Tuesday, November 17, 2009

Would a College Football Playoff Be Fair?

The following is a guest column written by two economists on the merits of a college football playoff. This article also appeared in RealClearSports.

By Michael Davis and Tim Kane

College football decides its champion in a unique way that has become somewhat controversial because every other major sport in America uses a playoff. Over time, the sizes of those playoff systems have expanded, making college football stand in ever sharper contrast.

College football crowns its Bowl Championship Series (BCS) champion after pairing the top-ranked two teams in a single game. The top teams are determined largely by expert polls with some input from computer algorithms. The team ranked third often has a semi-legitimate case that it deserved an opportunity to play in the championship game, especially since the BCS formula has been repeatedly tweaked. The issue of fairness is a common attack thrown at the bowl tradition by playoff agitators. But fairness is impossible to measure. Or is it?

Any playoff system requires a cutoff that leaves a single team out. The wider the net, the more arbitrary that cutoff becomes (requiring ever more complicated tie-breaker rules). The result is that any playoff introduces another kind of unfairness. An 8-team playoff gives an arguably weaker team the chance to defeat a squad that was much better during the regular season. That may make for enjoyable entertainment, but it is definitely unfair in its way. The argument is that a playoff cheapens the regular season and all its games.

Professional football in the NFL uses a 12-team single elimination playoff to determine its champion. During the most recent Super Bowl, a team with a 9-7 regular-season record (Arizona Cardinals) played and nearly won. That kind of finale happens because with 32 teams in the NFL, more than one-third make the playoff cut.

And consider professional basketball in the NBA and hockey in the NHL. Sixteen teams are included in the NHL's Stanley Cup playoff - selected from just 30 teams. Likewise, in the NBA, 16 playoff teams are chosen from 30 in the league. Literally below-average teams make the playoffs in those sports every year. Is that fair?

Wide bracket playoffs reward casual play during the regular season. Instead of striving for excellence, the smarter strategy is to avoid injuries, especially during the late season games. Such a structure is one way of defining greatness, but is it the only way?

These kinds of arguments can be had in any sports bar in America. But now college football is under assault, with President Obama suggesting a playoff, and Senate hearings grilling the BCS as "un-American." Now that's a low blow. With all the sports statistics available, it's about time somebody took a look at what's fair using quantitative analysis.

The Fairness Index

Being number crunchers by training, we decided to create the Fairness Index. Our index measures the regular season record of a league's champion against its top team. Let's say the champ has a 12-4 record, while the top-seeded team went undefeated during the regular season, 16-0. That's easy. The fairness index for that league in that year is 75 percent. In another case, the top team might have a 15-1 record and go on to win it all, so the fairness index would be 15/15 or 100 percent.

How do you think the fairness index for pro football compares to college? If you think a playoff is fair, then you probably think they're about the same, right? Not even close.


College Football
97.2 % BCS era
96.3 % Pre-BCS era

Professional U.S. Sports
96.6 % Basketball (NBA)
92.6 % Baseball (MLB)
91.6 % Football

* The Fairness Index measures the average ratio of the champion's regular season record to its team with the best regular season record. For example, the average NFL champion has 91.6 percent as many wins as the team with the best record that year. Each of the professional average includes only the years with the current number of playoff teams.

The fairness index is much higher in college football (97.2 percent) than in the NFL (91.6). The higher level of fairness for college ball was true before the BCS, but is even more true today. Gnash your teeth all you want, but the one thing an NCAA football playoff would not be is fair. By our estimate, it would be about 5 percentage points less fair. Translation: the odds of the best team winning the championship would be 5 percentage points lower.

Critics will point to the fairness index for basketball, which at 96.6 percent is roughly the same as the BCS. The NBA seems to prove that a playoff does not mean a low fairness score. But wait, these are different sports, and the playoff design is critical. Three reasons why the NBA index is deceptively high: its playoff follows a best-of-seven format for each series, better teams enjoy home-court advantage, and scoring is frequent (thus less subject to luck rather than talent). The better question is whether the fairness index would rise or fall outside of a playoff. If only there was a way to test that.

