Touching BasesFebruary 25, 2010
Shot Location Efficiency
By Jeremy Greenhouse

A couple weeks ago, I wrote an article using data from basketballgeek showing shot location visualizations. The logical next step from visualizing the data is to use it for more analytical purposes. So I set about to build a model to predict points based on shot location.

Here is the expected field goal percentage based on shot location. The data set runs from 2006-2007 to this year's All-Star Break and contains over 600,000 shots.


That is the starting point for my model. I take the expected field goal percentage for a given spot on the floor, and multiply it by either two or three, depending on whether the shot is an attempted two pointer or three pointer.

Another part of my model is offensive rebounding rate. From the field goal percentage chart, you can see that some three point locations are as high percentage shots as some two point locations, yet the value of a three pointer is inherently higher. Offensive rebounding rate on three pointers as compared to long two pointers is another reason that mid-range jumpshots are inefficient plays.


The value of an offensive rebound is contested in the basketball analytics community, as I recently learned. I understand why player evaluations based on linear weights don't work at all in basketball, but I'm not sure why they wouldn't work on the team level. Why can't we say that the average value of an offensive rebound is roughly equal to the average value of adding another possession. If somebody can enlighten me on if and why this assumption is faulty, I would appreciate it. Regardless, the average possession yields something like 1.05 points, so for each shot location, I multiplied the expected missed field goal percentage by the expected offensive rebounding percentage and again multiplied that by 1.05.

Then, I found the shooting foul rate based on shot location. This was a challenge, since the play by play files don't chart foul locations. I therefore used three resources to try to predict shooting foul locations. Ryan Parker collected data that tracks the locations of nearly every event over ten games, including 200 or so shooting fouls, which definitely helped. 82Games has charted shooting fouls, though the data isn't very granular, and they don't mention the magnitude of the study. Lastly, I found the shot locations of all made baskets where there was an and1. Here's what I came up with.


I think the above graph reasonable. It's too smooth, since I think there is probably a steep breaking point where players stop taking mainly jump shots and start playing with their backs to the basket. Jump shots are much less likely to draw fouls than post-ups, however my model can't capture that since I use smoothing techniques. The play-by-play data does include shot type information, so if I had a do-over, I would do some testing based on jumpers vs. other shot types. Anyway, what I do with my shooting foul model is multiply the rate of missed shots at a given location by the shooting foul percentage at that location, and then multiply that by either 2 or 3, and again by either 0.76 or 0.81, depending on whether the respective shot was a 2 or a 3, which represent the number of free throws a player earns for a shooting foul on a missed shot and the made free throw rates on those shots. I also multiplied the rate of made shots by the expected And1 percentage, which is much lower than the shooting foul percentage.

Put that all together, and here's my ultimate point expectancy model.


The average is up around 1.25. That's about 0.2 points better than the average possession, since plays that don't result in shots either end up as personal fouls or turnovers, mainly turnovers, which net 0 points. I applied the model on five-man units as well as individual players.

First, the top and bottom five five-man units in shot location efficiency, or expected points per shot. Ideally, some of the shooting, free throw, and rebounding percentage would be customized but I'm using league average rates for this entire study. Minimum 500 shots.

Unit Shots Efficiency eFG%
Dwight Howard Hedo Turkoglu Jameer Nelson Maurice Evans Rashard Lewis 768 1.34 60.81%
Boris Diaw Gerald Wallace Nazr Mohammed Raymond Felton Stephen Jackson 629 1.31 51.67%
Amare Stoudemire Leandro Barbosa Raja Bell Shawn Marion Steve Nash 598 1.31 55.52%
Dwight Howard Hedo Turkoglu Jameer Nelson Keith Bogans Rashard Lewis 1480 1.30 55.07%
Boris Diaw Emeka Okafor Gerald Wallace Raja Bell Raymond Felton 1147 1.30 53.10%
Antonio McDyess Chauncey Billups Rasheed Wallace Richard Hamilton Tayshaun Prince 1974 1.20 50.48%
Derrick Rose Joakim Noah John Salmons Luol Deng Taj Gibson 546 1.20 45.79%
Kevin Garnett Mark Blount Mike James Ricky Davis Trenton Hassell 1243 1.20 51.05%
Brandon Roy Joel Przybilla LaMarcus Aldridge Martell Webster Steve Blake 1036 1.19 50.43%
Earl Watson Jeff Green Johan Petro Kevin Durant Nick Collison 517 1.19 45.16%

