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

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

Using matchup files, I decided to test a few theories. There has been past research on some of these topics but the articles I saw used a very small sample size. The sample size I had is pretty big so I'm confident with the results I got.

X= Lineup combined usage%

Y= Actual Offensive rating minus Expected Offensive rating

As you can see, there is a tradeoff between usage and efficiency. The tradeoff is even higher at low usage than at high usage. At 80-89% combined usage, teams underperform by 4 points per 100 while at 110-119 they overperform by just 1.7. From 90-99 usage they underperform by 2.1 while at 100-109 they overperform by just 0.4. Usage lineups with under 80% underperform by a whopping 7.1 points per 100 while lineups over 120 overperform by 2.8. This falls in line with past research which indicated that low usage is more sensitive to usage changes than higher usage lineups. In box score based stats, low usage players should be punished a lot more than high usage players get rewarded.

X= Lineup Combined Dreb%

Y= Actual Dreb%

There are a lot of diminishing returns to defensive rebounding. My research indicates that for each 1% a lineup is in combined Dreb%, they acquire just 0.21% more Defensive rebounds.

X= Lineup Combined Oreb%

Y= Actual Oreb%

The diminishing returns for Offensive rebounds are much lower. For each 1% increase in lineup combined OReb%, They get 0.62% more offensive rebounds. Low offensive rebounding lineups do outperform expectations. For example, lineups with a combined 10-11% Offensive Rebounding% acquire have a 20% Oreb rate when they play.

X= Lineup combined average D rating

Y= Actual D rating of those lineups

There are no diminishing returns at all for D rating. When high D rating players play together, they typically perform as expected. Same with low D rating players. .996 R^2 value.

X= Lineup combined BPM

Y= Actual point differential

As you can see, BPM does correlate with Points differential per 100 but high BP lineups typically underperform expectations. These lineups tend to underperform by around 2 points per 100. The reason might be opponent competition.

X= Lineup combined BPM minus opponent BPM

Y= Actual point differential

Once you adjust for competition, BPM does a good job of explaining lineup performance. A .992 R^2 value. Lineups with a BPM difference over 20 outperform their opponents by 22 points per 100.

X= Lineup combined average age minus opponent age

Y= Actual point differential

Age is a significant variable for the NBA. Older lineups kill younger lineups. For each 1 year in age differential, the older lineup gains 0.94 points per 100

X= Lineup combined usage%

Y= Actual Offensive rating minus Expected Offensive rating

As you can see, there is a tradeoff between usage and efficiency. The tradeoff is even higher at low usage than at high usage. At 80-89% combined usage, teams underperform by 4 points per 100 while at 110-119 they overperform by just 1.7. From 90-99 usage they underperform by 2.1 while at 100-109 they overperform by just 0.4. Usage lineups with under 80% underperform by a whopping 7.1 points per 100 while lineups over 120 overperform by 2.8. This falls in line with past research which indicated that low usage is more sensitive to usage changes than higher usage lineups. In box score based stats, low usage players should be punished a lot more than high usage players get rewarded.

X= Lineup Combined Dreb%

Y= Actual Dreb%

There are a lot of diminishing returns to defensive rebounding. My research indicates that for each 1% a lineup is in combined Dreb%, they acquire just 0.21% more Defensive rebounds.

X= Lineup Combined Oreb%

Y= Actual Oreb%

The diminishing returns for Offensive rebounds are much lower. For each 1% increase in lineup combined OReb%, They get 0.62% more offensive rebounds. Low offensive rebounding lineups do outperform expectations. For example, lineups with a combined 10-11% Offensive Rebounding% acquire have a 20% Oreb rate when they play.

X= Lineup combined average D rating

Y= Actual D rating of those lineups

There are no diminishing returns at all for D rating. When high D rating players play together, they typically perform as expected. Same with low D rating players. .996 R^2 value.

X= Lineup combined BPM

Y= Actual point differential

As you can see, BPM does correlate with Points differential per 100 but high BP lineups typically underperform expectations. These lineups tend to underperform by around 2 points per 100. The reason might be opponent competition.

X= Lineup combined BPM minus opponent BPM

Y= Actual point differential

Once you adjust for competition, BPM does a good job of explaining lineup performance. A .992 R^2 value. Lineups with a BPM difference over 20 outperform their opponents by 22 points per 100.

