*Last updated 1/17/2013
What is Expected Points Per Shot Allowed?
Expected Points Per Shot (XPPS) is a statistic that measures the quality of a player or team’s shot selection. When we looked at Expected Points Per Shot Allowed, we are assessing the effectiveness of a team’s defense through the quality of shots they allow their opponents
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 or team’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 or team’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 or team’s shot attempts, including the calculated trips to the free throw line. The result is Expected Points Per Shot. To calculate Expected Points Per Shot allowed I mirror the same process but use the statistics each team allowed their opponents.
It’s important to remember that this is a measure of the quality of a player or team’s shot selection. Players or teams who take a lot of easy shots like layups or corner three-pointers will have a higher value. However, players and teams under and over-perform league averages all the time. For that reason I compare Expected Points Per Shot Allowed to Actual Points Per Shot Allowed. 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 central graph marks each team, going back to the 2000-2001 season by both their Actual Points Per Shot Allowed and their Expected Points Per Shot Allowed. The shape of each mark indicates the season it came from. The color of each mark represents that team’s Defensive Rating (points scored per 100 possessions).
Below the central graph are set of filters. This will let you control the display of the graph. You can filter by team and season, or narrow the results by DRtg., XPPS Allowed, Actual Points Per Shot Allowed, 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.
I need to do some adjustments to my data so that the visualization can build a summary table at the bottom. At this point the only way to view the actual numbers is to scroll over the mark for a team. A dialog box should pop up identifying the team and showing their actual numbers.