I'm happy to see that the Eastern Conference Champion Magic are the top team on this list because I'd always assumed that their offense last year was extremely efficient. The Magic had two options on offense. Dwight Howard took shots at the rim, while Hedo Turkoglu and Rashard Lewis hoisted threes. That unit was also by far the best in effective field goal percentage in the league, so they were getting high percentage shots, making high percentage shots, and though I can't include their free throw rates or offensive rebounding rates since those would be pains to calculate, I'm sure that with Dwight Howard, the Magic were successful at getting to the line and grabbing rebounds. The Suns, of course, are one of the top five teams.The Bobcats, surprisingly, take highly efficient shots, but don't make many of them. On the other end, we already knew the Bulls run an inefficient offense, and I'm not surprised to see the Pistons do too. That Thunder offense last year must have been absolutely brutal.

Now turning to defense, teams that force the least efficient shots.

Unit Shots Efficiency eFG%
Dikembe Mutombo Juwan Howard Rafer Alston Shane Battier Tracy McGrady 766 1.20 46.54%
Dwight Howard Hedo Turkoglu Jameer Nelson Maurice Evans Rashard Lewis 845 1.21 48.58%
Aaron Brooks Luis Scola Ron Artest Shane Battier Yao Ming 670 1.21 46.19%
Bruce Bowen Fabricio Oberto Michael Finley Tim Duncan Tony Parker 858 1.21 48.95%
Chuck Hayes Rafer Alston Shane Battier Tracy McGrady Yao Ming 1007 1.21 43.15%
Emeka Okafor Gerald Wallace Jason Richardson Jeff McInnis Raymond Felton 766 1.29 52.87%
Marc Gasol Mike Conley O.J. Mayo Rudy Gay Zach Randolph 1700 1.29 52.56%
Jeff Green Kevin Durant Nenad Krstic Russell Westbrook Thabo Sefolosha 1691 1.29 49.91%
C.J. Miles Deron Williams Mehmet Okur Paul Millsap Ronnie Brewer 768 1.29 54.75%
Boris Diaw Gerald Wallace Nazr Mohammed Raymond Felton Stephen Jackson 631 1.29 55.23%

It's no surprise that the Rockets force teams into low percentage shots, as they boast three of the top five five-man units. That defensive lineup containing Chuck Hayes, Shane Battier, and Yao must be impregnable. And what do you know, but the Magic offense that generated the most efficient shots also had the defense that allowed the second most inefficient shots. Interestingly, the Bobcats offense that ranked second in shot efficiency actually allowed the most expected points per shot on the other end of the floor. I don't think I've watched a Bobcat game this year, but I'd be interested to know what's going on with that unit. A couple surprises on the bottom five list. The Thunder have made noise throughout the league for their much-improved defense, yet it's not a matter of holding opponents to inefficient shots. Instead, their opponents have gotten quality shots off, but have not made them, which would point to an impressive ability to contest shots. Also, the Thunder might do a good job of defensive rebounding and not fouling, which wouldn't appear in the numbers I'm showing.

The next table includes defensive stats for individual players, but still uses data based on the entire five-man opposition. I raised the minimum to 1,000 shots.

Name Shots Efficiency eFG%
Dikembe Mutombo 2826 1.21 43.77%
David Harrison 1360 1.21 47.65%
Shaquille O'Neal 8909 1.22 49.34%
Yao Ming 8181 1.22 45.74%
Jacque Vaughn 2878 1.22 45.95%
Sam Young 1334 1.28 50.64%
Salim Stoudamire 1815 1.28 48.51%
Russell Westbrook 6876 1.29 49.45%
Chris Douglas-Roberts 2590 1.29 51.51%
Louis Williams 3580 1.29 49.50%

I could've guessed that the top defenders at forcing low percentage shots would be centers, since preventing shots at the rim is the best way to force inefficient jump shots. Dikembe Mutombo, even at (insert whatever made-up hilarious age here), remained an astonishingly good defender. He forced opposing teams into inefficient shots, and no player held rivals to as low an effective field goal percentage as Deke. I'm not sure if any of the guys who show up on the bottom five have reputations as poor defenders. Basketballvalue exhibits poor defensive ratings for Russell Westbrook and Lous Williams and says that by adjusted +/- Sam Young has been a flat-out awful player in general this year, though the guy who runs basketballvalue is the stats guy for Sam Young's team, the Grizzlies.

This table shows how a player's five-man unit performed while he was on the court.