X= Lineup combined average age minus opponent age

Y= Actual point differential

Age is a significant variable for the NBA. Older lineups kill younger lineups. For each 1 year in age differential, the older lineup gains 0.94 points per 100

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

Spectacular work.

Spectacular.

Some of the previous posts on this subject:

Eli Witus at http://www.countthebasket.com/blog/2008 ... g-returns/

Jon Nichols at http://basketball-statistics.com/blog1/ ... her-stats/

Spectacular.

Some of the previous posts on this subject:

Eli Witus at http://www.countthebasket.com/blog/2008 ... g-returns/

Jon Nichols at http://basketball-statistics.com/blog1/ ... her-stats/

Developer of Box Plus/Minus

APBRmetrics Forum Administrator

GodismyJudgeOK.com/DStats/

Twitter.com/DSMok1

APBRmetrics Forum Administrator

GodismyJudgeOK.com/DStats/

Twitter.com/DSMok1

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

Thanks for these graphs.

How frequently do lineups have over 116 combined usage in NBA? Wondering if the efficiency fall off is more about small sample or actually hitting an overload bump.

The age chart is new and very important. Sam Presti and a few others either don't know this or are really bucking the overall data history.

Any chance you do some or all these charts for playoffs only and / or regular season but playoff ranked teams only? These cuts would test whether the lottery teams are distorting the pattern amongst teans that matter. This is particularly important for the age graph.

How frequently do lineups have over 116 combined usage in NBA? Wondering if the efficiency fall off is more about small sample or actually hitting an overload bump.

The age chart is new and very important. Sam Presti and a few others either don't know this or are really bucking the overall data history.

Any chance you do some or all these charts for playoffs only and / or regular season but playoff ranked teams only? These cuts would test whether the lottery teams are distorting the pattern amongst teans that matter. This is particularly important for the age graph.

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

Agree with Daniel: great work.

A question and an observation:

1) Have you attempted to account for quality of opponent? I'm assuming not. For USG-EFF, it would be interesting to know if there is any substantial difference in opponent defensive rating for high- and low-usage lineups. (One could imagine that low-usage lineups might often play against weak opponents in blowout situations, and vice-versa, making the actual curve still steeper.)

2) I think I disagree with this conclusion: "In box score based stats, low usage players should be punished a lot more than high usage players get rewarded." The point of rewarding high usage players is not necessarily because they have a handicap, but because they improve the efficiency of teammates by allowing them to benefit from a low usage rate. Your data suggests this is indeed a valuable contribution, because those low usage players would perform much worse if forced to shoot more often. (Obviously, this tradeoff could vary a lot depending on the composition of a specific team.)

A question and an observation:

1) Have you attempted to account for quality of opponent? I'm assuming not. For USG-EFF, it would be interesting to know if there is any substantial difference in opponent defensive rating for high- and low-usage lineups. (One could imagine that low-usage lineups might often play against weak opponents in blowout situations, and vice-versa, making the actual curve still steeper.)

2) I think I disagree with this conclusion: "In box score based stats, low usage players should be punished a lot more than high usage players get rewarded." The point of rewarding high usage players is not necessarily because they have a handicap, but because they improve the efficiency of teammates by allowing them to benefit from a low usage rate. Your data suggests this is indeed a valuable contribution, because those low usage players would perform much worse if forced to shoot more often. (Obviously, this tradeoff could vary a lot depending on the composition of a specific team.)

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

Here is the average opponent DBPM faced by combined lineup usage:Guy wrote:Agree with Daniel: great work.

A question and an observation:

1) Have you attempted to account for quality of opponent? I'm assuming not. For USG-EFF, it would be interesting to know if there is any substantial difference in opponent defensive rating for high- and low-usage lineups. (One could imagine that low-usage lineups might often play against weak opponents in blowout situations, and vice-versa, making the actual curve still steeper.)

Low usage lineups definitely face lower quality defenses.

Blowout situations and low minute players isn't a huge problem because I removed all lineups that had a player that played 250 Minutes played or less. This includes opponents with a 250 or less MP player. It wouldn't be right to include those low minute players in the sample.

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

1. I have 12,582 possessions for lineups with a usage higher than 116.Crow wrote:Thanks for these graphs.

How frequently do lineups have over 116 combined usage in NBA? Wondering if the efficiency fall off is more about small sample or actually hitting an overload bump.

