## December 11, 2009

### College football playoffs

Since Congress and the President are taking positions on a college football playoff system, it must be time for Econbrowser to weigh in as well.

I want to suggest first that the purpose of a playoff cannot be to determine the best team in the country. I say that for two reasons. First, there is no such thing as the best team in the country. Different teams have different strengths and weaknesses that will match up differently against different opponents. In any given game, anything can happen. In 2007, for example, Appalachian State beat Michigan who beat Florida who beat Kentucky who beat the supposed national champions LSU. So you've either got to declare Appalachian State the best team in the country, or drop your insistence on transitivity.

Second, if you do believe in such a thing as the (probabilistically) best team in the country, the more teams you put in the playoffs, the less likely it is that the best team ends up being declared the champion. Suppose for example that there's a team that with 80% probability would win its game against any other team that might make the playoffs. With a single championship game, that superior team gets declared the champion with probability 80%. With a 4-team playoff, the best team must win both its games, the probability of which is (0.8)(0.8) = 0.64. With an 8-team playoff, the best team is only going to be declared the champion about half the time.

I therefore suggest that the primary purpose of the system is not so much to determine "the" best team as it is to bring enjoyment and satisfaction to the fans. Granted, the proposed playoff games themselves would do that very well for the handful of teams and games that get included in the playoffs, but at the cost of subtracting from the excitement of the 30 or so other post-season games that would have to be diminished as a result. Of course, the parties with a vested financial stake in those other games are for that precise reason opposed to the playoff idea, and that opposition is the main reason it hasn't yet happened. But if you took the objective to be to maximize the economic surplus of all the post-season games combined, I say you'd want to stick with a system like the present one. The lobbying power of those vested interests is precisely a lobby on behalf of maximizing total economic surplus.

But whatever you may think of the merits of a college football playoff, doesn't it bother you to see the U.S. Congress acting as if it's the nation's ruler on this matter?

It does me. Which is why I wrote this.

Posted by James Hamilton at December 11, 2009 06:44 AM

digg this | reddit

Arguments over BCS, playoffs, and Congress all serve the same purpose: entertainment. Some are drama, some comedy, but it's all fodder for the Daily Show.

Posted by: Dave Backus at December 11, 2009 07:04 AM

From a probability standpoint, it could end up being much lower than what you suggested because offensive-defensive matchups from one game to the next can significantly affect the chances of a team winning or losing, not to mention injuries, etc. A playoff sounds appealing in theory (sports theory) and could eventually work; however, the fact that Congress is getting involved only because Joe Barton (TCU) and Orrin Hatch (U of Utah) are p-o'd that teams from their district/state have been left out of the BCS title game the last couple of years should bother anybody with a pulse.

Posted by: BL at December 11, 2009 07:06 AM

"doesn't it bother you to see the U.S. Congress acting as if it's the nation's ruler on this matter?"

Now you have upset me.

Posted by: Walter Sobchak at December 11, 2009 07:33 AM

It starts with JB condorcet and finishes with Arrow ?

Posted by: ppcm at December 11, 2009 07:50 AM

Why would the other 30 games be diminished?

Currently, 1 bowl game decides the 'national champion' and the other 30 do not. 2 teams play for the championship, 60 other teams play games but have no chance of winning the big prize.

How would this change under a playoff?

An 8 team playoff would mean 7 playoff/bowl games eventually decide the champion and 27 do not. 8 teams play for the championship, 54 other teams play games but have no chance of winning the big prize.

If the other 54 teams have their fun diminished....how on earth are they enjoying their current bowl game?

As far as the economic surplus goes, you just kind of snuck that in there without any justification. The parties with current vested interests might lose out under a playoff system, but someone else would gain. They arent arguing against a playoff because the total economic surplus would be diminished, they are arguing against it because their payday might be diminished.

If you propose a change where 1 guy loses \$10 but 10 people gain \$10 each....that 1 guy is going to argue against it regardless of what the total economic change looks like. Why would he care that in total everyone is better off?

I dont know if that is the case with a playoff, but stating that "lobbying power of those vested interests is precisely a lobby on behalf of maximizing total economic surplus." is clearly false. They are lobbying on behalf of their economic interests, they dont care about the size of the total pie, just their slice.

Posted by: jason11 at December 11, 2009 07:52 AM

Wow, in one post, you almost changed my mind.

However, football is a team sport and to be the "best" you need to be the "best" over multiple games. Hence, in a playoff system, not only are you tested physically in a single game, but also your teams emotional and psychology is tested by having to stay "up" week after week. I think the real problem is the amount of time needed to recover and prepare for a game. You're really pushing it to play two games in a week.

Even in your mathematical example, if a team has an .8 probability of winning, the second best team may only have a .75 chance, the third best .7, and hence their probability of winning the tournament declines over multiple games even worse.