But there is!

Fairness Declines as Playoff Bracket Expands

Consider the problem of "playoff creep." As you increase the number of teams in the playoffs, you increase the likelihood that the best team will not win, since they will face more chances to be upset by an inferior team. Most plans for a college football playoff imagine a small number of qualifying teams, maybe four, maybe eight. That way the regular season would still matter to a great degree, and the top teams would not have to face as many playoff games, pivotal injuries, and possible upsets. Realistically, it is unlikely that the bracket would remain small. History says so. Look at the NCAA I-AA (now FCS) football playoffs. Look at the bloated NCAA basketball playoffs. Look at the NBA and NHL mentioned above. Over the decades, they all suffered playoff creep so severe that the regular season is now little more than a pre-season.

But no case of playoff creep is clearer than Major League Baseball. Once upon a time, the Pennant Race was as hallowed and glorious as anything in Sport, and it meant simply finishing the 162-game season with the best record. Winning the World Series was icing on the cake, sure, but it wasn't the cake. Only the team with the very best record in the regular season won the Pennant. Period.

Until 1969, the best team in the American League won its pennant, same for the best team in the National League. That was what determined the two - two! - teams that made it to the World Series. And winning the pennant wasn't just some kind of cheap semi-final for the Series, it was an achievement all its own. From 1969 to 1993, the same logic applied to four divisions. Then in 1995 they converted to a full-blown 8-team playoff, complete with wild cards.

Guess what happened to fairness? Playoff creep in Major League Baseball is associated with a clear decline in the fairness index, from an average of 97.5 percent up until 1968 (the highest in our data), to 95.5 percent when the playoff was introduced, then 92.6 percent when the playoff bracket was expanded after 1984.

A College Football Playoff?

The playoff creep that occurred in those sports is almost certain to hit college football, and with it, a decline in fairness. Again, lower fairness scores with bigger playoff systems means without a doubt that more teams with worse records will get crowned champion than before. It's happened in other sports, which the data proves.

The consequence is that regular season records will not matter. The difference between the BCS and NFL average fairness index is equivalent to one less win in a season. One way to interpret that is that a single loss will essentially have no consequence on a team's chances to be recognized as champion. In other words, every game in the regular season will be not only less important than it is now, but unimportant. There is no question that a playoff would reduce the importance of the regular season.

Famous games such as the series of Florida State-Miami games in the early 1990s would be changed from elimination games in the National Championship chase to warm-ups to possible future play-off matchups. Those games would still have appeal to fans of those teams but would lose their appeal to much of the nation.

College football is unique, though many wish to change it and end its traditions. College football has a more important regular season than any other sport. And because of that, college football has rivalries that maintain their intensity while those of other sports fade. The one knock on college football has long been that its championship crown just isn't fair. But now you know the real story.


Michael Davis, Ph.D., is an Associate Professor of Economics at Missouri University of Science and Technology and can be contacted at davismc@fidnet.com. Tim Kane, Ph.D. is an economist at the Ewing Marion Kauffman Foundation and can be contacted at tkane@kauffman.org. {These view are their own.}


Jason said...

This is interesting, but isn't the underlying issue that there's no way to tell how "good" that 16-0 record is in the fairness index? (Or maybe I missed something.) Like SEC teams can play no one out of conference, then say they play a good schedule because they have the best conference. Which may or may not be true, but how would you ever know?

(Not to pick on the SEC, but I just noticed who Florida was playing this week. Obviously--as others have pointed out--the smart money is to not play anyone decent out of conference. What did Ohio State gain, after all, by losing to USC?)

Anonymous said...

A playoff is the only "fair" soution! Top eight bcs teams! The best of both worlds, and let's be real the bcs is about money and a lot of it. Bcs games act as the playoff games now there's more meaning to the games which means more money! Not that it matters either way the sec will always rule! Geaux Tigers!

AdamT said...

I think one thing the authors of this article failed to touch on is the fact that there are so many more college football teams than there are in the other leagues mentioned. With a college football playoff system, a regular season loss would still be much more debilitating in college football than in any other league.