The age chart is new and very important. Sam Presti and a few others either don't know this or are really bucking the overall data history.

Any chance you do some or all these charts for playoffs only and / or regular season but playoff ranked teams only? These cuts would test whether the lottery teams are distorting the pattern amongst teans that matter. This is particularly important for the age graph.

2. The age differential numbers are much lower if you just look at playoffs.

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

Wow, thanks for quick reply. Very interesting.

Unless I'm misreading something (certainly possible), it looks to me like the equations in the two rebounding charts are wrong. For example, your equation is showing that a projected 74% DREB% lineup actually performs at about 80%. The scale on the DREB% chart also seems to be off (every lineup is below average).

Unless I'm misreading something (certainly possible), it looks to me like the equations in the two rebounding charts are wrong. For example, your equation is showing that a projected 74% DREB% lineup actually performs at about 80%. The scale on the DREB% chart also seems to be off (every lineup is below average).

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

That's because of the way that Basketball-Value counts Rebounding on their matchup files. I believe they include team rebounds. Here is an adjusted version that gives a multiple of 1.06 to account for team rebounds.Guy wrote:Wow, thanks for quick reply. Very interesting.

Unless I'm misreading something (certainly possible), it looks to me like the equations in the two rebounding charts are wrong. For example, your equation is showing that a projected 74% DREB% lineup actually performs at about 80%. The scale on the DREB% chart also seems to be off (every lineup is below average).

The equation changes a lot depending on how I group the data. For example, grouping by 1 is different than grouping by 0.5.

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

Thanks for the playoffs age graph. In the plotline function is the residual really subtracted? It is not making sense to me. Can you show an example x,y that lines up with graph coordinates?

To put the # of possessions over 116 combined usage in perspective, what is the total # of possessions in the data set?

To put the # of possessions over 116 combined usage in perspective, what is the total # of possessions in the data set?

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

The plotline might be negative because the playoff sample size is small and could be distorted by outliers. Its the same way with the regular season age diff too so I'm not sure why Excel has it that way.Crow wrote:Thanks for the playoffs age graph. In the plotline function is the residual really subtracted? It is not making sense to me. Can you show an example x,y that lines up with graph coordinates?

To put the # of possessions over 116 combined usage in perspective, what is the total # of possession in the data set?

My sample has a total of 1.008 Million possessions and around 273K different Lineup combinations.

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

Why the googly eyes? These results are compatible with Jeremias' aging curve results.colts18 wrote:

X= Lineup combined average age minus opponent age

Y= Actual point differential

Age is a significant variable for the NBA. Older lineups kill younger lineups. For each 1 year in age differential, the older lineup gains 0.94 points per 100

Don't know if you're interested in, say, breaking up your sample, but it would be interesting to see how lineups consisting only of prime age players do, first against youth and then against oldster lineups. Then also how exclusively young lineups do against exclusively old ones.

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

3 things

1) THANK YOU for doing this.

2) Is this the expectation based on DeanO's ORTG and DRTG? I'm assuming that these are the averages at each point along the X-axis...in real life I don't think we'd see a 99% R^2 prediction (or retrodiction) w/ DRTG

3) Can you test this with Wins Produced?

1) THANK YOU for doing this.

2) Is this the expectation based on DeanO's ORTG and DRTG? I'm assuming that these are the averages at each point along the X-axis...in real life I don't think we'd see a 99% R^2 prediction (or retrodiction) w/ DRTG

3) Can you test this with Wins Produced?

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

How much lower of an effect did you find the age differential to have in the playoffs versus the regular season?

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

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 lineupsschtevie wrote:Why the googly eyes? These results are compatible with Jeremias' aging curve results.colts18 wrote:

X= Lineup combined average age minus opponent age

Y= Actual point differential

Age is a significant variable for the NBA. Older lineups kill younger lineups. For each 1 year in age differential, the older lineup gains 0.94 points per 100

Don't know if you're interested in, say, breaking up your sample, but it would be interesting to see how lineups consisting only of prime age players do, first against youth and then against oldster lineups. Then also how exclusively young lineups do against exclusively old ones.

### Re: Proof of Diminishing returns on Rebounds, USG-EFF, and m

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.)

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.)