Name Shots Efficiency eFG%
Steve Francis 1405 1.31 48.01%
Eddy Curry 5605 1.30 49.02%
Stephon Marbury 5168 1.30 48.13%
Renaldo Balkman 3842 1.30 47.07%
Donyell Marshall 2634 1.30 46.70%
Antonio McDyess 9614 1.21 48.42%
Cuttino Mobley 8225 1.21 46.33%
Earl Barron 1592 1.21 44.91%
Will Solomon 1127 1.21 49.56%
Sam Cassell 4017 1.20 46.93%

The top four players were all Knicks during this time frame, as were three of the next eight on the leaderboard. All this is telling us is that Stevie Franchise, Starbury, and Baby Shaq all excel at hanging and banging, and that Isiah is attracted to that type of player. Sam Cassell, on the other hand, can't get to the rim. So I decided to take out a player's own shots, and include only shots by a player's teammates while he was on the floor.

Name Shots Efficiency eFG%
Steve Francis 1161 1.32 49.61%
Jameer Nelson 7475 1.31 52.49%
Stephon Marbury 4137 1.31 48.65%
Steve Nash 11406 1.30 56.11%
D.J. Augustin 2986 1.30 48.44%
Amir Johnson 3566 1.21 47.80%
Joel Anthony 3196 1.21 47.70%
Roko Ukic 1124 1.21 50.09%
Joel Przybilla 7054 1.20 48.28%
Erick Dampier 8368 1.20 49.46%

At one end are players who spread the ball around and at the other end are players who inhibit floor spacing. Steve Nash's teammates had easily the highest effective field goal percentage, and oh by the way, Nash's own eFG% beats out that of his his teammates. Erick Dampier and Joel "Prezbo" Pryzbilla clog the paint like a hot fudge sundae clogs one's arteries.


Is it just me.......or is anyone else wondering how articles like this wind up on a baseball website?

This was fascinating (and I don't mind it being on a baseball blog!), but I wish the colors chosen for the visualization didn't all look the same between 0.8 and 1.2.

The main reasons I can think of that an offensive rebound may not be worth the same as an average possession (assuming you define "possession" so that a rebound starts a new one), are that:
A) they start from different places on the floor, and
B) they start with the defense in a different state of readiness.

Offensive rebounds would have an advantage over defensive rebounds in terms of A, but possibly a disadvantage in terms of B. It seems like there must have been a study by now that looks at average points per possession depending on the event that starts the possession (steal, made basket, offensive rebound of FGA, offensive rebound of FTA, defensive rebound of FGA, defensive rebound of FTA, dead ball, etc). If anybody knows of one, please post a link here.

RW, I was wondering if someone would say something to that effect. I'm impressed.

DavidH, I'm surprised there's so much debate over the value of an offensive rebound as well.

Could you do some efficiency differential calculations as well? Efficiency O - Efficiency D?

Jeremey, And the answer is.............?

@RW, I can't speak for Jeremy or the website, but sometimes it is kind of neat to mix things up, just for fun. You really need this explained to you?

@Jeremy, I for one am really enjoying these, and hope you throw some more in. I'm wondering if you're being too generous in explaining how this year's Thunder are so improved on defense despite giving up efficient shots to opponents. It's certainly possible that you're right, and they're just good at contesting shots without fouling (Durant definitely has the length for that!), but I'm curious if it could also just be luck, and they are due for a major defensive crash at some point. I really like watching them, but I think they're overperforming so far.

The saddest info in this post is that the Bobcats are taking the right shots but just aren't good enough to make them. Reminds me of my JV years.

DSMok1, good idea. I decided to divide the efficiency rates by each other instead of subtracting, so here are the best in efficiency+, as measured as teammates' shot efficiency on offense divided by opponents' shot efficiency on defense. It's a pretty sweet top 5 and bottom 5.

Top 5: Dirk Nowitzki, Tracy McGrady, Sam Cassell (not including his own shots, remember), Kobe Bryant, KG. Those guys are 2.5% better than average.

Bottom: DeJuan Blair, Leon Powe, Eddy CCurry, DeAndre Jordon, Josh Childress, Javale McGee, Joakim Noah. Those guys are 3% below average.

Jake, thanks for the comment. I think my knowledge of basketball has run its course. Interesting take on the Thunder.

I do know some Thunder... they run a basic, simple defense and focus on contesting everything. Westbrook, Sefolosha (in particular), and Durant are very long for their positions.

The breakdown:

The paltry number of comments reflect interest in this type of article on this site..... No offense - but it's not baseball.