Can a sub-optimal tournament be optimal when the prize can be collectively consumed? The case of college football's national championship

Abstract

One of the most heated debates in all of sports is the annual debate over major college football's national champion. Since its implementation in 1995, the Bowl Championship Series (BCS) system has often failed to quell the controversy concerning what team is the Division 1 Football Bowl Subdivision football champion. Many of the BCS controversies have spawned changes in the title selection format, while others are perhaps the result of certain changes. What remains now is the cry from some college football fans for an expanded ‘national championship playoff,’ though college and university presidents and many college football coaches continue to resist these cries. We try to explain this resistance to expanding the number of teams invited to compete for the BCS championship and the persistence of the two team playoff format in college football. For three championship eras–pre-BCS, BCS and a futuristic post-BCS expanded playoff–we first relate some of the controversial details to concepts such as optimal tournaments and the public goods concept of collective consumption.

Acknowledgement

The authors thank two anonymous referees of this journal for making suggestions to improve this study. We also thank Troy Andre, Brian Beaky, Michael Bonnette, Laurie Cannon, Allison George, Vicky Hammond and other officials in the Sports Information Departments at the University of Colorado, Georgia Institute of Technology, Louisiana State University, University of Miami, University of Southern California and the University of Washington for providing helpful information. Any remaining errors are our own.

Notes

¹ At all other levels of football, D1 Football Championship Subdivision (formerly D1-AA), Division 2, Division 3 and in all other sports the NCAA itself runs a post season tourney. In all cases more than two teams are invited to the championship playoffs.

² The current BCS conferences are the Atlantic Coast Conference, the Big East Conference, the Big Ten Conference, the Big Twelve Conference, the Pacific Ten Conference and the Southeastern Conference. The current BCS bowls are the Fiesta Bowl, the Orange Bowl, the Rose Bowl, the Sugar Bowl and the BCS Championship Game.

³ This is the same basic procedure as used for the 65 team NCAA basketball tournaments. In the football case a selection formula is used, while in basketball a committee decides using some of the same information included in the BCS selection formula.

⁴ The current system began in 1995 under the name of Bowl Alliance. It only included four of the six BCS conferences and three of the BCS bowls. The name was changed from the Bowl Alliance to the BCS after 1997 when the Big Ten Conference and the Pacific Ten Conference and the Rose Bowl joined in.

⁵ As is discussed later, college football teams can play different number of games, so it is natural to compare teams in terms of number of losses rather than number of wins.

⁶ The 2004 controversy came on the heels of one in 2003, when Oklahoma was soundly defeated by Kansas State (35–7) in the Big XII Conference Championship game, but was invited to play in the BCS National Championship Game against LSU (in the Sugar Bowl). After Oklahoma's loss to LSU, many fans were left wondering whether Southern California was the more appropriate opponent for LSU in the Sugar Bowl, especially after SC's Rose Bowl win over Michigan and final record of 12-1. The 2003 controversy was very similar to the one in 2001, wherein Nebraska was handily defeated in their final regular season game against Colorado, eliminating them from the Big XII Championship game. Nebraska was, however, selected to face Miami in the BCS title game–a game they lost resoundingly, thus confirming the widely held view among fans at the time that Oregon should have been selected to play Miami for the BCS title. In 2000, Florida State University was, with one loss, selected to play the University of Oklahoma in the BCS Championship game over a one-loss University of Miami team, despite the fact that University of Miami beat Florida State University in their game that year.

⁷ In addition to the use of tournament theory to examine sports contests as diverse as bowling, golf, horse racing and soccer (e.g., see Abrevaya, 2002; Grund and Gurtler, 2005; Lynch, 2005; Matthews et al., 2007), recent research continues to examine employee and firm performance using tournament theory (e.g., Zech, 2001; Heyman, 2005; Martins and Lima, 2006; Sutter, 2006). In the earliest of that listed here, Zech (2001) contends that church pastor compensation is typically tied indirectly to performance through promotion tournaments, wherein exceptional church pastors are rewarded by being called to larger and more prestigious church congregations. Finally, Fee et al. (2006) use tournament theory concepts to examine the promotion of coaches in professional football.