Paul said...

As pointed out by Jason, the article completely ignores one of the biggest reasons in favor of a college football playoff: the fact that not all CFB regular seasons are equal. If team A plays a 12 game season with only 1 or 2 challenging games, while team B has 6 or 7 tough games and loses two of them, would it really be an "unfair" result if team B came out on top over team A in a playoff? Not really. That, and that fact that unlike the pro sports you mentioned, it's common for multiple teams in CFB to end up with undefeated records. In CFB, a team can come out on top of every game it plays and still never have a chance for the national title. The author of this article apparently got so excited about their idea for a fairness index that they forgot to examine whether that measurement actually made sense in context.

Indivision said...

I'm sorry but I have a hard time finding any merit in this article at all.

First, they try to measure fairness by one calculation that may or may not have anything at all to do with what is fair. What if a team lost a few early games due to injury but, by the end of the season was clearly the best team in the league? Would it be fair to keep them out of a championship game because another less competent team is undefeated and played a weaker schedule?

The authors have no business creating that formula and then moving on to make statements comparing the fairness of leagues as if their formula captures it.

Second, "fairness" isn't even the heart of the problem. The reason that other sports have play-offs that ALMOST NOBODY complains about is that it removes or at least greatly diminishes subjective judgments from determining a champion. When a football player runs across the goal line, the rules say it's a touchdown. The rules don't say that a couple of poorly selected journalists should confer and decide whether or not it counts as a score. A play-off is natural to the sport because it relies on objective rules the same way that the actual game does.

Third, the argument that a play-off would remove the significance of regular season games is bogus and bordering on fear-mongering. There would be over a hundred teams competing for a small number of play-off spots. There would undoubtedly still have to be a seeding process dependent on formulas and possibly (hopefully not) human polls. Regular season games would continue to matter a lot and there is absolutely no reason to believe that a play-off would have any impact on the intensity of rivalries. Rivalries seem to do just fine in NCAA basketball with a play-off system.

College football is not "under assault". The crap-fest BCS which is much, much younger than "college football" is. How could college football be "under assault" due to the majority of college football fans completely rejecting the current BCS system?

Ute Fan said...

I can't believe I'm reading this. The "fairness" index measures how likely the team with the best record will be the one to win the championship. Thus a system is only unfair if it crowns a team that has a worse record than the best record in the league. So if there are multiple undefeated teams, it doesn't matter which is crowned, the system would be considered 100% fair. Come on! You've got to do better than that. Why not just post the 1 + 1 = 3 proof. What a joke.

The one thing that this article implies that is correct is that we already have a playoff. It's a playoff that only seeds two teams. Before the BCS there was no playoff in the bowl system (unless you got lucky and the 1-2 teams met in a bowl).

By their argument you would have expected no playoff to be better than a two team playoff, which even their own data doesn't support.

I'm all for a discussion about fairness of the BCS vs a playoff, but we'd need to find a much better definition of fair.

Clark said...

2 points that this article absolutely fails to address:

First, other professional sports leagues play a much more representative schedule. NBA teams play every other team in the league twice and every team in their conference 4 times. (There are a few exceptions.) Even NFL teams play 16 games against 31 possible opponents, and within divisions teams have about 10 common opponents. To have a better record than someone else really does mean something. College football has 12 games played against 119 possible opponents. Many programs only play 11 FBS opponents. Having a better record is much less meaningful.

Second, what's the fairness index for a team that goes undefeated but is left out of the playoffs? It is ludicrous to claim that college football is 97% fair when it is possible to go undefeated and not play for a championship. You can go ask Auburn, Utah, Boise State, TCU, and Cincinnati about that.

Jacob said...

I would like to second the comments left by Indivision, Ute Fan, and Clark.

What an absurd article. The author creates a metric, entitles it "fair" and twists it to support his predetermined conclusion that the B_S system is somehow more "fair" than a playoff system.

