SC occasionally likes to pick on ESPN for their laxity in the editing of any reference to scientific thinking (i.e., Bill Walton, theoretical physicist extraordinaire). This time, their NFL writer Len Pasquarelli comes under the gun for a classic tautology allowed to slip through as reporting.
In trying to explain how coaches take different approaches to how many plays to give their starting quarterbacks in the preseason, Pasquarelli commits a gorgeous piece of statistical reasoning:
Just four quarterbacks worked 100 or more snaps. Two of them, Young and the Cowboys' Tony Romo, are entering their first full seasons as starters, having opened the 2006 season as understudies. The Raiders gave Daunte Culpepper 105 snaps as they tried to determine whether to make him their starter. The only starter to post 100 or more snaps for a second consecutive preseason was Patriots veteran Tom Brady, who's about as well established in his starter's role as any quarterback in the league.
On the flip side, five quarterbacks worked fewer than 50 snaps in the preseason, and half the projected starters fell below the league overage [sic -- should be "average"] of 73.0 snaps.
A handy table of the number of plays run by each starting quarterback is provided at the end of the article. It crossed SC's mind that Mr. Pasquarelli might have meant that the average of all quarterbacks who played in the preseason was 73.0, and that half of all starters took fewer snaps than that, which would be an interesting indication that coaches were protecting starters (albeit not necessarily a statistically significant one, but hey, one step at a time). So just to be safe, your host plugged the numbers into his calculator -- twice -- and voila! 73.0 is most definitely the average of the starters. It would be a tedious, not to say difficult, task to track down the figures for all quarterbacks, but SC suspects that this didn't happen when the story was prepared the first time around. Rather than end this post with some sort of zinger, SC has decided it's time to be an agent for change -- so he e-mailed ESPN's ombudsman, and will post any reply that he gets.
UPDATE: ESPN's Le Anne Schreiber graciously responded:
Unless math has changed since I was in school, half of any sample is below the median by definition. More or less than half could be below the mean average, depending on the range and distribution of numbers in the sample.
Of course, it has been a long time since I was in school.
Le Anne Schreiber
And she's right, of course. Which just goes to prove that it's good to remember which average you're talking about.