Basketball Statistics Blog

Friday Press Clippings:
Diminishing Returns and the Value of Offensive and Defensive Rebounds

From Count the Basket
By Andrew Gelman
Download source here: ' Diminishing Returns and the Value of Offensive and Defensive Rebounds ' by Andrew Gelman

"... The idea behind diminishing returns in basketball is that in some areas of the game, players aren’t just competing with the five opposing players on the court, they’re also competing with their four teammates.

For example, no matter how many shot-creators/high-usage-players/ballhogs a team has, on each play the team can take at most one shot. Assemble a lineup of five players who each typically take 30% of their team’s shots when they’re in the game and something’s got to give. ..."

"... An initial hint that there could be diminishing returns for rebounding comes from the fact that the defense rebounds misses far more frequently than the offense. Last season 73% of missed shots were rebounded by the defense while 27% were rebounded by the offense.

One might be tempted to say that there must be diminishing returns for defensive rebounds - even if a defensive player tried and failed to grab a rebound, his teammates still would have got it over 70% of the time.

But this actually does not follow, and thus the offense/defense split fails to provide evidence for diminishing returns. ..."

"... One might think that this isn’t that big of a deal since coaches take into account a lot more than just rebounding in deciding who to play together. In addition, some coaches might go the other direction and pair up good rebounders to have an even greater advantage on the glass.

And because of factors such as foul trouble, injuries, and roster limitations, ultimately teams are going to give minutes to all variety of lineup combinations.

All of these rationales would seem to mitigate the impact of lineup choices on the marginal value of a rebound, but in reality the impact is large and pervasive because of an obvious but overlooked way in which teams balance their lineups. ... "

"... What’s the upshot of all this research? Are diminishing returns a factor in rebounding? If they are, how large a factor are they? Do player offensive rebounds contribute more to team offensive rebound totals than player defensive rebounds contribute to team defensive rebound totals?

Should players from some positions be credited more for their rebounds than players from other positions? How should rebounding we weighted relative to scoring and other aspects of the game?

I think we can come to some preliminary conclusions for some of these questions. Given the data showing that the slopes for defensive rebounding are consistently lower than the slopes for offensive rebounding, and that defensive rebounding slopes are far below one even when controlling for position, it does look like diminishing returns have a significant effect on defensive rebounding.

I also think it’s definitely worth considering the possibility that rebounds from different positions are worth different amounts on the team level, though one would need to look at a larger sample of data than I did here to establish the different values. ..."

Read more articles in Count the Basket.

To read today's 'Press Clippings' in Spanish, click this week above on the 'Español' tab or afterwards click here: ' Análisis de las Diferencias en el Juego en Función del Género y Categoria de loa Jugadores ' by Ibáñez, S. J.; Feu, S. y Dorado, G. .

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