Table 1rovides descriptive statistics for conferences.

.3. Procedures

The first hypothesis (i.e., conferences vote disproportionately forntra-conference teams) is tested with an affiliation matrix. Thistrategy represents affiliations as A, actors (i.e., football confer-nces) as i, and events (i.e., votes received by a conference) as j.f conference i were to give no votes to conference j then Aij = 0. Byontrast, if conference i were to give all its votes to conference jhen Aij = 325(t), where t represents the number of coaches polledrom conference i. Because conferences vary in number of polledoaches, values are standardized by reporting the mean number of

otes given per coach. The mean is preferable to the median becausehe BCS formula does not penalize outliers (Bowl Championshiperies, 2010a). Mean votes (represented as v) from conference i toonference j, then, is given by v =

∑Aij/t.

4.25 1.85 0.76

The matrix testing the first hypothesis reports the v for i and j.For the first hypothesis to be supported, v must be greatest wheni and j are a match, or h1a = vij > {vij1, vij2, . . . , vijn}. Statistical sig-nificance tests (e.g., t-tests) are not presented because the matrixcontains population-level data. For heuristic purposes, however,a second column reports a percentage value that can be used todetermine whether observed differences are substantively signifi-cant. Percentages indicate how votes received from one conferencecompare to votes received from all other conferences. For example,the ACC’s value for Big East teams is 2.71, which means that ACCcoaches gave 2.71% more of their votes to Big East teams than othercoaches overall.2 This 2.71% difference is likely not significant in asubstantive sense, but finding that ACC coaches give 19.33% moreof their votes to ACC teams than other coaches clearly is significant.

A second matrix tests hypotheses 2 (i.e., automatic-bid confer-ences band together) and 3 (i.e., non-automatic-bid conferencesband together). This matrix is limited to teams from non-automatic-bid conferences that were in contention for a BCS bid.There were six between 2007 and 2010: Hawaii in 2007, Utah in2008, Boise State in 2008 and 2009, and TCU in 2009 and 2010. Inthis matrix, v represents the mean ranking given by conference i.The value in the second column indicates how much lower con-ference i’s v was compared to the team’s intra-conference v. Forthe second hypothesis to receive support, the v from automatic-bidconferences (represented as g) will need to be at least one standarddeviation away from the intra-conference v, or h2a = z(v) − z(vg) ≥1. For the third hypothesis to receive support, the v from non-automatic-bid conferences will need to be within 0.5 standarddeviations of the intra-conference v, or h3a = z(v) − z(vg) ≤ 0.5.Each team’s ranking received from the BCS’s computer componentis also included in the matrix. The computer ranking provides cluesas to whether discrepancies tend to result from (a) intra-conferencecoaches providing inflated rankings or (b) underrating on the partof out-of-conference coaches.

A third matrix tests the final hypothesis (i.e., ranking disparitieswill be heightened when conferences attempt to procure a secondBCS bid for a marginal team). This matrix is limited to the lowestranked team from an automatic-bid conference to receive a BCS bidfrom each season: Illinois in 2007, Ohio State in 2008, Iowa in 2009,and Arkansas in 2010. In this matrix, v represents the mean rankinggiven by conference i. The value in the second column indicates

2 In this ACC/Big East scenario, votes given by ACC coaches would be comparedto all other coaches except for Big East coaches.

J. Sanders / Social Networks 33 (2011) 273– 280 277

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rom the v from all other conferences (represented as c), or h4a =(v) − z(vc) ≥ 1. As before, each team’s ranking received from theCS’s computer component is also included.

. Results

.1. Descriptive statistics

Six automatic-bid conferences and five non-automatic-bid con-erences comprise Division I football. Mean conference size is 10.55,ut automatic-bid-conferences tend to be larger (10.83 teamsersus 10.20 teams). Average percent of league was 8.79. Theean number of voters per conference was 5.30 per year. On aver-

ge, conferences had about half (50.03%) of their coaches polledach year. However, proportionately more coaches from automaticid-conferences were polled than coaches from non-automatic-id conferences (53.75% versus 48.83%). Because (a) there areore coaches in automatic-bid conferences and (b) coaches in

utomatic-bid conferences are overrepresented in the poll, the finalample contains more coaches from automatic-bid conferenceshan non-automatic-bid conferences (57.54% versus 40.32%). In anverage year, automatic-bid conferences as a whole are overrepre-ented by 3.4%, whereas non-automatic bid conferences as a wholere underrepresented by 2.2%.

