### 2.07.2006

## Considering statistics in a relative context

In the past, I've ranted on about sports announcers and writers using statistics that really don't mean much.

This postseason, NFL fans have been clubbed over the head with the statistic that Bill Cowher is 100-1 or somesuch in games in which the Steelers take a lead of 11 points or more. Now I'm willing to believe that Cowher is good at teaching his teams to sit on a lead, but how good is the average coach with a 11-point lead? 80 percent? 90 percent? 95 percent?

A related gripe is when analysts invariably talk about "keys to victory" for each team. Avoid turnovers. Don't get into foul trouble. And so forth.

Well, duh. Leaving aside correlation vs. causality for now, of course these things are keys to victory. Avoiding turnovers is good (provided your offense doesn't become too conservative). Staying out of foul trouble is good (provided you don't start playing matador D). It's much more important to weigh these things relative to each other. ESPN had a nice couple of articles on these sorts of truisms in football a while back, showing that some factors strongly correlated with winning, others not at all.

Sports media types need to ask, and figure out, which of these factors are more relevant than others. Is it more important to shut down Dwyane Wade or Shaq? (My bet would be on Wade.) How much blitzing is too much, and in which situations? (Blitz more on 1st-and-10, not as much on 3rd down or when the QB is in shotgun, and almost never on 3rd-and-long is my guess.)

Sites like Football Outsiders and 82games do a good job of asking these sorts of questions, and it's unfortunate (if unsurprising) that major media outlets, despite their greater technological and statistical resources, have writers and announcers who can't make use of them.

This postseason, NFL fans have been clubbed over the head with the statistic that Bill Cowher is 100-1 or somesuch in games in which the Steelers take a lead of 11 points or more. Now I'm willing to believe that Cowher is good at teaching his teams to sit on a lead, but how good is the average coach with a 11-point lead? 80 percent? 90 percent? 95 percent?

A related gripe is when analysts invariably talk about "keys to victory" for each team. Avoid turnovers. Don't get into foul trouble. And so forth.

Well, duh. Leaving aside correlation vs. causality for now, of course these things are keys to victory. Avoiding turnovers is good (provided your offense doesn't become too conservative). Staying out of foul trouble is good (provided you don't start playing matador D). It's much more important to weigh these things relative to each other. ESPN had a nice couple of articles on these sorts of truisms in football a while back, showing that some factors strongly correlated with winning, others not at all.

Sports media types need to ask, and figure out, which of these factors are more relevant than others. Is it more important to shut down Dwyane Wade or Shaq? (My bet would be on Wade.) How much blitzing is too much, and in which situations? (Blitz more on 1st-and-10, not as much on 3rd down or when the QB is in shotgun, and almost never on 3rd-and-long is my guess.)

Sites like Football Outsiders and 82games do a good job of asking these sorts of questions, and it's unfortunate (if unsurprising) that major media outlets, despite their greater technological and statistical resources, have writers and announcers who can't make use of them.

### Comments:

here is a related blog entry from a professional sports bettor. (november 30, 2005)

http://weighingtheodds.blogspot.com/2005_11_01_weighingtheodds_archive.html

http://weighingtheodds.blogspot.com/2005_11_01_weighingtheodds_archive.html

Learn to use HTML tags, dammit.

The axiom about leading after the first quarter is really just a manifestation of the arcsine law, which states that for a random walk, the probability density function for the time of the last zero-crossing is at time t is 1/(pi sqrt(t(1-t))), which becomes infinite at t=0 and t=1. It's called the arcsine law because its integral, the cumulative density function, is 2/pi times arcsin(sqrt(t)).

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The axiom about leading after the first quarter is really just a manifestation of the arcsine law, which states that for a random walk, the probability density function for the time of the last zero-crossing is at time t is 1/(pi sqrt(t(1-t))), which becomes infinite at t=0 and t=1. It's called the arcsine law because its integral, the cumulative density function, is 2/pi times arcsin(sqrt(t)).