Proof of Diminishing returns on Rebounds, USG-EFF, and more

[colts18]

I would second the request for seeing WP vs point differential (assuming it's not a huge amount of additional work).

I do wonder whether this methodology provides a good test of diminishing returns for Oreb? It seems unlikely (though possible) that each additional Oreb really translates into .6 additional rebounds at the team level. I say that because the standard deviation for Oreb% at the team level is fairly small, and no larger than the SD for Dreb%, which strongly suggests that much of the variation at the player level has to do with role rather than pure rebounding talent. Another reason to be skeptical is that Oreb%, unlike Dreb%, is in part a function of the kind of shots a team takes (and misses). So that will increase the in-season predictive power for lineups (because many of the the same players are taking these shots, in the same offensive system), totally apart from any rebounding talent that is being measured.

Perhaps we could better see the marginal impact of Oreb% by controlling for groups of four players who play in multiple lineups, and then see what the relationship is between the individual Oreb% of the 5th man and the total Oreb% of that lineup. Or maybe there's s a better approach. But to answer this question, I think we need to control for more factors than this methodology does. (And even so, a diminishing return of 38% is fairly substantial.)

1. I don't have WP data so I'm not sure I could work with that. If I have time, I could do BPM. And I might be able to do Prior Informed RAPM because J.E. took those directly from the BV matchup files.

2. That would be an interesting approach. Say we have a lineup with a combined 20% ORB for 4 guys. What happens when you add a Reggie Evans in comparison to a low O Reb guy like Dirk. Maybe some can find a way to do that.

Anyone interested in me uploading the matchup files and playing around with them? The file has about a 315K different lineup combos and 1.113 Million possessions. It also includes individual player Oreb%, Dreb%, O rating, D rating, OBPM, DBPM, BPM, Usage, Minutes played, and Age

[xkonk]

Age 25-29 lineups are +4.6 against 20-24 players and -4.42 vs Age 30+ lineups. Age 30+ lineups are +4.3 vs Age 20-24 lineups

This can't be right, right? If age 25-29 is +4.6 against 20-24, and age 30+ is +4.3 against 20-24, then 25-29 and 30+ should be about the same. How is age 25-29 -4.42 against 30+?

[colts18]

Age 25-29 lineups are +4.6 against 20-24 players and -4.42 vs Age 30+ lineups. Age 30+ lineups are +4.3 vs Age 20-24 lineups

This can't be right, right? If age 25-29 is +4.6 against 20-24, and age 30+ is +4.3 against 20-24, then 25-29 and 30+ should be about the same. How is age 25-29 -4.42 against 30+?

I'm going to look into that again because that shocked me too. I will double check to make sure I didn't make an excel error.

[Crow]

Performance between three groups isn't necessarily linearly transitive. It is likely but not required.

[colts18]

Age 25-29 lineups are +4.6 against 20-24 players and -4.42 vs Age 30+ lineups. Age 30+ lineups are +4.3 vs Age 20-24 lineups

This can't be right, right? If age 25-29 is +4.6 against 20-24, and age 30+ is +4.3 against 20-24, then 25-29 and 30+ should be about the same. How is age 25-29 -4.42 against 30+?

I just manually checked and my numbers are correct. 25-29 outperforms 30+ against young players despite getting killed when facing 30+. The sample for old vs young is about 11K possessions. Old vs prime has 56K possessions and Prime vs Young has 70K possessions.

[xkonk]

Performance between three groups isn't necessarily linearly transitive. It is likely but not required.

Age 25-29 lineups are +4.6 against 20-24 players and -4.42 vs Age 30+ lineups. Age 30+ lineups are +4.3 vs Age 20-24 lineups

This can't be right, right? If age 25-29 is +4.6 against 20-24, and age 30+ is +4.3 against 20-24, then 25-29 and 30+ should be about the same. How is age 25-29 -4.42 against 30+?

I just manually checked and my numbers are correct. 25-29 outperforms 30+ against young players despite getting killed when facing 30+. The sample for old vs young is about 11K possessions. Old vs prime has 56K possessions and Prime vs Young has 70K possessions.

I guess I'm still having a little trouble... basically, you're saying that 'old' lineups are about equally good against young and prime lineups (+4.3 and +4.42), and prime is better than young (+4.6), which would somewhat break transitivity, as Crow says. I could believe that. But then why is the last graph in your first post a straight line with a very good fit? The point difference of ~ +4 can be read off the graph for age groups about 5 years apart, but it says that old vs. young, which is more like 8 years, should be ~ +7 or 8.

Having just spend a little more time looking at your graphs, none of the intercepts in the equations seem right. Which has nothing to do with the issue above, just wanted to mention in case you can/want to fix it.

