Tuesday, April 27, 2010

Sports Standings and Sample Sizes

Are MLB standings more "accurate" than NFL standings, because of the larger sample size?

In the NFL, 16 games are enough to round out the season and decide which teams make the playoffs. Luck may play a factor in deciding a game or two, but rarely do people argue that horrible teams routinely finish with fluke records like 10-6.

In baseball, the standings after 16 games are pretty meaningless (here's what they were this year). This year, the Dodgers and Red Sox--both perennial powers--had losing records after 16 games, while the abysmal Padres shared the best record in the National League. Of course, 16 games only make up 10% of the baseball season, so it's no wonder why people often disregard statistics from the first month or so of the season (when there are also several players hitting above .400 and several pitchers with ERAs of zero).

Football is a brutal sport, impossible to play at the NFL level every day. But if there were some way to have the teams play 162 games instead of 16, would the final standings differ much from what they are now?

The variance is winning percentages are much wider in the NFL. In 2009, the best baseball team won 63.6% of the time, and the worst won 36.4% (standings). In the NFL, the analogous figures were 87.5% and 6.2% (standings). With enough repetition, would the St. Louis Rams eventually have a winning percentage around 35%? Or does football have inherently less parity than baseball? Or maybe football is played differently because there are so few games; i.e., if the baseball season were only 16 games, I doubt we'd see five-man starting rotations.

For those unfamiliar with statistics, see this page for more on sample sizes. The basic idea is making inferences about the underlying "true" quality of a league's teams. The more games, the better idea we should have about this underlying quality. This requires the rather dubious assumption that the team's quality hasn't fundamentally changed over the course of the season, such as a key player getting injured or a rookie blossoming into a star.

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