Height Matters
Posted: Sun Jan 07, 2018 3:29 pm
By Nathan Sliver
Editor sevenfortyseven.com
There has been a lot of debate around the league lately about height, which means it is time for us here as sevenfortyseven to crunch a bunch of numbers. It has been well established that the new draft classes are shorter (see excellent article here viewtopic.php?f=7&t=5799) so naturally my next question was, so what? What are we going to lose by having shorter players in the league? Is height a legitimate competitive advantage or disadvantage?
Tackling questions of this nature require comprehensive techniques because there are a lot of things that affect a players performance. As such I went to the old standby, multivariable regression to test the relationships between height and traditional performance measures. This allowed me to control for player attributes related to the outcome of interest, athleticism, year, and player. This allows me to make estimations based on a counterfactual, e.g. if I took 1995 Jamal Mashburn and made him one inch taller what would the effect be on his rebounding? All estimates below include controls for year, player, athleticism attributes, minutes, and weight. Keep in mind that the the adjusted R squared values for all of my analysis below are above 90%, meaning that my controls account for over 90% of the variation in outcomes. In other words, there isn't too much else going on that explains these statistics. Also note that all estimates shared in the report are statistically significant at the 0.01 level.
Points
Control Variables: Scoring attributes, position
The estimated marginal effect of one additional inch of height is .477 [Confidence inteval (CI): (.175,.779)]. In other words, one additional inch is worth about half a point more per game give or take a quarter of a point. To put this is perspective, the marginal effect of the inside scoring attribute is about .179, meaning that one additional inch is worth about 2 and a half inside scoring attribute points. Another way to look at this is that a 6'4" point guard will score about 2 points more per game than a 6'0" version of his clone.
Rebounding
Control Variables: Rebounding attributes
Height should matter for rebounding, right? If you throw in all positions, it doesn't. But if you limit the sample to just power forwards and centers it does. A lot. I think this is because rebounding at the other positions really isn't a function of height but probably relies mostly on individual player attributes, team game plan, etc. When it comes to trees hanging out around the rim though, height is an advantage. The estimated marginal effect of one additional inch of height is .453 [CI: (.118,.788)]. In other words, one additional inch is worth about half a rebound more per game, give or take a quarter of a point. To put this is perspective, the marginal effect of the defensive rebounding attribute is about .04, meaning that one additional inch is worth about 11 defensive rebounding attribute points. Another way to look at this is that a 6'10" power forward will snag about 2 rebounds more per game than a 6'8" version of his clone.
Steals
Control Variables: Defensive and steal attributes, position
The estimated marginal effect of one additional inch of height is .074 [CI: (.055,.093)]. In other words, seven additional inches ares worth about half a rebound more per game, give or take a quarter of a point. To put this is perspective, the marginal effect of the steal attribute is about .02, meaning that one additional inch is worth about 2.5 steal attribute points. Not a huge effect here but remember that the league leader in steals averages 2.9 a game so we're working on a smaller scale here.
Assists
Control Variables: Passing attribute
I wasn't sure about this one but thought I would try it out. Ish Smith and D-Rose (2 PGs of importance to me) are about even on assists. They have similar passing attributes and play on similar quality offenses but Derrick Rose is three inches taller. Buuuuuttt, he also shoots way less and probably, therefore, passes more. For this one I limited the analysis to just point guards. The estimated marginal effect of one additional inch of height is .557 [CI: (.244,.896)]. In other words, one additional inch is worth about half an assist more per game, give or take a quarter of a point. To put this is perspective, the marginal effect of the passing attribute is about .089, meaning that one additional inch is worth about 6 passing attribute points. Another way to look at this is that a 6'4" point guard (Ricky Rubio) will complete about 2 assists more per game than a 6'0" version of his clone.
Blocks
Control Variables: Defensive and Blocking attributes
Height should matter for blocks. They just should. For this analysis I once again limit the sample to big men. The estimated marginal effect of one additional inch of height is .554 [CI: (.353,.756)]. Note the tighter confidence interval for this one. That means that this estimate is more precise than the others. In other words, one additional inch is worth about half a block more per game, give or take a quarter of a point. To put this is perspective, the marginal effect of the blocking attribute is about .045, meaning that one additional inch is worth about 12 blocking attribute points. Another way to look at this is that a 6'10" power forward will block about 2 more times more per game than a 6'8" version of his clone. This is a monstrous effect size given that the league leader is averaging 3.9 blocks per game. It is a little hard to stomach. Look at Arther Hardie and Wilbert Brown. Same blocking attribute score, both on bad teams, both can't jump. But one is 6'9" and the other is 7'0".
