# 2012-2013 Expected Points Per Shot – Player

*Last updated 4/23/2013

What is Expected Points Per Shot?

Expected Points Per Shot (XPPS) is a statistic that measures the quality of a player’s shot selection.

How is it calculated?

Not all shots are created equal. A layup is much more likely to go in than a long jump shot. A three-pointer is also less likely to go in than a layup, but if it does go in it earns an extra point. All these trade-offs can be measured numerically. I used statistics from NBA.com and looked at every shot, made and missed, going back to the 2000-2001 season. The NBA groups those shots into five locations – Restricted Area, In The Paint (Non-RA), Mid-Range, Corner 3, Above The Break 3. By calculating the total number of points scored on shots from each location and dividing it by the number of attempts we arrive at an expected value for shots from each location. Here are those averages:

• Restricted Area –  1.183
• In The Paint (Non-RA) – 0.793
• Mid-Range – 0.788
• Corner 3 – 1.157
• Above The Break 3 – 1.048

For my evaluation I also included free throws. The basketball stats community has agreed on 0.44 as the standard modifier for calculating shooting fouls from total free throw attempts. That means that multiplying 0.44 by a player’s  total free throw attempts will give you a very close approximation of the number of times they went to the free throw line for two shots. I also calculated the average value of a trip to the free throw line for two shots as 1.511.

With those expected values we can calculate a player’s Expected Points Per Shot. We multiple their total attempts from each area by the expected value of shots from that area. We add that total to the totals from all other areas. We then divide that total by all of a player’s shot attempts, including the calculated trips to the free throw line. The result is Expected Points Per Shot.

It’s important to remember that this is a measure of the quality of a player’s shot selection. Players who take a lot of easy shots like layups or corner three-pointers will have a higher value. However, players under and over-perform league averages all the time. For that reason I compare Expected Points Per Shot to Actual Points Per Shot. Calculating the difference between the two lets us see who’s shooting accuracy is better or worse than we would expect.

How do I read and use the visualization?

The graph across the top shows all the players in the league, grouped by team. Players are marked above or below the horizontal axis by the difference between their Actual Points Per Shot and their Expected Points Per Shot. A positive difference places a player above the axis, a negative difference places them below. The size of each mark represents each player’s minutes per game.

The central graph marks each player by both their Actual Points Per Shot and their Expected Points Per Shot. Players marked in green are outperforming the expected value of their shot selection. Players in red are underperforming the expected value of their shot selection. Again, the size of each mark represents each player’s minutes per game.

Below the central graph are set of filters. This will let you control the display of both graphs and the bottom table. You can filter by team, focus on a specific player or players, or narrow the results by total minutes, minutes per game, Usage, XPPS, Actual Points Per Shot, or the difference between the two. If at any point you want to reset all the filters, click the button at the bottom of the page that looks like a circle with an arrow.

The table at the bottom shows many of the raw numbers used to create the visualization. For each player you can view their team, age, minutes, minutes per game, Usage, XPPS, Actual Points Per Shot, Difference. You can also view the percentage of a player’s field goal attempts that come from each area of the floor, as well as their FG% from each area. For free throws you can see each player’s FTA/FGA and their FT%.

• Z-man

Hi, Z-man from Knickerblogger here. Thought you might fond the following couple of comments on KB interesting…

http://knickerblogger.net/knicks-morning-news-friday-aug-30-2013/#comment-445716

What is your position on my contention that not all shots in the restricted area are the same, and therefore xPPS in that area is not telling an accurate story?

• http://hickory-high.com/ Ian Levy

Thanks for reaching out Z-Man.

You’re absolutely right that a not all shots in the restricted area are the same. But that’s essentially true for shots everywhere. Mid-range jumpers can be balanced, catch-and-shoot wide-open opportunities or they can be off the dribble, fade-away contested shots. And of course anything in between. At this point it’s just not feasible to incorporate all those different factors. With the data set I have available, shot location is as much detail as I can bring to the discussion.

I know that when I’m talking about evaluating shot selection here, we’re really only evaluating one component of shot selection. It’s all semantics but I’d prefer to say XPPS tells an incomplete or generalized story as opposed to an inaccurate one.

• Guest

This is cool! Question: Wouldn’t it make sense to measure expected points per shot by a player’s own shooting percentages from various locations, rather than league-average percentages? After all if Dirk Nowitzki takes a mid-range jump-shot, that’s better shot selection than if Josh Smith does.

• http://hickory-high.com/ Ian Levy

I had the same idea initially and spent a bunch of time on it but the result always turned out to be a complicated formula that replicated TS%. Then I finally figured it out. If you’re using a player’s own shot selection and their own percentages you’re just showing what they actually did – TS%.

XPPS controls for expected value and measures shot-selection. If you measure both at the same time you end up with FG% or eFG% (from Kirk’s work) and TS% (from mine because I included FTs). One of the things I’d like to tackle next is controlling for shot-selection and measuring a player’s shooting ability. I think that’s the natural next extension of this work.

• Guest

Right, I see how if you do things this exact way you just recover ts% or efg%. However, I could still see a measure of shot selection based on a player’s own percentages, ie the relationship between how many shots he takes from that location vs. how well he shoots from there. Perhaps even just the correlation between these two numbers would be interesting.

• http://hickory-high.com/ Ian Levy

Thanks for reading and commenting by the way!