Nice work, Eli. I had some similar data I was going to post on the old WOW thread, but it seems like a better fit with your work now. The results are generally quite consistent with yours and Ed’s, I think, and show an enormous diminishing returns effect.

I looked at rebounds by position, using 2006-07 data from 82 Games, and compared it both to rebounds at the other 4 positions on the same team and net rebounds for the team. Using positions rather than individual players has some advantages: MP is constant and it largely eliminates the good-rebounders-get-paired-with-weak-rebounders issue you raise. To deal with the underlying position differences, I converted the position values into rebounds above/below average for that position. So I get 150 “X” values, where X reflects the extra/fewer rebounds a team got from a given position.

Looking first at straight rebounds (position-adjusted), we see a negative correlation coefficient of -0.49 between one position’s rebounds and the team’s other positions. And regression indicates that for each additional rebound at a position, the other four positions lose 0.65 rebounds on average. If we look at the team total, each rebound at the position level translates into .27 team rebounds.

However, this actually understates the diminishing returns, because the shared rebounding opportunities (determined by pace and FG%) will tend to create positive correlations both among the five positions on a team and between a team and its opponents. So let’s look at the real benefit to the team, defined as rebounds above average (Reb - .5*(Reb + OppReb)). Now we find that for each additional rebound gained at the position/player level, the team gains only .18 rebounds. In other words, WP and Win Score are crediting rebounds at more than 5 times their actual value.

Following Eli’s lead, I also looked at Reb% by position, again normalized by position. Since we’re now controlling well for opportunities, we expect to see a stronger relationship between position and team rebounds, and we do. But still, each additional 1% from a position increases team Reb% by only 0.25. (And decreases the Reb% for the other 4 positions by 0.75).

Clearly, this analysis is leaving out two potentially important dimensions: OReb vs. DReb (it seems clear that ORebs result more frequently in a real gain for the team), and differences by position (it may be that player Reb totals are more meaningful at some positions than others). But I think this helps set overall values, which coefficients for specific rebound types or positions should then be consistent with.

Finally, the player SD for position-adjusted Reb% is .014, and at the team level is just slightly higher at .016. This also tells us that there must be a huge negative correlation among teammates. If each player’s rebounding was largely independent from that of his teammates, the team SD would then be sqrt(5*.014^2) = .032, or twice as large as it in fact is. (I think I misstated this gap as being much larger in an earlier post, because I had failed to control for player position, but the inter-dependence point stands).

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Eli: one thing you might consider is position-adjusting or height-adjusting your data. This gives you much larger samples for your regressions (though at the cost of learning about position/height differences).

There’s more discussion of this post in this thread:

http://sonicscentral.com/apbrmetrics/viewtopic.php?t=1641

Cherokee_ACB pointed out another study by Ed Küpfer that I had forgotten about which looked at the relationship of player to team rebounding by position:

http://www.sonicscentral.com/apbrmetrics/viewtopic.php?p=8433#8433