My last post had a lot of info, but was short on a few details. This post is going to fill in at least one of the holes.
Guy asked for the specifics on predicting WP48 from other box score stats. He also asked that position be accounted for. The WP info is from the automated site, so some players have mixed positions. If I take them out to avoid relabeling those 400ish players (it’s the holidays after all, and I didn’t expect to be on the computer this much), I still have 449 players in the past two years. I ran a regression predicting WP48 from three pointers made, two pointers made, free throws made, missed field goals, missed free throws, offensive rebounds, defensive rebounds, turnovers, steals, blocks, assists, position, and position interactions. Those are all the variables that are listed on the website I linked to for calculating WP, and the position and position interaction terms should account for what Guy asked for. All variables except for position are set to per-36 minutes and normalized to Z scores.
Center is first alphabetically, so it got set to baseline. There are 11 variables and 4 position comparisons to center, so there are 44 interaction terms. Only ten are significant (and an eleventh is marginal, p=.088). One of these involves rebounding; small forwards get reduced WP48 credit for offensive rebounds compared to centers. The other negative values (suggesting that centers get more credit) are on blocks for power forwards and point guards, missed field goals for small forwards and shooting guards, and free throws for power and small forwards. On the other hand, power and small forwards get more credit for two pointers, small forwards actually get more WP48 points for turnovers, and shooting guards get marginally positive credit for missed free throws. In all it’s a confusing picture, and I think tied to the fact that there’s a position adjustment already in place that is being taken apart in crude fashion. Also, all these interaction effects have significance values in the .001 to .08 range, whereas all the main effects have values of 2 x 10 (-13) or smaller. On the whole, I don’t think anyone could claim that WP48 gives tall players more credit for rebounds. But, for completeness, I’ll post the interaction info in a comment on this post.
I ran the model again leaving position in but taking all the interactions out. The R squared only dropped .0066 (from .979 to .9724), so the interactions weren’t buying us very much. The regression equation is WP48 = -.597+.423*3PM+.435*2PM+.191*FTM-.492*FGMiss-.108*FTMiss-.228*TO+.123*BLK+.353*AST+.477*ORB+.465*DRB +.337*PFor+1.01*PGuard+.846*SFor+1.11*SGuard. So if a player was completely average, he would have the lowest WP48 if he was a center (-.597), followed by power forward (-.26), small forward (.249), point guard (.413), and shooting guard (.513). Of course, these positions don’t produce equal amounts of the different stats; that’s why there’s a position adjustment (the different positions in my sample have roughly equal WP48, as it should be; centers are actually 3rd of the five positions numerically). Otherwise what we see is that missed field goals is the ‘primary’ driver of WP48, with a weight of -.492. This is followed by the two rebounding variables (.477 and .465) and made two and three pointers (.435 and .423). Keep in mind that all these values are on scaled variables, so a player would increase his WP48 by the values listed if he increased that statistic by a standard deviation.
Summary: I ran a regression predicting WP48 from all the variables that go into it, along with position adjustments. Position didn’t seem to interact with the variables in any meaningful way, and not particularly with rebounds (if this interaction is a sign of overweighting something, it appears that centers might get too much credit for blocks). Looking only at main effects, the biggest weight is placed on missed field goals (if a player missed 2.23 fewer field goals per 36 minutes, his WP48 would go up by .492). Rebounds do indeed follow next (getting just over two more of either kind of rebound would increase WP48 by about .47), and made shots are the last two variables with weights over .4 (WP48 would go up by about .43 if a player made 1.86 more two pointers or .89 more three pointers).
These weights only differ over a range of .06, so the effects aren’t that different. Let’s say a completely average player dropped his missed field goals as described. His scaled WP48 would move from 0 to .492. We convert it back to regular WP48 by multiplying it by the standard deviation (.2079) and adding the average (.05) to get .152. Doing the same thing for offensive rebounds, defensive rebounds, made two pointers, and made three pointers, you would get WP48s of .149, .147, .140, and .138. If each of these players played 2000 minutes, the range would cover 5.75 to 6.3 wins, so not big differences. So I think that shooting efficiency and rebounding are about equally weighted by WP48, although three of the top five variables are related to scoring.