APBRmetrics

[Ed Küpfer]

Using almost three complete seasons' worth of stats, I regressed individual player rebounding % against team rebounding %, for offensive and defensive rebounding. To qualify, players must have had at least 800 rebounding opportunities (both OR and DR) for a single team in one season. (Thanks to Roland for the data.) There were 994 players in my sample. Here's what they looked like:



Note the slope for each regression line -- it is four times greater for offensive rebounds.

Explanatory note for statistics newbs: the "regression line" is the line of best fit, which serves to explain as much of the relationship between the two variables (player OR% vs team OR%) as possible. The "slope" is the angle of the regression line. In the first graph, the slope is 0.2462 -- for every 1% increase in player OR%, team OR% increases by 0.2462%.

I divided up the sample into four different groups based on player height, each group containing about 250 players. You can see that for each group, the slope for the OR% line remains about 4 times greater than the slope of the DR% line.






The only way I can interpet this is to say that each player has a greater impact on his team's OR% than he does on the DR%. I read the results as saying that each percentage that a player adds in OR% has four times the impact as he does for DR%.
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ed

[Mike G]

Nice work, Ed !

It does indeed support the idea that if player A doesn't get the DR, teammate B or C is likely to get it. But only one player (or none) has a chance at a given OR.

Your "impact" conclusion might be open to a bit of interpretation. If an OR-attempt is analagous to a steal-attempt, might there be an opposite "impact" by going for and missing an OR ? That is, a potential positive effect on offense might have a negative impact on the defense. In other words, the guard who was crashing the offensive glass -- coming up empty -- wasn't back to cover his man at the other end.

Coaching/playing style varies enough from team to team, that it's plausible OR are less common and more difficult because some teams see even greater value in getting back on D. It's not hard (or rare) to get back on D, but it is essential.

[gabefarkas]

i agree with your interpretations, and have an additional one of my own:

guys that are "supposed to rebound" (taller than 6-foot-7) have less of an impact than rebounds from guys who are shorter. almost like those are bonus rebounds in a way.

[jkubatko]

Ed,

Based on your sample data, do all of the population regression lines have slopes that significantly differ from zero?

On a few of those plots (for example, offensive rebounding percentage for player 6'5" to 6'7") there are some highly influential observations. I would guess the removal of the two observations on the far right-hand side of the plot I mentioned would have a dramatic effect on the parameter estimates.
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Regards,
Justin Kubatko
Basketball-Reference.com

[Ed Küpfer]

[gkrndija]

Interesting graphs. Does that mean defensive rebounding is less sloped because it's more of a function of the various opposition rebounding philosophies than their own ability?

Also does rebounding% factor in FTA/FGA or missed FT's? For example, Utah is a half court team and likes to play very slow. Yet, they send the other team to the line more than any other team in the league. As a result they not only get more easy boards, but because of their slow pace these gimmes receive abnormal value. Coincidently, they are one of the better rebounding teams.

At the other end of the spectrum, Phoenix plays ridiculuously fast but they are the "worst" at sending the other team to the line. As a result, they get very few freebies, while also having these "rebounds" count for an abnormal value. Have they been getting a raw deal on the defensive glass?

[Ed Küpfer]

[gkrndija]