Mar 2 2009

Rating a Player’s Impact on Shooting Percentages in the Low Paint

Studying the relationship between shooting and defensive efficiency has made me wonder what, if anything, we can learn by rating a player’s impact on shooting percentages from various locations on the court.

The Model

Borrowing from the idea of adjusted plus/minus, I ran a logistic regression for data from the ’07-’08 regular season for the field goals made and missed in the low paint for each lineup combination in the data set. (Again, the low paint is defined as an area in the paint within 6 feet of the basket.)

For this fit, I only used data from players that took part in at least 1600 combined offensive and defensive shots in the low paint. I arrived at this number fairly arbitrarily, but it is close to 20 combined offensive and defensive shots per game. Also, I controlled for the home court advantage.

To run this regression yourself, simply download the archive. Inside you will find:

  • lp.R: From R, run source(“lp.R”) to run the regression.
  • lp.csv: A CSV file for the data used in the regression
  • lp.formula: The formula for the regression. You can modify this to add (or remove) players.
  • lp.players: A file listing the players and their IDs. The number of combined offensive and defensive shots is listed in parenthesis.
  • lp.results.txt: The results from my run of the regression

The Results

I’m sure a majority of the people reading this post will simply want to know who’s in the top ten and bottom ten on offense and defense. But that’s not really why I’m here, so the important nerd details can be found in the lp.results.txt file. I’ll leave it up to you to dig into the file.

Offense: Top 10 (from best to worst)

  1. Carlos Boozer
  2. Steve Nash
  3. Dwight Howard
  4. Marcus Camby
  5. Thaddeus Young
  6. Dwyane Wade
  7. Kobe Bryant
  8. LeBron James
  9. Steve Blake
  10. Amare Stoudemire

Offense: Bottom 10 (from worst to best)

  1. Allen Iverson
  2. Yi Jianlian
  3. Samuel Dalembert
  4. Chauncey Billups
  5. Beno Udrih
  6. Corey Brewer
  7. Delonte West
  8. Lamar Odom
  9. Ben Gordon
  10. Ben Wallace

Defense: Top 10 (from best to worst)

  1. Zydrunas Ilgauskas
  2. Kevin Garnett
  3. Brendan Haywood
  4. Joakim Noah
  5. Yao Ming
  6. Andris Biedrins
  7. Josh Smith
  8. Joel Przybilla
  9. Lamar Odom
  10. Manu Ginobili

Defense: Bottom 10 (from worst to best)

  1. Craig Smith
  2. Juan Carlos Navarro
  3. Hakim Warrick
  4. Morris Peterson
  5. Jason Williams
  6. Jeff McInnis
  7. Jordan Farmar
  8. Boris Diaw
  9. DeShawn Stevenson
  10. Jose Calderon

With these obligatory lists out of the way, I hope to get to some real substance.

What does this tell us?

The most important question to ask ourselves is: “What exactly is this telling us?” This data is conditional on a lot of stuff. Before I get to that, though, I certainly don’t want to give off the impression that a team’s sole goal is to maximize their probability of making shots in the low paint. Clearly basketball is much more than that, but measuring a player’s impact on all aspects of the game is important. So this is just one small piece of the overall puzzle.

That being said, ideally we could get a context free measure of how a player impacts their lineup’s probability of making a shot in the low paint, but this is far from it. These ratings merely hold for home court advantage and the strength of opposing lineups and teammates based on the strategies they’ve chosen to use. In a lot of cases, statistically significant coefficients were not found (again, see the regression results for the details), so even with the conditional aspects of the data to think about, there is still uncertainty with a lot of players’ ratings.

To get an idea of how we might (or might not) use this data, I’ll use the most interesting result from this regression: Allen Iverson’s offense.

Allen Iverson’s Offense

Because of the results in Detroit, Allen Iverson is getting a lot of attention. He seems to be the guy a lot of people love to hate right now. If we were to take these ratings at face value, then we could simply pile on top of Iverson, as he’s got the worst offensive rating. But is this fair?

One reason I don’t believe this is fair has to do with the fact that overall shot distribution is important. According to, Iverson took 30% of his shots close to the rim last year, where as a guy like Steve Nash took only 14% of his shots from the same location. Since it’s fair to say Iverson takes a larger percentage of his lineup’s shots compared to Nash, it’s fair to say that his low paint FG% will have a larger impact on his lineup’s low paint FG% when compared to Nash.

I think it’s safe to say that most every team would rather have Nash over Iverson, but I think it’s worth studying how Iverson’s shot selection hurts (or helps?) his team. Does his athletic ability that allows him to take this high percentage of shots close to the rim help, or is he rather forcing shots that are hurting his team’s efficiency? We can’t say for sure based just on this rating.

Looking at overall shot selection with respect to these ratings might shed some light onto the situation, but I’ll save that for another day.


I believe there is some value in these results, but like most everything else in basketball, we need to examine other measures to determine how a player will impact any given lineup combination. Hopefully this will prove to be a useful part of that toolkit.

Up Next: My plan is to run this regression with respect to mid-range jump shots.

5 Comments on this post


  1. Measuring the Relationship Between Players and their Lineup’s Shot Distribution wrote:

    […] my last post I looked at how we might rate a player’s impact on their lineup’s FG% in the low paint. With this came the obvious question of: “What about shot […]

    March 4th, 2009 at 12:05 am
  2. Measuring the Relationship Between Players and their Lineup’s Effective FG% wrote:

    […] already looked at the low paint, but now I need to present the results from the other two […]

    March 6th, 2009 at 1:44 am

  1. ed said:

    great stuff.

    March 2nd, 2009 at 1:43 pm
  2. Justin said:

    Great stuff indeed. Regarding Iverson, I wonder how his teams perform on the offensive boards with him on/off the court. It could be that his proficiency at drawing help defense while merely getting the ball in the vicinity of the rim has had a consistently positive effect on the offensive-rebounding of his teams. That 2001 Philadelphia team had plenty of players that couldn’t create their own shot (low usage was a necessity for George Lynch) but could certainly pick up Iverson’s mess.

    It’s exciting that you will be doing this regression analysis on so many aspects of the game. Then we can look at the sum total of a player’s influence along these lines. Lamar Odom is another good example, where we can see his presence in the bottom-10 offensively and top-10 defensively and then weigh those two facts against each other.

    Thanks for sharing your code and your findings.

    March 4th, 2009 at 2:24 pm
  3. Ryan said:

    Justin, I certainly have plans to look at the rebounding. Hopefully that paints a clearer picture.

    As for Odom, I think this speaks along the lines of having complimentary teammates. Based on this list, it sure helps to have Kobe in the game.

    March 4th, 2009 at 3:06 pm

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