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Abstract
Comparative judgments abound in sports. Fans and pundits bandy about which of two players or teams is bigger, faster, stronger, more talented, less injury prone, more reliable, safer to bet on, riskier to trade for, and so on. Arguably, of most interest are judgments of a coarser type: which of two players or teams is, all-things-considered, just plain better? Conventionally, it is accepted that such comparisons can be appropriately captured and expressed by sports rankings. Rankings play an important role in sports arguably because of the conventional acceptance that rankings capture and express all-things-considered relations between the ranked teams or players. Standard ranking practices rely on a number of widely held assumptions. I discuss three of the most important and argue that at least one of them must be false. If this is right, the strong and growing commitment to using rankings to determine participation in tournaments and the awarding of championships is mistaken. At the least, given the conventional wisdom about rankings, my argument provides good reasons to be skeptical that any particular ranking ‘gets it right’. At the limit, it suggests that our most basic assumptions about all-things-considered athletic quality are wrong.
Acknowledgments
I thank many with whom I have discussed the ideas in this paper, among them Jan Boxill, D. Kenneth Brown, Ruth Chang, Shahar Dillbary, Michael Horton, Justin Klocksiem, Kabe Moen, Jason Scofield, and Chase Wrenn. Special thanks to Stuart Rachels, Norvin Richards, and Kurt Smith for reading and commenting on earlier drafts. Any errors that remain are mine entirely. Versions of this paper were presented at Cal Poly San Luis Obispo (June 2014), and the University of Southern Mississippi (November 2014), as part of the wonderful Philosophical Fridays series. I thank both departments for their invitations to speak. Finally, I thank NBA great Horace Grant for his encouragement and indulgence at a chance meeting. His perspective as a sports professional, on and off the court, was particularly revelatory.
Disclosure statement
No potential conflict of interest was reported by the author.
Notes
1. Though, of course, the price of cod might be relevant after all if, say, the starting quarterback considers it a good luck pre-game meal, for instance. And, even when all things are considered, some of them may turn out to be irrelevant. This just reinforces the difficulty in considering all things. I thank Stuart Rachels and an anonymous referee for independently suggesting these points.
2. Though rankings are especially important to American team sports, the problems I identify herein apply as well to individual sports, and to non-American leagues. Take, for instance, the role that rankings play in UK football (soccer) where, at the end of the Premier League season, the three lowest-ranked teams are relegated to the Football League Championship. To the extent that rankings are (a) closely linked to a team or player’s win/loss record or (b) treated as a measure of that team or player’s all-things-considered quality, the problems I discuss will apply.
3. Some rankings aim to be predictive – to order teams according to how they are expected to perform in the future. Team A will be ranked higher than Team B if it is expected that, were they to play head-to-head, A would usually beat B. Other rankings are meant to be retrodictive – to order teams according to their actual performance in the past, showing which team was all-things-considered ‘best’ over some period of time. So, holding constant other factors, if Team C beats Team D, C will be ranked ahead D in subsequent retrodictive rankings, even if there are reasons to believe that D would beat C in a future rematch.
4. For the moment, I set aside the possibility of ties since they are exceedingly rare in such rankings.
5. As with many aspects of sports, the conventional wisdom of rankings may not be endorsed openly or entirely by any one participant in ranking practices, just as the conventional wisdom that one should never go for it on 4th-and-long from deep in one’s own territory early in a football game may not be a hard and fast rule. Nevertheless, despite the occasional exception and notwithstanding the absence of any official proclamations, the behavior of football coaches generally bespeaks the existence of such conventional wisdom about going for it on 4th-and-long. Likewise, the behavior of rankings (and occasional statements of those doing the rankings) bespeaks the existence of the conventional wisdom of ranking I here describe.
6. See Ali, Cook, and Moshe. (Citation1986).
7. See Coleman (Citation2005, Citation2013).
8. This is holding fixed the assumption that the ‘Team A’ that beat Team B is the same as the ‘Team A’ that lost to Team C. Call this the assumption that a team’s nominal identity entails its numerical identity. I think a strong case can be made that this assumption too is wrong. But, letting go of this assumption would make nonsense of having season-long competitions to begin with, and at any rate, discussing this more fully is beyond the scope of this study.
9. Dixon (Citation2001) discusses five factors that might produce a ‘failed athletic contest’, i.e. a contest where the better team loses. (Shortly, I will suggest a sixth.) On Dixon’s view, determining which of two competitors is superior is part of the point of sporting contests, hence his calling contests in which the better team loses ‘failed’. Not all failed contests are injustices, however. According to Dixon, sometimes the better team can deserve to lose. Still, in most cases, Dixon counts failed athletic contests as unjust outcomes. The most common cause of such failed contests might be officiating mistakes and biases. The data suggest that officiating biases may account for as much as 80% of the variance of home field advantages. And some such advantages are truly staggering. In college football, home teams win 64% of games; in college basketball, home teams win 69.1% of the time. What this means, though, is that in a great many contests that home teams win, we are right to wonder whether it is due to their being athletically superior or whether the influence of honestly intended but biased officials tipped the balance in their favor. For the relevant data, see especially Moskowitz and Wertheim (Citation2011). On the philosophical issues attending officiating mistakes and some proposals for addressing them, see especially Bordner (Citation2015).
10. Let us call this formulation Strong WIB: the winner of any given individual head-to-head contest is thereby better (all-things-considered) than the loser.
11. One might respond that Strong WIB and TR are not, even in this case, inconsistent if the ‘better-than’ relation established by Strong WIB and the results of the games are time-indexed. So, A is better than B in the morning, but B becomes better than A by the evening. But, remember, rankings are taken to model all-things-considered comparisons over the course of a season, not a single day.