.2. Affiliation matrices

As shown in Table 2, the first affiliation matrix found that teamseceive disproportionate shares of rankings from within confer-nce, between 10.61% and 27.83% more in every case. The WACave the most disproportionately to its teams, whereas the Big2 was the least disproportionate. An unexpectedly strong inverseorrelation of −0.709 was found between votes received and dis-roportionate voting. Thus, conferences that received more votese.g., Big 12, SEC, and the Big Ten) gave the least disproportionatelyo their teams, whereas conferences that received fewer votes (e.g.,CC, Big East, and WAC) gave the most disproportionately to their

eams. On average, conferences gave 16.14 percent more of theirotes to their teams than other conferences gave.

A bipartite graph shown in Fig. 3 provides a visual represen-ation of ranking patterns reported in Table 2. The i are listed onhe left-hand side and j are listed on the right-hand side. The lineetween i and j represents v. A 1-point increase in line width rep-esents a 1-vote increase in v. Presenting ties across 11 conferences

ould render the graph indiscernible. Thus, only ranking patterns

or the conferences that gave the most disproportionately to theirwn teams are included. The graph is useful because it demon-trates that even when a conference gives disproportionate votes Ta

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78 J. Sanders / Social Ne

o its own teams, it may (and does in many cases) still give moreotes to teams from other conferences.

As shown in Table 3, the second affiliation matrix found evi-ence that automatic-bid conferences band together to give lowerankings to teams from non-automatic-bid conferences that aren contention for a BCS bid. In every case analyzed, automatic-bidonferences ranked the team in question more than one standardeviation lower than the team’s own conference. The 2007 Hawaiieam was the most extreme case: Compared to mean ranking giveny WAC coaches, the weighted mean ranking given by coaches

n automatic-bid conferences was 5.7 spots (or 123%) lower. Inerms of standard deviations, automatic bid conferences rankedawaii 1.76 standard deviations lower than the WAC. Although thether ranking discrepancies were not as extreme, rankings fromutomatic-bid conferences were universally lower than rankingsriginating from teams’ own conference: the mean difference was.2 rankings (50.7% lower) and the median difference was 1.9 (33.5%

ower).Data in Table 3 indicate that other non-automatic-bid confer-

nces do not band together to give higher rankings to a teamn contention for a BCS bid. Although the gap in rankings givenetween other non-automatic-bid conferences and the team’s ownonference tended to be smaller, in no case was it within 0.5tandard deviations. The two-tiered system of conferences pro-uces a three-tiered ranking pattern of teams in contention forCS bids from non-automatic-bid conferences: Intra-conferenceoaches rank the team most favorably, and are followed at someistance by coaches from other non-automatic-bid conferences.oaches from automatic-bid conferences comprise the third and

owest tier.The affiliation matrix presented in Table 4 evidences that rank-

ngs given to marginally qualified teams are more discrepant thansual. Of 40 cross-conference comparisons shown in the table, onlyne team was ever voted higher by an outside conference—in 2009he Big East and Big 12 conferences gave a slightly better rankingo Iowa than the Big Ten (9.25 and 9.50 respectively versus 9.67).n three of the four cases analyzed in the table, mean ranking giveny intra-conference coaches was more than one standard devia-ion higher than mean ranking given by all others.3 On the whole,he mean drop in ranking received out of conference was 1.9 spots17.71%) and the median drop was 1.55 spots (13.94%). The mostxtreme example of discrepancy in marginal team ranking patternsas the 2007 Illinois team: Other conferences ranked Illinois 3.6

pots (34.07%) lower than the Big Ten. In terms of standard devi-tions, the Big Ten ranked Illinois 1.88 standard deviations higherhan all other conferences.

The composite BCS computer rankings included in Tables 3 and 4end to be lower than the mean ranking received from within con-erence (true in 8 out of the 10 cases). Although not as common (5ut of the 10 cases), mean ranking received from coaches outside ofonference was at times lower than the computer ranking. Thus, thenswer to the question of whether ranking discrepancies stem fromntra-conference coaches providing inflated rankings or underrat-ng on the part of out-of-conference coaches may be “both”, thoughhe former appears somewhat more likely to happen.