I cannot, however, touch your economic analysis.

Posted by: Anonymous at December 11, 2009 07:58 AM

James - I think the purpose of a playoff is not to try to identify some difficult to define "best" team, rather its purpose is to crown a "champion" which is quite a bit different. The New York Giants were the NFL champions in early 2008 after defeating the Patriots who may have been the best football team ever. But it was still a satisfying result (maybe not to New England fans) because a victor was identified on the field, playing the game.

There are two primary elements about college football that cause dissatisfaction:

1) Lack of objectivity - the teams are chosen to compete for the title. This is why the BCS incorporates the "computer" rankings - to impart a veneer of objectivity to the process. What should be obvious is that this merely elevates the the subjective biases of the computer programmers, though with the virtue of seeing those biases applied consistently.

2) Not everyone has a chance to win. Indeed, a team has to build a reputation over several years to have its great season recognized with a chance to play for the title.

A playoff described by Dan Wetzel at Yahoo! Sports, modeled after the college basketball system seems so trivial to implement and a definite gusher of cash for the colleges, it's truly puzzling to wonder why it hasn't happened. Invite all 11 conference champions and 5 at-large teams, play it out over 4 weeks.

Clearly every team on the first day of the season has a chance to win and the subjectivity only comes in to play in deciding between the 5th and 6th at large team. Most years this is going to be deciding which team is about #11 or #12 which is a lot lower stakes call than between who is #2 and #3 as in the current system.

I'm a Texas Longhorn alum so I know how it is for the system to work both for and against you. My interest in the topic is more curiosity about why an inefficient system survives against such simple and obvious improvement. I wonder if there's a connection to our health care debate?

Posted by: Trevor at December 11, 2009 08:22 AM

Every minute they spend on this is one not spent screwing up something else. We should all write letters to our congressmen calling for more steroid investigations.

Posted by: Mike at December 11, 2009 08:53 AM

Maximizing total economic surplus?!?!? Clearly spoken by someone who has not researched the history of college football's postseason or knows anything about the bowl system. No one watches 90% of the bowls that are every played. Only fans of those teams.

Who is going to watch Iowa State play Minnesota in the battle for mediocrity? No one outside of the bowl location or the states of Iowa or Minnesota. Add a playoff and this doesn't change in any way, shape or form. You can still have the bowls and a playoff. Use Dan Wetzel's plan. Frist two weeks of December are the first two rounds. Next two weeks are the bowl games. New Years is the semi-final games, one week later is the championship, same timeline as now.

Every other division of NCAA football has a playoff that works just fine. There's absolutely no reason not to implement a playoff. More money to the schools, more fans watching more games, and an objective way of getting a champion.

Posted by: College Football Cafeteria at December 11, 2009 09:43 AM

"Suppose for example that there's a team that with 80% probability would win its game against any other team that might make the playoffs. With a single championship game, that superior team gets declared the champion with probability 80%."

But what if that superior team with an 80% chance of winning is only correctly put in the BCS championship game 75% of the time (left out 20%). Then the proability of the superior team winning the national championship is only .6. With the playoff system, the team with the highest probability of winning a single game will still have the highest probability of winning the playoff. Besides that, the bracket pools would be AWESOME! (which I guess is part of that entertainment value)

Posted by: Tim Haab at December 11, 2009 10:05 AM

Oops...that should be "left out 25%."

Posted by: Tim Haab at December 11, 2009 10:06 AM

Clearly the education that the players should be getting isn't as important as the cash a playoff system would generate.

Posted by: Dave at December 11, 2009 10:13 AM

Good analysis but, why shouldn't Congress rule on this, they have obviously expanded to the point that they are expected to satisfy every single issue any single constituent might imagine. I agree with Mike, the more time they might spend on matters such as this, the better off the rest of us will be. I think we need a new permanent committee assigned to this task. I suggest we rename the global warming committee since their task is virtually complete now. The EPA has taken the baton. If we can convince Ms Boxer that there are votes to be had and that her constituents are demanding action on this front, then who knows, we might be able to afford to heat our homes next winter.

Posted by: Hitchhiker at December 11, 2009 10:42 AM

I have very little to add but have very much enjoyed the debate which reminds me a lot of the book I am currently reading: "Drunkard's Walk"

All I can say with great confidence, is that I am delighted to see us debating in December college football play offs as opposed to how best to bailout the world economy and financial system.

Posted by: David J. Mayer at December 11, 2009 10:46 AM

So, we appear to have a case of non-governmental, non-market failure. We have an academic market failure. College football should have had a play-off series years ago. The failure of academia to provide a market-demanded (I am demanding it on behalf of the market) play-off clearly shows...well, I'm not sure what it shows, but we need a play-off anyway.

