Chad is bemoaning the increase of “stat-geekery” in sports:

I’ll admit that I’m somewhat torn about this. I am, after all, a professional nerd, and enjoy working with numbers, so I can see the appeal of quantitative data. And a lot of the regular statistics used in basketball are pretty crude measures, so I can understand trying to develop better statistics.

Very, very crude. And that is where my beef comes from. Can you think of a sports’ statistic that includes a measure of error?

Statistics as a field studies the distribution of random variables, which means considering both a measure of location (like an average) and a measure of dispersion (like a standard error). I cannot think of a single statistic in common use in sporting which involves an estimate of error.

The use of “statistics” in sports has long been an argument for the secret numeracy of Americans. After all, if people can memorize the batting averages for the entire 1993 Yankee organization, surely they have the ability to balance a check book, or to appreciate Fermat’s Last Theorem.

The problem is that memorizing a bunch of averages tells you nothing without some measure of variability. Knowing that one pitcher’s ERA is higher than another’s is only interesting if the range of variation intrinsic in pitching is smaller than the difference between ERAs.

Even worse than that casual misuse of statistics is the bizarre use of conditional probability without justification. “Joe Schmoe has a .342 batting average against left-handed pitchers over 200 pounds with runners on second.” Is there any statistical basis for thinking that the player bats differently depending on the pitcher’s weight, where the runners are, or even whether a runner is on base? If not, there’s no statistical reason for slicing up the probabilities like that.

Statistics and the measurement of error, is an important part of life in the 21st century. Presenting statistics without any assessment of error limits their utility, and enforces unhelpful ways of thinking about measurement with error.