. Discussion

The results of analyses conducted for this paper offer compelling

vidence that structural aspects of college football shape rank-ng patterns in the coaches’ poll, and ultimately in BCS rankings.hese structural impacts are largely unaddressed by current BCS

3 The 2009 Iowa team was the lone case in which the difference in standardeviations was less than one—it was 0.46. Ta

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J. Sanders / Social Networks 33 (2011) 273– 280 279

Table 4Affiliation matrix of mean ranking given to lowest ranked team that received an at large bid.

Conference Teams from automatic-bid conferences

Illinois (2007) Ohio State (2008) Iowa (2009) Arkansas (2010)

Mean rank Spots lowera Mean rank Spots lower Mean rank Spots lower Mean rank Spots lower

Computer Rank 16.0 5.6 11.0 3.0 10 0.3 6.0 −1.7Allb 14.0 3.6 9.7 1.7 10.5 0.9 9.1 1.4ACC 15.0 4.6 10 2.0 10.8 1.2 8.8 1.2Big East 14.0 3.6 9.8 1.8 9.3 −0.4 8.5 0.8Big Ten 10.4 – 8 – 9.7 – 9.3 1.7Big 12 14.2 3.8 9.3 1.3 9.5 −0.2 9.3 1.7C-USA 13.2 2.8 9.8 1.8 9.8 0.2 8.7 1.0MAC 13.7 3.3 9.5 1.5 10.0 0.3 9.7 2.0MWC 14.0 3.6 9.8 1.8 11.5 1.8 8.0 0.3Pac Ten 13.4 3.0 9.8 1.8 12.8 3.1 9.4 1.7SEC 13.4 3.0 9.7 1.7 10.2 0.5 7.7 –SUN 15.0 4.6 9.8 1.8 11.5 1.8 8.8 1.1WAC 14.8 4.4 10.3 2.3 10.8 1.1 9.5 1.8

n 60 60 59 59Total mean 13.567 9.533 10.441 8.915SD 1.890 0.873 1.859 1.330Exaggerated disparity? Yes Yes Noc Yes

ranki

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a Spots lower than the team’s own conference.b Excluding the team’s own conference. Value is weighted.c Big Ten’s mean ranking was only 0.46 standard deviations lower than the mean

rocedure, which seeks to mitigate undue influence in its pollshrough use of samples that approximately reflect the Divi-ion I football landscape (Bowl Championship Series, 2010b).o reiterate and drive home the findings, the discussion sec-ion is framed around the hypotheses developed in the paper’sackground.

(1) Teams receive proportionately more votes from within con-erence. Consistent with group solidarity theory, coaches rankntra-conference teams more favorably than others. The first affilia-ion matrix constructed here included 80 conference-to-conferenceomparisons. In every case, teams (at the conference-level)eceived proportionately more votes from their own conference. Byanking intra-conference teams favorably, coaches increase pres-ige of intra-conference victories and minimize the embarrassmentf defeats. Moreover, affiliation with a conference made up of highlyanked teams improves their own team’s standing (cf. Bourdieu,986; Hechter, 1987). Thus, all intra-conference teams have extra

ncentive to vote favorably for one another.This finding has important implications in light of two struc-

ural aspects of the BCS: conferences vary in size and conferencesary in degree of representation in the coaches’ poll. Generally,utomatic-bid conferences are larger and better represented in theoll. These discrepancies can engender an advantage in the poll for

arge automatic-bid conferences. It is worth mentioning here thathe Big East (the smallest automatic-bid conference) has never pro-ured two BCS bids in the same season. Not surprisingly, it (alongith the Pac Ten and Big Ten in 2011) is scheduled for expansion

n 2012.(2) Automatic-bid conferences band together in hopes of minimiz-

ng the presence of teams from non-automatic-bid conferences in BCSowls. Automatic-bid conferences possess numerous competitivedvantages (Eckard, 1998). Advantages are threatened, however,nytime an outside team busts the system. Keeping non-automaticonferences out of BCS Bowls, then, helps automatic-bid confer-nces maintain the favorable status quo. In all cases analyzed here,oaches from automatic-bid conferences ranked teams that weret risk of busting the system more than a standard deviation lower

han intra-conference coaches. In five of six cases analyzed here,oaches from automatic-bid-conferences also gave worse rankingso a potential “BCS Buster” than coaches representing the otheron-automatic bid conferences.

ng given by all others.