That Congress has finally acted demonstrates the utility of this august institution.

Posted by: Steve Kopits at December 11, 2009 11:16 AM

One nice thing about reality is that we never do know who the (probabilistic) best team is. So we don't have to worry about the hypothetical one with the 64% chance of winning.

In fact, the best playoff proposals (notably: brian@mgoblog's pet proposal) are sort of like self-fulfilling prophecies because the winner of the playoff will, by design, have the best-looking resume when all is said and done.

This deflects potential controversy in two ways: the teams get to decide it "on the field" and the champion is almost always the team that would have been #1 in a vote or computer analysis anyway.

In other words, at the end of the season, the probabilistic best team (by any measure we have available to us) is, ipso facto, the team that won the playoff.

Posted by: Rob L. at December 11, 2009 12:16 PM

I don't know much about Congress and football, but after much study in Mark Oristano's book, A Sportscaster's Guide to Watching Football, I have learned just about everything else. I think I will be able to finally enjoy watching the game with my boyfriend now.

Posted by: Melissa at December 11, 2009 12:52 PM

From an economic standpoint, the problem seems to me to be that the colleges/system only get 12 or 13 games to earn a return on their investment -- obviously too short a season. A solution would be a 32 team playoff. That way they get an extra 5 weeks of football, and they could have the championship the week before the Super Bowl. (This might also put the Pro Bowl out of its misery as a worthwhile side effect). In this system we would cut out much of the dead (unprofitable) time before "March Madness". My plan does leave in a couple weeks to run the Winter Olympics.

Posted by: scott s. at December 11, 2009 01:32 PM

Trevor for president!
Yes keep them on football and off of economics for as long as possible.

Posted by: Anonymous at December 11, 2009 01:53 PM

People should be much more upset about the thousands of kids that enrich academics and TV networks for a distracted tenure at crap classes and a lifetime of often crippling injuries.

But they aren't. They don't care.

Posted by: j6p at December 11, 2009 06:06 PM

"But whatever you may think of the merits of a college football playoff, doesn't it bother you to see the U.S. Congress acting as if it's the nation's ruler on this matter?'
I dunno - college football plays an important role in alumni contributions, and this particular market transcends local jurisdictions. So maybe there is a congressional role in setting rules for it.

Posted by: don at December 11, 2009 06:15 PM

Let's see:

Our government teaches us how to wash our hands.
Our government tells us what toilets we can and cannot buy.
Our government passes out condums to our kids.
Our government uses our tax dollars to pay for their sex (Max Baucus just the latest revelation)
Our government tells us what tv we must buy and what tv format is the best for us.

So what is so wrong with the "nanny state" telling us how to watch sports games?

Professor, I bet you believe they take over \$100K per year to deal with unemployment, national security,economic prosperity, and such. Come on, the only reason we exist is to pay for their entertainment - oh yes, and we must always show them that we love them or they will take away our toys and send us to bed early.

Oh, you are so such a silly boy!

Posted by: RicardoZ at December 12, 2009 04:39 AM

I think your analysis of "the" best team is flawed. With a playoff there is a clear criteria for a team to meet to be called the best team: Get to the playoff and then win all your games. In college football what do you tell the Utah players last year that went undefeated or Boise State, TCU or Cincinnati this year? Win all your games and then depending on the whim of the voters you may be able to compete for the championship game.

So a playoff is not just for the fans. Either ways I agree that it's not the government's business to meddle in college football.

Posted by: Anonymous at December 12, 2009 09:23 AM

Remember, there is no problem that can't be solved by simply coming up with a new inflation index.

Posted by: Cedric Regula at December 12, 2009 11:38 AM

JDH: "So you've either got to declare Appalachian State the best team in the country, or drop your insistence on transitivity."

While this makes perfect sense in the context of your discussion, it's also *great* deadpan humor - it conjured up images of a mathematicians Tea Party, with placards protesting the proliferation of ill-formed equivalence classes, non-normal topological spaces, etc.

Posted by: Robert Bell at December 12, 2009 11:51 AM

Where does it say in the Constitution:
"Congress shall make no law respecting ... college football playoff systems."

It doesn't! So Congress should most certainly take over this subject. What took them so long???

:)

Posted by: David at December 12, 2009 12:09 PM

I was really for adding a playoff system for most of my life, then I started to learn about win probabilities and advanced statistics for sports, and then I became oddly (maybe a little begrudgingly) grateful of the BCS, which works to counteract the chaos of a playoff bracket (see: March Madness -- I think it's called "Madness" for many good reasons).

Great critique, Mr. Hamilton! Now, if only Congress would instead of collegiate sports worry about (or become informed and concerned about) -- oh, let's say -- economics...

