My Problem With PER

From a chat with John Hollinger:

Mike (Chicago)
I know you love PER, but it’s YOUR made up stat. Why should fans trust it when clearly our eyes can tell us that D Rose is playing way better than Paul and when PER doesn’t account for how a player has to play when teammates are hurt?

John Hollinger
I trust you reached this eye test after watching all the Hornets’ games too?

Everybody’s right here. As Hollinger says, statistical measurements are absolutely necessary. You can’t watch all the games or distinguish by eye between a 91% free throw percentage and an 87% free throw percentage.

But it’s also true that Hollinger’s PER formula is an oddly arbitrary mix he dreamed up one day. I think you can easily see this my trying to total PER up and ask what the resulting number is supposed to be. PER, after all, is an individual stat representing a per-minute quantity. So if we take a player’s PER and multiply it by his minutes played, we’ll get that guy’s PERMinutes. Then we can add up all of a team’s PERMinutes and we get . . . what?

The idea of a system like Dave Berri’s “wins produced” is that if you add up all the “wins produced” of the individual 2009-2010 Los Angeles Lakers you get a number that’s approximately equal to the total wins of the Los Angeles Lakers. People can (and have, and do, and should continue to) raise questions about whether the Berri formula is accurately allocating credit for these wins to individuals, and also can (and have, and do, and should continue to) raise questions about the predictive value of these quantities. But there’s no question of what’s being measured. By contrast, what happens when I add up the 2009-2010 Lakers’ PERMinutes:

What is this supposed to be a model of? If you calculated the total team PERMinutes for each time, would the resulting quantities have a strong correlation with team performance? If so, I’d love to see Hollinger work up the spreadsheet.

But I have my doubts. For starters, by definition the average player has a PER of 15. And if you take the Lakers’ aggregate PERMinutes and then divide them by minutes to get a measure of the quality of a statistical construct “Laker,” the team turns out to have a 15.73 PER—just slightly above average. But the team in question won 57 games and the NBA championship.