In light of the downward pressure exerted on rankings for highlysuccessful teams from non-automatic-bid conferences, the deci-sion to under-represent these conferences in the coaches’ poll iseven more problematic. Automatic-bid conferences have a num-bers advantage to start with (6 conferences versus 5 conferences)and over-representing them in the polls extends their advantagesbeyond what is reasonable. Based on recent history, it is unlikelythat a qualified team representing a non-automatic-bid conferencewould miss the cutoff for BCS eligibility (Boise State was eligiblein 2008 but not selected), but it is also unlikely that such a teamwould earn a high enough ranking to qualify for the championshipgame. For example, in the four years examined here, teams fromnon-automatic-bid conferences received ten votes for either first orsecond place, but none of these votes originated from automatic-bid conferences. Whether teams from one conference or anotherare worthy of the chance to play for a national championship isbeyond the scope of this paper, but at a minimum, it seems thata conferences should receive proportionate representation whenthey attempt to make their case.

(3) Non-automatic-bid conferences do not band together. In thecases analyzed here, mean rankings given by other non-automatic-conferences failed to come within 0.5 standard deviations of theteam’s own conference. Thus, despite occupying similarly dis-advantaged structural positions, these conferences generally donot act in concert in an attempt to shape poll outcomes (unlikeautomatic-bid conferences). One potential reason behind non-automatic-bid conferences being “on their own” in the poll isthat two or more teams from non-automatic-bid conferences areoften competing with one another for a single BCS bid. The non-automatic-bid team that ends up with the lower ranking willlikely be denied a bid (e.g., Boise State in 2008). Consequently,non-automatic-bid conferences can ill afford to do many favorsfor others in similarly disadvantaged positions. Moreover, helpingbust the BCS system as an individual conference engenders greaterrewards than helping to bust the system as one-fifth of a tier of con-ferences. Lastly, if non-automatic-bid conferences were to throwtheir weight behind a non-conference team, it could send a poten-

tially negative message about their own conferences: “We’re notall that good, but our neighbor sure is.”

(4) Discrepancies are greater when conferences’ second best teamsare only marginally qualified for at large bids. Of all teams analyzed,

2 tworks

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ball polls: the wisdom of point spread markets. Journal of Sports Economics 8,412–424.

Rogowski, R., 1981. Representation in political theory and in law. Ethics 91, 395–430.Stern, H.S., 2004. Statistics and the college football championship. The American

80 J. Sanders / Social Ne

he two pushed the most in the polls by their own conferencesere Illinois in 2007 (BCS ineligible based on computer ranking

lone) and Hawaii in 2007 (barely BCS eligible based on computeranking alone). If their conferences had not ranked them so muchigher than others, both teams might have been left out. The casef Illinois is remarkable not only for evidencing how conferencesush hardest when teams are on the bubble, but also because itseceipt of an at-large bid highlights how overrepresentation of aonference may influence poll outcomes. Seven Big Ten coachesarticipated in the 2007 poll, making it the most overrepresentedonference. Were it not, Illinois may have ended up outside the top4 and been ineligible for a BCS bid.

The finding that discrepancies are greatest when teams’ merits suspect is indicative of a larger pattern in the data: Conferenceshat received more votes overall tended to show the least amount ofntra-conference favoritism (see Table 2). When a conference (e.g.,he WAC) is the only one convinced that one or more of its teamsre BCS worthy, its rankings will deviate more sharply from oth-rs. Conversely, when teams in a conference (e.g., the SEC or Big2) are judged by outsiders to be good, the conference appears lessnreasonable when it ranks its teams well. These differences likelyave little to do with conferences possessing disparate numbers ofbjective coaches, but rather stem from differential odds of attain-ng BCS bids. The ability to appear reasonable within the polls, iteems, is a luxury afforded to those who are most loved.

. Conclusion

The BCS selection system has generated controversy since itsnception. In its current iteration, undue influence within the pollss mitigated by reliance on pools of voters that are generally rep-esentative of the 11 Division I conferences. The current approach,owever, has not taken into account important structural realitiesithin college football that shape ranking patterns. This paper has

learly demonstrated that conference ties, conference tiers, andhe design of BCS payouts influence poll outcomes. These reali-ies must be considered in order to create a selection system thats more fully theorized and more satisfactory. Coaches and theiranking decisions unavoidably exist within the larger structure ofollege football. Where they stand within it and what occurs aroundhem shapes their voting decisions. Research on other sociologi-al elements of the BCS selection system will help to advance theramework developed here.

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