Phil has a couple of new posts on rebounding. In his initial post (the first link), he ran a regression using the number of rebounds a team’s centers get per game to predict how many rebounds the rest of the team would get per game. He found that there is a negative relationship between center rebounds and rest of team rebounds. I thought I would contribute some more stats.
I got the same data that Phil did, also entered manually. I reran his rebounding analysis and got some slight differences, but nothing that big; they could be due to a typo here or there. Here are the coefficients I found if you predict rest of team from each position, with the standard error in parentheses: center-.695 (.15), PF -.677 (.182), SF -.729 (.291), SG -.643 (.34), PG -.874 (.303). You’ll notice that if you add and subtract twice the standard error to get the usual 95% confidence interval, the estimate for each position contains -1 (except for centers, where it’s very close). For this reason, I’ll add more data to the analysis by running the regression on every player instead of breaking it out by position. I get -.968 (.0327). So in general, each rebound gathered by a position takes a rebound away from the rest of the team.
When I got the data, I also entered the other count variables listed, which were FGA, FTA, assists, blocks, turnovers, and fouls. Here are the numbers from the same analysis for assists: centers -.557 (.2976), PF .062 (.359), -.968 (.241), SG -1.015 (.252), PG -.692 (.122), all players -.939 (.0452). You get some differences across positions that I think are mostly noise; I would be surprised if someone can come up with a good reason why power forwards don’t have diminishing returns with their assists but every other position does. Just presenting the all player numbers, here are FGA -.787 (.083), FTA -.62 (.109), TO -.211 (.15), blocks -.805 (.0797), and fouls -.687 (.0996).
Like Phil, I also looked at the standard deviation for team stats per game and the same stat at the player level. Phil was surprised that centers had more variability than teams did, although I’ll admit I’m not entirely sure why. I have the same team data I’ve used before, which covers 10 years. I find that not only do centers vary in rebounding more than teams do, but this is also true for point guards and assists.
Given the acceptance Phil’s analysis got in his comments, I think these results should be pretty uncontroversial. We might be able to do a little better, as in Phil’s second post, by using some percentage values instead of per-game values. The reasoning by Phil and his commenters was that since defensive rebounds have a coefficient of about .7-.8, they should be worth .2-.3 rebounds at the player level; offensive rebounds have a coefficient of maybe .5 (hard to tell with it broken out by position), so they should be worth about .5. Under this logic, at the player level I would give a player .2 credit for assists, .4 for FGA and blocks, .5 for FTA and fouls, and .8 for turnovers. For example, since so many assists are just assists stolen from teammates, a player should get very little credit for the ones he gathers in the boxscore.
For the record, let me say that I don’t believe any of this. I think there’s a better explanation, but I need more data to check it and don’t have the time to enter more seasons by hand. If anyone wants to help out, let me know.