The author's whole underlying metric is based on the erroneous assumption that the B_S polls are in of themselves fair to begin with--which it is not. But even if the polls were somehow able to "fairly" determine who should be number one and two, the fact that the teams with the best records do not always play for the championship shows the glaring inconsistency in the author's article.

The article is self fulfilling garbage.

mike said...

If you look back at previous years and consider how many teams were really in the argument for being in the BCS I think it's quite clear that 2 is not enough, while I think 8 is too many. I don't think we should turn this into a search for a Cinderella team by including clearly inferior teams and giving them a chance (see George Mason). Typically there are in the end only 3-4 teams that have a legitimate claim to being in the top spot. A 4 team playoff (add one bowl game) would be sufficient. It gives teams a little room for error/injury (one loss and you can still work your way in IF you have a good schedule).

I don't think a matchup of top schools is going to diminish at all. And if we make sure only one team from each BCS conference can go (and one team from the non-BCS AQ pool which can be re-evaluated if needed) then conference championships still matter too.

This year's lineup could be Florida/Alabama, Texas, TCU, and whoever finishes next highest.
2008: Oklahoma, Florida, USC, Utah
2007: Ohio State, LSU, Virginia Tech*, and Oklahoma*
2006: Ohio State, Florida, USC, and Louisville
2005: USC, Texas, Penn State, Notre Dame*
* lost non-championship BCS bowl

A pretty good balance with mostly BCS winners. If you start teams that didn't win their conference (a necessity for 8 teams) then it really dilutes the regular season.

I personally don't think a team like TCU or Boise could make it to the top 4 in a big time conference but if they manage to beat 2 other conference champs, I'll give all the credit in the world to them.

Paul said...

A 4 or 8 team playoff would still be too small...all that does is make it impossible to take risks with scheduling (and does college football really need more Florida/The Citadel games?) and lean heavily on the ability of polls to correctly sort out which conferences get a team in the mix. 12 teams would probably be adequate, but if you're going for 12 you might as well do 16.

Anonymous said...

The jealousy of the 'have nots' as opposed to the 'haves' is as clear as day based on the responses... everyone complains when UF or Bama plays FIU, where are all the complaints for TCU and Boise playing San Jose State ? The truth is this article is probably dead on... what a sham ! If UF played Boise's schedule this year or even TCU's, you know they wouldn't lose a game.

Xeifrank said...

Comparing college football or any college sport to a professional sport playoff is apples to oranges. How many Div I teams are there? How many pro football teams are there? How many games does each play? Apples vs Oranges!!!

imho, NOT having a playoff makes the college football regular season games less meaningless. In most seasons there are only a half dozen or so teams that have a shot at the Natl title game halfway through the season. In most cases, one loss and your season is over with and none of your remaining games mean anything. With an 8 team playoff, you can lose a game and still feel confident that if you win your remaining games you will control your own destiny for a National title.

I am for and have devised an 8 team playoff system that takes into consideration a teams BCS Ranking and if they won their conference. To me, it would be more fair and much more exciting than what we currently are stuck with.

vr, Xeifrank

Anonymous said...

I'd really like to point some criticism at BCS GURU! This article is so laughably misguided that the only reason to include it on your site is due to a) nothing else better to write or b) a hope that you rile up the readers ala shock radio hosts on a hot topic. You're better than that. You TYPICALLY have very unique AND insightful commentary. This article may be unique....but certainly not insightful.

couldge said...

So let me get this straight. Right now the regular season in college football is so great because every game matters. What about Florida (the team currently ranked #1 in the BCS) playing Troy, Florida International, and Charleston Southern. 3 games that definitely mean a whole lot of nothing.

The way to give the regular season more importance would be to have a playoff that

1) Only allows conference champions to enter (analogous to the NL, AL pennant champs). This would make every conference game mean something even through the end of the season. Let's face it - if you can't win your conference you have no business in staking a claim to the national championship.

2) Rewards teams that take risks in their non conference schedule in scheduling quality teams through a seeding process. Sure some teams might still schedule a preseason game like Charleston Southern but how is that any different than the way it is now?

Overall - I believe that a playoff would increase fairness.

Anonymous said...

