Arrow's Impossibility Theorem and College Football

Economics can tell us something about the CFP

Photo by Gene Gallin on Unsplash

I should have known the fix was in. Watching the ACC Championship Game between Florida State (FSU) and Louisville was infuriating. The announcers kept on talking about whether an undefeated FSU team should make it to the College Football Playoff (CFP) over a one-loss Alabama team, which plays in the SEC, the best conference in college football. This made no sense. Obviously FSU, an undefeated 13-0 conference champion from a power conference, would make it into the CFP. Since the advent of a national championship game in 1998, EVERY undefeated conference champion from a power conference has been invited to either the BCS championship (1998-2013) or the CFP (2014-Present). I started yelling at the TV, thinking the announcers were trying to stir up controversy where none existed. But as the announcers continued to talk about Alabama, even more than Louisville, the team actually playing on the field in front of them(!), the truth should have dawned on me. There was no way the SEC would be left out of the CFP.

College football is unique in that the four teams that get to play in the CFP each year aren’t chosen objectively. Because there are so many teams from so many different conferences that never play each other, it’s impossible to have a system similar to professional sports, where the best team from each division automatically is chosen for the playoffs, and a few others are picked based on their record. Every major sports league in the US has around 30 teams, so it’s possible to objectively pick the best for the playoffs. There are 169 teams in the top division of college football, and 69 in the so-called Power 5 (P5) conferences. Instead of using objective criteria, college football has decided that a committee would decide which four teams make it into the playoff every year. It’s not a perfect way to do it, but there doesn’t seem to be a better option.

This year was almost easy. Going into the final weekend, four teams, Michigan, Washington, FSU, and Georgia were all undefeated and from a P5 conference. If all four win, one would have to argue about the ranking 1-4, but I think it’s obvious all four get it in. Four undefeated teams, four slots. Michigan, Washington, and FSU all held serve and won their respective conference championships. Georgia, however, lost to one-loss Alabama. Now there’s a big problem. Assuming Michigan, and Washington, have punched their ticket, who should the third and fourth teams be? There were four options:

1. Florida State. Went undefeated and won the ACC, the weakest of the P5 conferences. Finished 13-0.

2. Georgia. The number-one ranked team all year. They lost their final game, the SEC Championship Game to Alabama 27-24 on a technically neutral field, but one in Georgia. Finished 12-0.

3. Alabama. The dominant college football team over the last 15 years. Their only loss was to Texas 34-24 at home. Finished 12-0.

4. Texas. They won the Big 12 Conference and beat Alabama, but lost to Oklahoma 34-30 earlier in the year on a technically neutral field, but one in Texas. Finished 12-0.

So who should get the final two slots? Here is where Arrow’s Impossibility Theorem comes in. The whole thing is a bit complicated, but here is the summary from Wikipedia:

In short, the theorem states that no rank-order electoral system can be designed that always satisfies these three "fairness" criteria:

• If every voter prefers alternative X over alternative Y, then the group prefers X over Y.

• If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).

• There is no "dictator": no single voter possesses the power to always determine the group's preference.

The key is that no system can be designed that satisfies the “fairness” criteria. In this case, in a vacuum, I think that committee voters prefer FSU to Texas. The former was undefeated, while the latter lost to Oklahoma before winning the conference viewed as the second weakest. However, voters also prefer Alabama to FSU. The former is the conference champion of the best conference, and their only loss came to Texas. That would seem to imply that Alabama>FSU>Texas. But this seems cosmically unfair. Both Alabama and Texas have one loss, and Texas beat Alabama, at Alabama, by ten points! So Texas must be preferred to Alabama. We are now in a contradiction, where Texas>Alabama>FSU>Texas.

The addition of Alabama makes voters change their preference to prefer Texas to FSU. This violates the second criterion above - the addition of option Z (Alabama) reveres the preferences between X and Y (FSU and Texas). This isn’t a proof that Arrow’s Impossibility Theorem holds. It is an example that there isn’t a consistent way to rank the teams. Alabama narrowly beating Georgia shouldn’t have changed the relative ranking between FSU and Texas. But it did.

The result, as every college football player fan knows, is that the CFP committee ranked the teams in this order:

1. Michigan

2. Washington

3. Texas

4. Alabama

5. Florida State

6. Georgia

Poor Florida State dropped from four to five, despite beating a ranked team (Louisville) in their conference championship! This will go down as the most controversial decision in CFP history. There have always been accusations of SEC favoritism in the polls. And SEC fans have always responded by saying, “So what? We’re the best conference. Go undefeated in your piddling conference and you’ll get your chance.” That rule has now been blown apart.

Every argument used by people who support leaving FSU out is specious. FSU failed the “eye test”? So did Alabama, with their narrow wins against Texas A&M and Arkansas. Not to mention their miracle win over Auburn. FSU should penalized because their star QB is hurt? Fine, then why were they still ranked #4 going into the final game? If there’s a hurt QB penalty, it should have been reflected in the polls when it happened. SEC is a better conference than the ACC? On paper I agree, but the ACC had a winning record against the SEC this year! FSU alone went 2-0 against the SEC. Even if these arguments held water, which they don’t, how did FSU wind up behind Alabama and Texas but above Georgia? Any argument that puts at FSU below Texas and Alabama should have also put them below Georgia.

Of course the real answer is money. College football is big business, with billions of dollars at stake. The CFP committee has an interest in letting the biggest teams with the largest fan bases in. For whatever reason, despite all its success and blue-blood pedigree, FSU does not have the popularity of Alabama or Texas. So they got the shaft. Additionally, it’s impossible to look past the conflict of interest that ESPN has. Along with the commentary during the ACC Championship Game, ESPN anchors had been talking for weeks about whether Alabama should get into the CFP. This is a network that has been in bed with the SEC for decades. ESPN runs the SEC network and paid $3 billion for a TV deal with the SEC. Go to SECSports.com, the official website of the SEC. What’s in the top corner? A link to ESPN!

Imagine if CNN signed a deal with the Republican party that said every Republican presidential debate would be held on CNN, and that if a Republican was president, every presidential press conference would be held solely on CNN. Would anyone trust CNN to be an unbiased commentator? Of course not! Yet that’s the exact system we have in place with ESPN and the SEC.

If there’s a silver lining to any of this, it’s that this corruption is out in the open. The majority opinion online is that FSU got snubbed and Alabama was allowed into the playoffs for reasons off the football field. Next year the playoff expands to an unwieldy 12 teams, so any future snubbing will be for a much lower slot. The best hope for FSU is that they beat Georgia in the Orange Bowl and can claim a share of the national championship, especially if there’s no other undefeated team left. Regardless, they got screwed. To quote the Athletic Director of Florida State:

For many of us, today's decision by the committee has forever damaged the credibility of the institution that is the College Football Playoff. And, saddest of all, it was self-inflicted. They chose predictive competitiveness over proven performance; subjectivity over fact. They have become a committee of prognosticators. They have abandoned their responsibility by discarding their purpose – to evaluate performance on the field.