TL;DR version: height matters.
Editor sevenfortyseven.com
There has been a lot of debate around the league lately about height, which means it is time for us here as sevenfortyseven to crunch a bunch of numbers. It has been well established that the new draft classes are shorter (see excellent article here viewtopic.php?f=7&t=5799) so naturally my next question was, so what? What are we going to lose by having shorter players in the league? Is height a legitimate competitive advantage or disadvantage?
Tackling questions of this nature require comprehensive techniques because there are a lot of things that affect a players performance. As such I went to the old standby, multivariable regression to test the relationships between height and traditional performance measures. This allowed me to control for player attributes related to the outcome of interest, athleticism, year, and player. This allows me to make estimations based on a counterfactual, e.g. if I took 1995 Jamal Mashburn and made him one inch taller what would the effect be on his rebounding? All estimates below include controls for year, player, athleticism attributes, minutes, and weight. Keep in mind that the the adjusted R squared values for all of my analysis below are above 90%, meaning that my controls account for over 90% of the variation in outcomes. In other words, there isn't too much else going on that explains these statistics. Also note that all estimates shared in the report are statistically significant at the 0.01 level.
Points
Control Variables: Scoring attributes, position
The estimated marginal effect of one additional inch of height is .477 [Confidence inteval (CI): (.175,.779)]. In other words, one additional inch is worth about half a point more per game give or take a quarter of a point. To put this is perspective, the marginal effect of the inside scoring attribute is about .179, meaning that one additional inch is worth about 2 and a half inside scoring attribute points. Another way to look at this is that a 6'4" point guard will score about 2 points more per game than a 6'0" version of his clone.
Rebounding
Control Variables: Rebounding attributes
Height should matter for rebounding, right? If you throw in all positions, it doesn't. But if you limit the sample to just power forwards and centers it does. A lot. I think this is because rebounding at the other positions really isn't a function of height but probably relies mostly on individual player attributes, team game plan, etc. When it comes to trees hanging out around the rim though, height is an advantage. The estimated marginal effect of one additional inch of height is .453 [CI: (.118,.788)]. In other words, one additional inch is worth about half a rebound more per game, give or take a quarter of a point. To put this is perspective, the marginal effect of the defensive rebounding attribute is about .04, meaning that one additional inch is worth about 11 defensive rebounding attribute points. Another way to look at this is that a 6'10" power forward will snag about 2 rebounds more per game than a 6'8" version of his clone.
Steals
Control Variables: Defensive and steal attributes, position
The estimated marginal effect of one additional inch of height is .074 [CI: (.055,.093)]. In other words, seven additional inches ares worth about half a rebound more per game, give or take a quarter of a point. To put this is perspective, the marginal effect of the steal attribute is about .02, meaning that one additional inch is worth about 2.5 steal attribute points. Not a huge effect here but remember that the league leader in steals averages 2.9 a game so we're working on a smaller scale here.
Assists
Control Variables: Passing attribute
I wasn't sure about this one but thought I would try it out. Ish Smith and D-Rose (2 PGs of importance to me) are about even on assists. They have similar passing attributes and play on similar quality offenses but Derrick Rose is three inches taller. Buuuuuttt, he also shoots way less and probably, therefore, passes more. For this one I limited the analysis to just point guards. The estimated marginal effect of one additional inch of height is .557 [CI: (.244,.896)]. In other words, one additional inch is worth about half an assist more per game, give or take a quarter of a point. To put this is perspective, the marginal effect of the passing attribute is about .089, meaning that one additional inch is worth about 6 passing attribute points. Another way to look at this is that a 6'4" point guard (Ricky Rubio) will complete about 2 assists more per game than a 6'0" version of his clone.
Blocks
Control Variables: Defensive and Blocking attributes
Height should matter for blocks. They just should. For this analysis I once again limit the sample to big men. The estimated marginal effect of one additional inch of height is .554 [CI: (.353,.756)]. Note the tighter confidence interval for this one. That means that this estimate is more precise than the others. In other words, one additional inch is worth about half a block more per game, give or take a quarter of a point. To put this is perspective, the marginal effect of the blocking attribute is about .045, meaning that one additional inch is worth about 12 blocking attribute points. Another way to look at this is that a 6'10" power forward will block about 2 more times more per game than a 6'8" version of his clone. This is a monstrous effect size given that the league leader is averaging 3.9 blocks per game. It is a little hard to stomach. Look at Arther Hardie and Wilbert Brown. Same blocking attribute score, both on bad teams, both can't jump. But one is 6'9" and the other is 7'0".
TL;DR version: height matters.