Sunday, March 02, 2008

Defensive rebounding stats: barely meaningful?

Back about a year ago, I suggested, following similar arguments by King Kaufman and others, that The Wages of Wins "Win Score" overvalues rebounds by assigning 100% of their value to the specific players who grab them. I argued that rebounds are the result of team play and positioning, and you shouldn't just credit the player who grabs the ball. As Guy put it in the comments to that post, first basemen make many, many more outs in the field than third basemen, but that doesn't mean they're better fielders. They just happen to be assigned to the spot where the ball often goes.

Since then, there have been some additional research to support that idea. Here's a couple that I found.

First, a couple of months ago,
Guy posted these results on the "Wages of Wins" site:

-- the correlation between RB/G for a team’s top rebounder and RB/G for the other players on that team is -.76. Clearly, many of the RBs by the top rebounders are just taken from other players. (As TG notes, we don’t see this in baseball.)

-- the SD for RB/48min at the player level is around 3.8, but at the team level is just 1.4. It’s actually lower at the team level! (If each player’s rebound opportunities were independent of his teammates’, then the team SD would be about 8.5, or 6 times as big.)

Clearly, these results show that the NBA's top rebounders are simply taking opportunities that other players would be getting in their absence. I think Guy's findings are pretty convincing.

If you want more, check out these two blog posts by Eli W., of "Count the Basket." In the second post, Eli looks at the empirical data a different way. He finds cases where the five men on the court have, overall, above-average rebounding stats, and cases where they have below-average rebounding stats. If players weren't taking opportunities from their teammates, you'd expect that when five "20% better than average" rebounders are on the court, they should still each be grabbing 20% more defensive rebounds.

It turns out that they don't. Only a very small part of their statistical profile remains when you put them together. Looking at Eli's graph, it appears than when, based on their individual stats, you expect 80% rebounding, you get only 75% rebounding. When you expect 61% rebounding, you get 70% rebounding. No matter how good (or bad) your players look on paper, based on their individual defensive rebounding stats, when you put five of them together, you get much closer to average rebounding than the naive observer would expect. Again, this suggests that individual statistics in this category depend more on opportunities than on skill.

What's interesting is that this doesn't apply to *offensive* rebounding. On the offensive side, there is a bit of an effect of diminishing returns, but not very much: if your five players snag offensive rebounds at a combined rate of 32% (rather than the league average of somewhere in the high 20s), they won't actually hit that 32% -- but they do come in at about 31%.

So it looks to me like if you want to credit individual players for their offensive rebounds, you won't be too far wrong. But if you do the same for *defensive* rebounds, you're going to be very inaccurate.

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