Posted by: Brad at December 12, 2009 01:42 PM

(a)A seeding system changes your example materially & improves the ex ante odds of "the best team" winning the tourney.
(b)Conference champions for the Big 10, Big 12, ACC, & SEC are not determined by round-robin play within their own conferences and are, therefore, not even "the best," when they have the best conference record, within the limited set of their own conference. A playoff system built from conference "champions"--a necessary practical ingredient of any proposal--and at-large teams would at least need a reasonably definite conference champion. But, last year's Big XII South illustrated that currently there is not even a definitive on-field-determined champion for conference sub-divisions. Rationalized play-off structures may need to start with conferences, their size, and their regular seasons. Otherwise all current NC debates can be recast at the conference/sub-divisional level logically prior to any NC play-off structure.
(c)Consumer surplus arguments are so cute, aren't they? The surplus adds up weighted marginal utilities, wherein those utilities are themselves entirely ordinal and thus incapable of addition, and uses for weights the current income distribution.

Economists would do well to abandon all pretenses and abolish "normative economics" arguments of persuasions, including Pareto optimality concerns as well as consumer surplus. The inherent non-transitivity issues in such arguments are legion: Pareto optimality is not per se desirable, only the social welfare function optimum is; otherwise Pareto inferior positions can be--pick your cardinal utility measure & assume "egalitarian" distributional weights--quite "socially" superior to a given Pareto optimal set.

Economists desirous of making normative arguments--and with currently so little to show on the positive economics score--are in no position to throw stones at Congressmen who prefer NC discussions to substantive legislative activity.

Posted by: d4winds at December 13, 2009 09:03 AM

Yeah, all those other sports have it wrong. Duh

Posted by: ricky at December 14, 2009 06:50 AM

A playoff system for DIV 1 will take over as soon as the college presidents can make more money from the playoff system, than from the existing bowl/BCS system. Everyone else, including congressmen, sportswriters, and economists are just bystanders.

Posted by: MarcoGator at December 14, 2009 12:11 PM

If enforcing playoffs on Div 1A does not bring you a true champ, then March Madness should be dissolved and just have the top two teams play for it all.

The only one who is going to suffer is the fat cat like (Bill Hancock, the BCS executive director). Bowl games will still be around with the playoffs. The teams that are hot towards the end of the season will continue to play until they lose, without weeks of idle.

Point being it doesn�t matter how a playoff system comes about as long as it does; after all, it takes your mind of off the economy.

How long before Bill Hancock (BCS) implements a playoff system??????

Posted by: Wrong at December 15, 2009 02:48 PM

Trevor has it. The purpose of a playoff is not to pick the best team, it's to give every team a chance to be the champion.

For som-- *most* teams, no matter what they do on the field, they CANNOT win the championship. What other sport is this the case in?

Boise State could win every game by 200 pts and however unlikely manage to be the unanimous #1 team in both coaches and Harris polls. Even so their computer ranking could easily be tied for 6th (as they are now) and they would finish behind a consensus #3 and not get in the title game (100 + 100 + 78

That is about as big an absurdity as you can get and a playoff corrects it. Howver a playoff doesn't seem in the cards for the near future so I'll offer something more likely and almost as good based on the ncaa hoops idea of "bracket buster" midseason matchups.

Of course it would be called something way cooler like "The Gauntlet". Here's how it would work:

(1) every team that wants to be in the title hunt (i.e. every team) leaves 2 games in mid November open, one home and one away.

(2) Now after the first week of November we've had 10 weeks of football, 9 games for most teams which leaves time for the traditional end of the season rivalry game and the conf championships.

(3) The home-away schedule is preassigned to allow presale of tickets with TBD opponent and is seeded on previous years performance to minimize the probability of all the top teams having home games assigned the same week.

(3) The first priority of the matchup formula takes the lowest ranked undefeated schools and matches them up with the highest ranked major conference school possible.

(4) After that, schools that are not competitive for the title games can be matched up with a combination of geography and record to minimize expensees.

(5) Polls and computers are removed from BCS. The ranking formula is simplified as follows:
(a) Team A with X losses is ranked ahead of Team B with X+1 losses.
(b) If Team A and B have the same number of losses, the Team with higher Strength of Schedule is ranked higher. {If SoS is equal the Team with more Wins is ranked first. If Wins are equal the team with higher net of Points Scored less Points allowed is ranked higher.}

Posted by: Steko at December 16, 2009 07:06 PM

I am a BYU football fan and I know that if any team in our conference is undefeated we still we have no chance to become the national champions. Utah in 2008 went undefeated and still had no chance to become national champions. It happened to TCU this season and they have no chance. That's why we need a playoff system.

Posted by: Person at January 3, 2010 05:42 PM