Hey couldge,
what about TCU playing New Mexico, Texas state, San diego State, UNLV, Wyoming, and colorado State. There are at least 20 FBS teams that could have gone undefeated playing TCU's schedule. and there are probably 40 teams that could have gone undefeated playing Boise's schedule.
TCU may be a top 10 team but the whole Mtn West is a joke conference. 5 out of 9 of your teams are in the bottom 25% of teams and airforce is barely average. Plus Utah and BYU always schedule one FCS and Utah State (another crap team). It must be nice having 8 gimme games every single year.
But you all keep complaining that Florida schedules two gimme games each year. Your whole conference is a joke.

couldge said...

Hey anonymous (November 18, 5:45):

I never argued that BYU or Utah had a tougher schedule than Florida. Nor did I ever claim that the Mountain West Conference was better than the SEC. Although, I don't think you can argue that the MWC is a joke with 3 teams consistently ranked in the top 25. And by the way neither BYU or Utah scheduled an FCS team this year.

My point was that under the current system there is an inherent incentive not to schedule tough teams. For both AQ teams (Florida) and non AQ teams (Hawaii in 20006).

And which 20 teams do you think could have gone undefeated playing TCU's schedule? Although you may be correct - we'll never know. I bet TCU could have gone undefeated playing Florida's schedule. Again, we'll never know.

So why not let them duke it out on the field?

PeteP said...

Anonymous at 5:45: Since only one team in the nation has defeated Clemson at home, I do not think you even understand the difficulty of TCU's schedule. Moreover, TCU has defeated 3 currently ranked teams, two by blow-outs.

How many currently ranked teams have Florida, Texas, and Alabama combined defeated: 3 schools (LSU twice,so 4 total wins).

Florida's schedule was almost as bad last year --- they played two decent teams and lost to won at home....

TCU would be undefeated with the schedule of any of the so-called big three....

The current BCS system encourages cupcake scheduling, which is why Florida does it. Previous versions did not, which is why back in 2002 everyone, including Florida, played tough OOC schedules.

Of course, in 2002, the two teams that had performed the best against the toughest schedules, USC and Georgia, were not only excluded from the BCS title game, but were prevented from playing each other in the Sugar Bowl. As much as I liked the Ohio State-Miami Fiesta Bowl, neither team had played nearly as hard of a schedule as USC or Georgia, nor had either team won as many games against good teams.

But the BCS is a mere beauty contest, not a national championship. And a fraudulent one at that....

Peter said...

First off, economists wrote this? I have a bachelors in Econ, with an emphasis in econometrics (using econ tools to analyze stuff), and I see no use of econ here. All the authors did was see if the team with the best regular season record was crowned champion, regardless of other factors. A one variable metric is so vulnerable to conflation that it is worthless as a measuring tool. Once the authors take into account things variables such as opponent's winning percentage, margin of victory, etc., then the analysis will be more 'fair', separating out the one-loss-by-one-point-in-overtime teams from the one-loss-in-a-blow-out-because-of-their-own-ineptitude teams.
This article ostensibly ignores the fact it explicitly states: sometimes winning a football game can come down to nothing more than luck. The wind blows a field goal wide right; the referees don't have a good enough view on the replay to overturn a dubious call, etc. To be undefeated in football is extremely difficult and means that you've played your games so well that you've taken luck out of the equation, usually by dominating your opponents to the point where a blown call doesn't end up mattering.

As for what one anonymous poster said, I'm bothered by it. He or she said that a team such as Florida should be able to schedule vastly inferior teams because other teams also have a weaker schedule. This is the classic race to the bottom. Ostensibly, Florida and other top teams could easily handle middle and upper-middle tier teams with as much ease as the lower tier opponents they are playing, but they chose not to. Why? Because everyone else is doing it. College football needs a system (be it playoff or otherwise) that rewards (a) playing the most difficult schedule you can and (b) playing well against that schedule. This will increase competition and the quality of play faster than rewarding teams for playing lesser teams "because everyone else does it.” If the top team really is the best, they shouldn't be trying to simply be a hair better than the #2 team, but put enough distance between the #1 and #2 (by difficult scheduling) that there is no reasonable question that they are, indeed, the number one team in the country.

