Bears-Saints and small sample size

There's a basic principle in statistics known as small sample size error. It means if you don't have enough data, your can't draw conclusions that are accurate. If you ask five people who they're voting for in an upcoming election and four pick the same candidate, you really can't conclude anything much less that "80% of voters support Smith".

An individual sporting event and thus single elimination tournaments like the NFL playoffs suffer from the same fate, which is why you rarely see the best team win the NCAA basketball championship. Over the course of the 16-game season, it's pretty easy to conclude that the Bears are better than the Dolphins and the Saints are better than the Redskins. But when they met on the field, the teams that will be playing on Sunday both lost.

I already wrote my thoughts on the game. I think the Bears have a 60-65% chance of winning. The national view is pretty interesting. On ESPN, all eight of their experts picked the Saints to win though their computer picked the Bears. In their unscientific poll, about 61% of the voters have picked the Saints (though of course that's popularity as much ability). When people have to put their money where their mouth is though, the Bears are still 2 1/2 point favorites.

The truth (as much as one can divine truth from subjective data) is that the teams are close. Those that favor the Saints overlook some of their weaknesses, like being 10-6 against weak competition, a negative turnover ratio and having to play on the road, while playing up the Bears weaknesses like Grossman's wide variance and the Bears defense having fallen off the past few weeks. I think there's also the destiny and "great story" card in play here. It's just the opposite for those who favor the Bears.

Come Sunday, one team will win and one will go home. But, and here's the interesting part, because it's just one game, the people who picked the losing team weren't necessarily wrong in their analysis. It's possible the game is a blowout and the backers of the team that loses really say "oops, we were wrong". But the likely outcome is a close game where the "fans" of the winners say "I told you so" and the losers claim the better team didn't win or got unlucky. (While as fans we hate to admit it, luck plays a huge role in the outcome of a game -- we're a couple of "lucky" breaks away from this game being the Cowboys and Eagles; the total margin of victory in the four NFC games so far is 10 points.) And really we have no way of knowing if team X won because they were better or if this time was the 30-40% of the time the lesser team won. While the outcome will determine the NFC Champion, I don't think it will change many people's minds on the two teams involved.