Monday, January 3, 2011

BCS vs Playoffs

Rick Reilly with a column on having a playoff in college football.

I agree with him, but not for the reasons he gives.

Reilly seems to think that the point of having a playoff is so that we can determine who the best team is. If TCU won the national championship playoff then it would be the best team.

But would it?

The best counterexample comes from the NFL. In 2007 the Patriots went 18-1 but lost the Super Bowl. The Giants clocked in at 14-6, but were the champions. And no one (oustide the tri-state area) thinks the Giants were the best team.

Indeed, with one-and-done rules for the playoffs it's common for that a team that isn't the best to win the Super Bowl. The 1986 Bears were 14-2 and dominated the regular season, but one down game in the postseason cost them a Super Bowl repeat. The 1976 Steelers didn't win the Super Bowl despite giving up a mere 138 points in 14 games. They may have been the best Steelers team of the decade--better than the four that won Super Bowls.

The key here is that we can't know the team that is really the best. We can just use the rules of statistical inference to infer the best team. We start with our prior beliefs based on who plays on each team, and update them based on who beat who. There is little reason to think that the best decision rule for deciding which team is (most likely) to be the best is to choose the Super Bowl winner. In fact, we know from probabilistic reasoning that most of the time we would be wrong. The BCS process on the other hand sounds like a decent implementation of Bayesian reasoning. If I had to venture a guess, the BCS process might actually find the "best team" more often than a playoff might.

So I'm not sure I agree with Reilly.

But I still support a playoff. It's more exciting.  And sports isn't about finding out who the greatest is, it's about finding out who is the best "on any given Sunday."

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