Sample Size in Football

Posted on January 9, 2007 by

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Colorado State is the National Champion

Playoffs in football are the perfect example of an extremely small sample. Last night Florida defeated Ohio State – and according to the Associated Press – this game proves that Florida is the best team in college football.

But on October 14th, Florida lost to Auburn by ten points. So I guess this means Auburn is the best team.

Wait a minute… before we crown the Tigers we should note that Auburn lost to both Arkansas (by 17 points) and Georgia (by 22 points). Georgia, in turn, lost four games this year. One of these losses was to Vanderbilt (by 2 points), who lost eight games in 2006.

If we continue with the story we see that one of Vanderbilt’s losses was to Alabama (by 3 points), who lost to Mississippi State (by 8 points), who lost to Tulane (by 3 points), who lost to Southern Methodist (by 5 points), who lost to North Texas (by 18 points), who lost to Louisiana Tech (by 3 points), who lost to Fresno State (by 7 points), who lost to the alma mater of the authors of The Wages of Wins, Colorado State (by 12 points).

Yes, if we follow the trail, our 4-8 Rams are truly the National Champions in college football. In fact, adding up the scores of these games and we see that one should expect the Rams to defeat the Gators by 120 points.

And this is why we won’t see this game. Who wants to see a game where the difference between the teams is 120 points? But even though we will never see the Rams trounce the Gators, we now have conclusive evidence that the Rams are the true National Champions this year.

You can probably do this same step-by-step process and argue that any team – that won at least one game this year – is truly the National Champion. Perhaps the voters should have just given the title to Boise State, who deserves the title for winning the most memorable game of this past season.

The Wild Card Weekend in the NFL

The Wild Card QB Score Ranking

For those who are interested, the above link will take you to the QB Score ranking for the first weekend of the playoffs in the NFL. Like what we see in college football, playoffs in the NFL also suffer from too small of a sample. With a sample of one, we really are not able to determine who the “better” team is (or is not). Still, you go with the sample you have, not the sample you would like to have.

The Wild Card weekend “proved” that Tom Brady can’t be stopped in the playoffs, while Peyton Manning cannot play when the games matter most.

Okay, one game doesn’t prove anything. Still, of the eight starting quarterbacks this past weekend, Brady posted the highest QB Score. Peyton Manning was the 7th best, finishing behind his brother. Despite playing badly, Peyton’s team won and his brother’s lost. So Eli gets to watch his brother continue on in the playoffs next weekend.

The lowest ranked quarterback from last weekend was Trent Green. In the discussion of the final QB Score ranking for 2006 it was noted that Damon Huard – Green’s back-up – was the fourth highest rated signal caller this last season. Green did not qualify for the rankings. Had he attempted enough passes, though, he would have ranked as the fourth worst quarterback in 2006. So the Chiefs substituted the fourth best quarterback with the fourth worst. Again, as noted earlier, Green has historically been a very good quarterback. He just wasn’t in 2006 in either the regular season or his one playoff game.

One final note on the playoffs: Tony Romo finished with the second highest QB Score last weekend. If we treat his failure to hold on the field goal attempt as a turnover (which it basically was), his QB Score drops to 22. This mark only exceeds the output of the Manning brothers and Green. Again, the playoffs are a very small sample and one play can cost you a game, and your standing in the QB Score rankings (the latter being the most important issue). Of course that’s not going to stop me from ranking the players and talking about all this as if it truly means something.

– DJ

Posted in: Football Stories