12. Of particular note are two recent upsets in college basketball. In 2014, an undefeated and No. 1-ranked Syracuse team lost at home to unranked Boston College, which then had a record of 6–19. Basketball statistician Ken Pomeroy estimated that Syracuse had a 96% chance of winning, making BC’s win one of the biggest upsets in college basketball history. Also, in the NCAA championship tournament, No. 3-seeded Duke lost to No. 14-seeded Mercer. Statisticians at FiveThirtyEight.com estimated Mercer’s chances of winning at barely 7% ahead of the game. Then, there are the all-time historic upsets. In an individual sport, there is perhaps no upset greater than Rulon Gardner’s win over Aleksandr Karelin in the gold medal match in Greco-Roman wrestling at the 2000 Sydney Olympics. Karelin had not lost a match for 13 years prior and had not even surrendered a point to an opponent in more than six years.
13. Here, ‘consistently’ might be understood as either ‘consistently (thus far)’ or ‘consistently (would)’. In either case, the same problem arises.
14. I borrow this example from Temkin (Citation2012, 468). Note one can easily cash out the same problem in terms of probabilities.
15. See Temkin (Citation2012, 468). Oddly, Temkin argues for a non-transitive ‘better-than’ relation in moral domains, yet he plumps for transitivity in sporting comparisons.
16. In such a case, presumably, head-to-head results may serve as a tiebreaker. If so, though, this opens Overall WIB to the same kinds of worries that motivated the view to begin with.
17. As Temkin’s proposal suggests, it is quite ordinary for an apparently superior team or player A to have trouble against a given inferior opponent B. We speak of B ‘having A’s number’, of A being ‘jinxed’. For a real-world case, take the 1998 New York Yankees, thought by some to be the best team in MLB history. That year, the Yankees had a losing record (5-6) against the Anaheim Angels. The Angels finished second in their division and missed the playoffs. But the repugnant conclusion for Overall WIB is more extreme than this. Suppose the 1998 Yankees lost all 11 games to the Angels, how many would still claim that the Yankees were nevertheless the better team?
18. Suppose that the best team in football is merely 51% likely to win in any given game. In a 10-game season, there would be a miniscule – but non-zero – chance (.079%) that the best team would go winless. But even such a miniscule chance is far greater than the chance that a winless team would occupy the top spot in any ranking.
19. Nor is it necessary. There are any number of possible explanations for why a team or player might lose to an inferior opponent that have nothing to do with either team’s skills (e.g., forfeits, ‘tanking’ or ‘sand-bagging’, corruption).
20. To my knowledge, all computer-based rankings assign some basic value for all wins and losses, which in some cases can be augmented by considering the strength of the opponent, the strength of schedule, whether the game was played at home or away, or the margin of victory. Still, even if such values are augmented with further information, the fact that there is some same-for-all basic value attributed to all wins and losses speaks to the fundamentality of the assumption that the winner is thereby better.
21. The inaugural season of the College Football Playoff showed how susceptible human pollsters are to thinking in terms of WIB. In the penultimate week’s poll, TCU was ranked third, ahead of Florida State, Ohio State, and Baylor. That week, TCU demolished Iowa State, 55-3, thereby claiming a share of the Big 12 conference title along with Baylor. But, TCU had lost to Baylor earlier in the season. So despite winning handily, in the final poll TCU dropped three spots, below Florida State, Ohio State and Baylor and out of the four-team playoff. It was as if the CFP committee simply could not bear to rank TCU ahead of a team they lost to when the rankings actually mattered.
22. Temkin (Citation1987). See also (Rachels Citation2001).
23. See Rachels (Citation1998, Citation2001) and Temkin (Citation2012). For a very recent response in defense of TR in moral contexts, see Klocksiem (Citationforthcoming).
24. See Rachels (Citation2001, 217).
25. In 2012, Ohio State went undefeated but was ineligible to play in any postseason games due to sanctions from NCAA rules violations. But for being ineligible, they would likely have been included in the BCS title game over one-loss, eventual-champion Alabama.
26. In 1998, Tulane finished undefeated while a one-loss Florida State team played in the title game. Boise State finished undefeated in 2006, but a one-loss University of Florida team played in the championship game. Most slighted of all is the undefeated 2008 Utah team that watched as both participants in the championship game – Florida and Oklahoma – played with a loss on their records.
27. Here is why: what determines the strength of a schedule is, typically, the collective record of one’s opponents (and sometimes one’s opponents’ opponents). So if A’s opponents collectively have a 20-5 record and B’s opponents have a collective 5-20 record, A’s schedule is significantly ‘stronger’ than B’s. But taking strength of schedule into account at all makes sense only if we suppose TR: beating a ‘strong’ schedule is better than beating a ‘weak’ schedule – why? – because on a strong schedule, one’s opponents are better than their opponents.
29. See Dixon (Citation2001) for a discussion of other factors that might result in the better team’s losing.
30. Chang argues that for any such comparison to be possible, there must be a ‘covering value’ that applies to each object of comparison. Nominal/notable comparisons, she maintains, disclose to us the existence of such covering values, even if they are nameless. See Chang (Citation1997, 33).
31. Parfit (Citation1984, 431). Ruth Chang defends a similar comparative relation – being ‘on a par’. See Chang (Citation1997, Citation2002, Citation2004a, and Citation2004b).
32. Parfit (Citation1984, 431).
Additional information
Notes on contributors
S. Seth Bordner
S. Seth Bordner, Philosophy, The University of Alabama, 336 ten Hoor Hall, Box 870128, Tuscaloosa, AL 35487, USA. E-mail: [email protected]
