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Roll (the Random) Tide: BCS By the Numbers

Crunching the numbers of college football

by 1/11/2013 7:54 AM
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What's that old saying? "Don't confuse brains for a bull market"?

So, if you watched that National Championship game the other night, you probably came away thinking two things:

  1. Alabama QB A.J. McCarron has a very attractive girlfriend.
  2. How in the world did Notre Dame make it to a national championship game?

Well, question No. 1 pretty much broke Twitter, with the help of Brent Musburger. Question No. 2, though? There's a Fooled By Randomness lesson in there somewhere.

Let's separate college football national title aspirants into two groups.

On one side, we have the SEC. You can probably make the case that five of the top six teams this year were from the SEC ('bama, Texas A&M, Georgia, Florida and LSU... maybe even South Carolina next, and Oregon's the only interloper). One team is going to emerge from the SEC undefeated, or with one loss, and be almost guaranteed a spot in the title game.

The other group is every other BCS conference school. And here's my case on the randomness that fools us each year. There are going to be 15-20 schools in that group with somewhat similar talent levels. They're all going to play a 12-game schedule that breaks down roughly as follows:

  • Four games with near-100% certainty of winning, generally out-of-division games vs. smaller FBS teams.
  • Four games vs. underdogs who maybe can beat you. Win probability of about 75%.
  • Four toss-up games. Win probability of 50% each.

That projects out to a 9-3 season. But they're obviously not all going to go 9-3; someone's winning all their close games, someone's splitting them, and someone's losing them. The team that goes 11-1 likely has little more actual talent than the team that went 8-4, it just got a couple of breaks.

Let's say we have 20 teams that fit this 9-3-ish profile. But instead of having them play each other, we'll just determine their results by coin flip. We'll award them the four cupcake wins, flip a weighted coin for the 75% wins, and a regular coin for the 50% games. Pure randomness.

The result? Each individual team has a shade-under-2% chance of going undefeated. But there's a 1-in-3 chance that at least one team runs the gauntlet to 12-0. And we read all sorts of hagiographies on that team and their ability to "do what it takes to win," et. al. (OK, we wouldn't have read as many if K-State made it, but that's a different subject).

My point isn't to say that Notre Dame didn't deserve to make the title game, they clearly did. It's just that the sample size is so tiny -- roughly eight contested games -- that we almost can't help but get a somewhat random outcome.

There were 18 teams in BCS conferences not named "SEC" that finished 8-4 or better in the regular season. My point is that many of them could have made a couple more plays here and there and run the table. One other did, in fact: Ohio State, which was ineligible for a bowl game. And another, Kansas State, came within an upset at Baylor.

So, basically, if Ohio State didn't take their bowl penalty this season, they'd have played Notre Dame in a title game featuring teams probably somewhere between 5th and 15th best in the country, while Alabama's third-stringers were routing Louisville in an unwatched Sugar Bowl.

On the plus side, the BCS championship probably would have been a close game.

You'll never really get away from randomness in football results, there's just not enough games, even at the NFL level.

Disclaimer: The views represented on this blog are those of the individual author's only, and do not necessarily represent the views of Schaeffer's Investment Research.


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