⁸ See Ryvkin and Ortmann (2006) for further discussion and also for additional references, Ehrenberg and Bognanno (1990a and 1990b) and Bognanno (2001) for more on binary elimination tournaments and Levin and Nalebuff (1995), Ben-Yashar and Nitzan (1997) and Esteben and Ray (2001) for use of round-robin formats in public choice settings.

⁹ The difference between the average number of poll champions in the pre-BCS era of Table 1 (i.e., 1980–1994) and that from the BCS era is not statistically significant at the usual levels (p-value = 0.373).

¹⁰ Various scientific (i.e., mathematic/computer) polling services have declared Auburn as the 2004 National Champion (e.g., the Bowl Poll Index [BPI], EFI Ratings, GBE Poll, etc). Other Internet polls (e.g., fanspoll.com) and periodicals (e.g., The Eufaula Tribune) also voted Auburn as national champions. A few of these (e.g., fanspoll.com, The Eufaula Tribune, etc.) awarded national championship trophies to Auburn officials and ‘The Parade of Champions’ celebration was held in downtown Auburn on 15 January 2005 (auburn.edu, 2005).

¹¹ Georgia Tech's scoreboard sign commemorates their 1990 UPI National Championship that was awarded by a panel of Division 1-FBS coaches. Colorado's 1990 national title was awarded by the AP (i.e., sportswriters and broadcasters).

¹² Admittedly our collective consumption goods argument is stronger when it focuses on the two most recognized (by fans, etc.) polls–the sportswriters'/broadcasters' and coaches' polls. However, other organizations/polls (e.g., Sargarin, etc.) are gaining broader acceptance over time. Our argument also holds for splits of any individual poll, such as the AP (i.e., two teams can collectively consume the AP National Championship in a given year). We also do not doubt that ‘split’ national tittles of any sort spawn numerous ‘what if ?’ arguments between fans of the relevant teams. Because these arguments involve hypothetical scenarios only, two or more schools can continue to claim national titles.

¹³ Obviously, the pool will never have more than two champions in a given season if one restricts the pool to those teams that are named national champions by either of the major polls (currently AP that polls media members and USA Today that polls coaches).

¹⁴ An anonymous referee points out that, when more than one team is named champion, fans of each team want ESPN's Sports Center and other national media outlets to declare their team National Champion. In other words, fans who view their team as the best want their view validated by others. We do not disagree here. In fact, our point is that such validation is available not only from ESPN, but also from the many ncaa.org-listed organizations that recognize a national champion in D1-FBS college football each year. These include, but are not limited to, organizations such as The Sporting News, The New York Times and the National Championship Foundation.

¹⁵ Our ‘sub-optimal tournament is optimal for college football’ model is applicable to football only because college football is a ‘small sample’ sport, unlike basketball and baseball which are ‘large sample’ sports. Making the NCAA Tournament in basketball, or earning a bid to an NCAA Regional in baseball, is usually enough of a seal of approval for college basketball and baseball coaches, respectively. Because college football is a ‘small sample’ sport, only a small number of teams would earn a playoff bid relative to the number that participate in bowl games each year. One could also argue that university presidents and athletics directors want to ‘muddy the waters’ about which team is the national champion in football in order to generate more revenues and fundraising. Other college sports (e.g., baseball, etc) do not serve a fundraising/public relations function for universities in the way football often does.

¹⁶ The extra practice time that accompanies participation in the current D1-FBS bowl system yields both current and future benefits to participating teams.

¹⁷ Had such a policy been in place in 2004, the most recent year with controversy included within the Table 1 time frame, perhaps Auburn would have joined Southern California as national champion.