Advanced Stats for Basketball

Below are all the posts from March 2008. Click here to view all posts.

March 29, 2008

Rebounding by Shot Location

Posted by Eli in Raw Stats

Here’s a chart of offensive rebounding percentage by shot location, as suggested by Eric in the comments to my last post. The chart doesn’t show where players grab rebounds on the court (I don’t have that data), instead it shows which shot locations result in more offensive rebounds.

This took a little more work to construct because rebounds are listed in separate lines of the play-by-play than shot attempts (and not always on the very next line), and because the league credits a rebound for all missed shots, even half-court heaves at the end of a quarter where the clock expires while the ball is in the air. I tried to eliminate as many of these bookkeeping rebounds from the data as I could (though the red squares on the longest threes suggest that some still remain, as the offensive team is typically credited with the bookkeeping rebound).

I smoothed out the data as I did on the FG% chart, so each 1×1 ft square actually represents the offensive rebounding percentage on shots taken from the surrounding three-foot by three-foot square on the court. The color scale runs from blue (low ORB%) to yellow (average ORB%) to red (high ORB%). The data is from the 03-04 to 06-07 seasons.

Which Shots are Offensive Rebounded - ORB% by Shot Location:

The conventional wisdom on this topic that one usually hears from broadcasters is that it’s easier to get offensive rebounds on three-pointers because of the long caroms. However, Dean Oliver, John Hollinger and others have done research suggesting that there is actually a higher offensive rebounding percentage on twos than threes (see this thread and this study).

This chart suggests that both sides are onto something - longer three-point jumpers are rebounded by the offense more often than shorter two-point jumpers, but shots in the paint are rebounded by the offense even more frequently than three-pointers. Interestingly, it also looks like jumpers from the right baseline are offensive rebounded more frequently than jumpers from the left baseline, but I’d have to take a closer look at the data to confirm that.

March 27, 2008

More Shot Charts

Posted by Eli in Raw Stats

Here are a few more shot charts along the lines of those from my previous post.

First, a chart of effective field-goal percentage by shot location, which some commenters requested. eFG% is basically a measure of points per shot (excluding points from free throws) that is different from FG% in that it gives extra credit for made threes. The formula is 0.5*(2*2PM + 3*3PM)/(2PA + 3PA). I didn’t smooth out the data like I did in the FG% chart, so each one-foot by one-foot square contains the eFG% on shots from that spot. The color scale runs from blue (low eFG%) to yellow (average eFG%) to red (high eFG%).

Where Players Score Points - eFG% by Location:

As expected, three point shots get a big boost by looking at eFG% rather than just FG%. Shots right around the basket (dunks and layups mainly) also rate well, as do elbow jumpers, anything down the center line of the court, and small areas on the left and right blocks. The red squares just inside the three-point line are artifacts of three-point makes that were mistakenly coded as being taken from inside the three-point line.

The other new chart shows in which locations shots are most likely to get blocked. Each one-foot by one-foot square represents the percent of field goal attempts from that spot that were blocked. The color scale runs from blue (few blocks/FGA) to yellow (some blocks/FGA) to red (many blocks/FGA). The results are basically as expected - most blocks occur close to the hoop.

Where Shots Get Blocked - Blocks/FGA by Location:

If anyone has any other suggestions let me know.

Where Players Take and Make Shots

Posted by Eli in Raw Stats

I haven’t posted in a while, but I have a good excuse. I’ve been assembling a database of play-by-plays from the last five seasons. This will make it much easier to investigate many areas of the game. It’s not completely finished yet, but already there’s a lot of interesting stuff that I can pull from the database. For example, I can quickly calculate that in the four seasons from 2003-04 to 2006-07 (I’m missing a few games, but I have over 99% of games from that time period), there were 14,216 hook shots taken. 45.5% of those shots were made, 54% of those makes were assisted, and 4% of all hook shots were blocked. But that’s not what I really want to examine in this post. Instead I’m going to look at shot location data.

During all NBA games, diligent game charters sit courtside and mark the location of every shot taken on the court down to the square foot. I believe this is done by using a stylus on a touchscreen monitor with a replica of the court on it. This is the source of the shot charts you can see after a game on or CBS Sportsline, and of the compiled shot charts of’s Hot Spots (which I discussed in my first post). With the play-by-play database I’ve constructed it’s possible to look at this shot location data in a number of ways.

First, below is a picture showing where players shoot from. Again it’s based on data from 03-04 to 06-07. The court dimensions are to scale, and each one-foot by one-foot square on the court is color-coded based on the number of field goal attempts from that spot. The color scale runs from blue (few FGA) to yellow (some FGA) to red (many FGA). Obviously the charted locations aren’t 100% accurate, but there are still some very interesting patterns that emerge.

Where Players Take Shots - FGA by Location:

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March 6, 2008

Diminishing Returns for Scoring - Usage vs. Efficiency

Posted by Eli in Stat Theory, Studies

In the wake of my last few posts on diminishing returns in rebounding, a lot of people have suggested looking at how diminishing returns applies to scoring. This is a more complex issue, but I think some of the same methods can be used to try to understand what’s going on in this part of the game of basketball. For rebounding, we were just looking at the relationship of player rebounding to team rebounding. For scoring, we have to look at the relationship of player efficiency and player usage to team efficiency. Diminishing returns for scoring is really just another way of framing the usage vs. efficiency debate which has been going on in the stats community for years. Does efficiency decrease as usage increases? By how much? What, if any, value should be placed on shot creation? Are coaches using anything near to the optimal strategies in distributing shot attempts among their players? Is Allen Iverson wildly overrated? Was Fred Hoiberg criminally underutilized? The big names in basketball stats like Dean Oliver, Bob Chaikin, John Hollinger, Dan Rosenbaum, and Dave Berri have all staked out positions in this debate. For some background, see here and here and here and here and here and so on and so on. A lot of words have been written on this topic.

The major difficulty in studying the usage vs. efficiency tradeoff is the chicken-and-egg problem - does a positive correlation between usage and efficiency mean that players’ efficiencies aren’t hurt as they attempt to up their usage, or just that in seasons/games/matchups where players are more efficient (for whatever reason) they use more possessions? For instance, if a player is facing a poor defender (which will increase his efficiency) he (or his coach) might increase his usage. But it could be that this positive correlation is drowning out the presence of a real diminishing returns effect. If players go from low-usage, low-efficiency against a good defenders to high-usage, high-efficiency against poor defenders, it still could be the case that if they tried to increase their usage against average defenders their efficiency would decrease. Defender strength is just one of the factors that can cloud things - another confound comes from game-to-game or season-to-season variation in a player’s abilities (e.g. a player being “hot” or having an “off game”, a player being injured or tired, or a player using more possessions as his skills improve from year to year).

By using the method from my last study on diminishing returns for rebounding, it’s possible to largely avoid this chicken-and-egg problem. This method looks at situations in which some or all of the players on the court were forced to increase their usage (relative to their average usage on the season). And on the other side, it looks at lineups in which some or all of the players on the court were forced to decrease their typical usage. By looking at these forced cases the method minimizes the confounds from players increasing or decreasing their usage by choice in favorable situations.

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