[colts18]

I guess I'm still having a little trouble... basically, you're saying that 'old' lineups are about equally good against young and prime lineups (+4.3 and +4.42), and prime is better than young (+4.6), which would somewhat break transitivity, as Crow says. I could believe that. But then why is the last graph in your first post a straight line with a very good fit? The point difference of ~ +4 can be read off the graph for age groups about 5 years apart, but it says that old vs. young, which is more like 8 years, should be ~ +7 or 8.

Having just spend a little more time looking at your graphs, none of the intercepts in the equations seem right. Which has nothing to do with the issue above, just wanted to mention in case you can/want to fix it.

A lot of is small sample size.

Age diff, Point Diff per 100, # of possessions
0-1 1.9 129092
1-2 0.7 115575
2-3 3.5 95790
3-4 4.2 69474
4-5 6.0 46082
5-6 5.4 29084
6-7 8.6 16870
7-8 7.7 8926
8-9 4.4 4098
9-10 10.0 1611
>10 8.6 496


The Sample at 8+ age is about 6K which is small.


As far as the equations, they don't mean much to me. They change quite a bit depending on how I group the data. Changing the Minimum and Maximum for the group range makes a huge change. If I don't group the data, the R^2 is low. If I group it by say 0-1, 1-2, 2-3, etc., the R^2 goes up significantly.

[v-zero]

Was anything done to account for selection bias? If not then that probably explains the odd age values.

[colts18]

I found WP/48 data. I can run a predictive test if anyone is interested. I will use BPM, PI RAPM, NPI RAPM, xRAPM, WS/48, and WP/48 for this test.

I'm not an expert on these so I need to know I am supposed to handle players who didn't play the season before? Do they get a -2 value?

Is there a minute limit I need to use for lineups like a minimum of 100 MP, 250 MP or 500 MP for each player in the lineup?

[Crow]

I am interested in tests but probably should say specifically what you are testing. Replacement level seems right if player didn't play previous year for testing yr to yr predictiveness of individual. For prediction of lineup results, wonder if it might be better to divide same yr data into two or more groups, sequential or random.

[AcrossTheCourt]

Well, if you were looking for articles on usage/eff with bigger samples, you missed mine:
http://ascreamingcomesacrossthecourt.bl ... iency.html

I think I used the same matchup files you did but I'm not sure.

[Guy]

Questions for Colts18 and/or Acrossthecourt:

1) how much do the differences in opposition defense reported by Colts18 change the steepness of the usage/efficiency curve?

2) Is there any way to know whether the usage distribution changes materially in high- and low-usage lineups? That is, your models assume that in a low-usage lineup every player expands his usage proportionately. But perhaps that isn't true. If higher-efficiency shooters disproportionately increase their shots, then the usage-caused decline is even larger than it appears (and vice-versa).

[colts18]

Questions for Colts18 and/or Acrossthecourt:

1) how much do the differences in opposition defense reported by Colts18 change the steepness of the usage/efficiency curve?

2) Is there any way to know whether the usage distribution changes materially in high- and low-usage lineups? That is, your models assume that in a low-usage lineup every player expands his usage proportionately. But perhaps that isn't true. If higher-efficiency shooters disproportionately increase their shots, then the usage-caused decline is even larger than it appears (and vice-versa).

1. Here is the chart with lineups adjusted for defense (using DBPM for opponent defense). The 2nd chart is the original chart (not adjusted for defense):

[colts18]

Can anyone explain to me how I am supposed to run a R^2 for each of these stats at the lineup level? I've compiled these stats so that each lineup has the stats of the previous season (I will also do 2 year and 3 year correlations) line up. For example, Here is a line I have in the matchup file. All of them are combined together in excel (though I split it up here for aesthetics purposes).

Code: Select all

Year	UnitPlayer1Name	UnitPlayer2Name	UnitPlayer3Name	UnitPlayer4Name	UnitPlayer5Name	OpponentPlayer1Name	OpponentPlayer2Name	OpponentPlayer3Name	OpponentPlayer4Name	OpponentPlayer5Name
2008-2009	Howard, Josh	Kidd, Jason	Nowitzki, Dirk	Terry, Jason	Wright, Antoine	Aldridge, LaMarcus	Fernandez, Rudy	Outlaw, Travis	Rodriguez, Sergio	Roy, Brandon

Code: Select all

Net Points	Poss/2 	Net Per 100
-2	0.5	-400.0

Code: Select all

		08 BPM									
BPM	BPM	BPM	BPM	BPM	BPM	BPM	BPM	BPM	BPM	BPM1	BPM2
0.8	2.7	4.7	2.5	-2.6	0.6	-2	-1.8	-4.6	3.2	8.1	-4.6

How should I run the correlation for predictive purposes?