Twisted Logic said...

One mistake the author made was that it's starting from the conclusion and working backwards. You can't say that the team with the best regular season record deserves the crown (regardless of what anyone else has done), and then say that a loss in a playoff is unfair. If they really were the best team, wouldn't they have won the playoff AND the regular season?

If you're really interested in fairness, don't separate the playoff analysis from the regular season analysis; who ends up with the best record? A team who lost twice in the regular season and didn't make the playoff, or a team that lost once in the regular season and then lost once in the tournament. Both are two loss teams, but due to when the loss comes (could even be to the same teams!) one team is rewarded better than the other.
The flipside: a two loss team wins the playoff, a one loss team loses in the playoff, giving it a total of two. Who really had the better season and record?

Anonymous said...

Florida has a Sagarin SOS rating of 51. Alabama has 41. TCU has 60. Iowa has played a schedule tougher than all three, at 40.

Way to go with the 'tough' schedule, SEC.

Anonymous said...

maybe the solution is to put a greater significance or weighting on the strength of schedule.

I guess one challenge though is a team cannot control the strength of others within the conference. Last year Texas played all those ranked teams in a row. This year most are not ranked.

one issue I do have is conferences with split divisions. SEC/Big 12 and big 10 since everyone doesn't play everyone else (11 teams)

the pac 10 probably is fairest in that they play 9 conference games.

Of the teams in there, it's interesting to think that Oregon St has played a pretty tough schedule- all 9 pac 10 games plus Utah and Cincy.

Come to think of it Oregon played Utah and Boise. USC scheduled Ohio State.

Florida played.....oh never mind.

So one of the things I would like someone to comment on is how to handle the strength of schedule argument when a team loses.

So if Oregon had beat Boise St, they are probably in top 4 or so. Since they lost to a #4 team, it really hurt them. So losing to a ranked team was much more a detriment than having played Delaware Machine Shop College and winning.

So I guess the problem still is, if a team plays solid opponents and takes a loss, it doesn't payoff. Why not schedule cupcakes?

not sure if a playoff would be any fairer though. I like that each week means something. I like that we have these debates.

I think if anything we need to stop ranking teams in preseason before a game is played. If Tcu and Boise were ranked 1 and 2. They would still be 1 and 2 until they lost period. That seems to be the biggest issue. So before a game was played, someone hypothetically in thin are decided one team was better than another.

So what are the action steps?

Don't rank teams until end of week 1.
Increase strength of schedule weighting in bcs
use strength of opponents in two ways
strength of schedule period.
for wins, strength of opponent defeated.

comments? thoughts?? suggestions? ideas? lets hear em!

Ben Wiles said...

Fairness isn't about outcome; it's about opportunity. What you do with your opportunity is on you. Whether you get an opportunity at all is on the system.

That said, Arrow's Theorem states conclusively that any system that relies on compiling human opinions to reach a "fair" outcome is mathematically impossible. No matter how "fair" you try to make it, somebody will always find a way to screw something up.

Yes, the system is flawed. Yes, better systems are out there. But let's abandon the pipe dream that a perfectly "fair" playoff system exists in any sport.

kyle said...

Alright, sorry, but i think the fairness index your calculating is wrong. Upsets make things interesting, and if a team gets upsetted, hey guess what, they dont deserve to be in the championship game. The best team shouldnt always win, we need upsets to keep things interesting, i mean, how boring would it be if the same team won the championship every single year. Itd get boring quick. Now, how many unbeaten teams each year get left out in the bcs national title game? Dont get me started. Calculate that into your fairness level. Each year normally two undefeted teams play each other, thats why the fairness level is so high. Now, another reason why these teams normally go undefeated is because of there cake schedule. And i think a top 12 team bcs title game would be fair. Normally a team has one loss, they played a bad game, now, give that team another chance to prove themselves. Itd be nice, and itd add FAIRNESS to the system. All i have to say.