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Updating Expected Points Per Shot

May 2, 2014; Portland, OR, USA; Houston Rockets head coach Kevin McHale watches the replay of Portland Trail Blazers guard Damian Lillard (0) hitting a last second shot in the second half in game six of the first round of the 2014 NBA Playoffs at the Moda Center.Mandatory Credit: Jaime Valdez-USA TODAY Sports

Two years ago at Hickory-High, I shared a metric I had been working on, which I called Expected Points Per Shot (XPPS). The idea was to create a metric which gave an, admittedly rough, evaluation of the quality of a team’s or player’s shot selection. Here is the original explanation of the statistic:

The foundational piece of Expected Points Per Shot is the understanding that 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 of 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 generally uses 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.

Initially, I was very diligent about updating the numbers but I kind of fell off the wagon last season. However, I’m committed to keeping them updated and available here at Nylon Calculus and I even have a few expansions planned. Right now team and team allowed (measuring the shot selection a team allows their opponent) are both available going back to the 2000-2001 season. These metrics will have a permanent home under the “Our Stats” tab on the site’s main menu. By the end of the summer the plan is to also have these numbers available for all individual players, also over the same time span.

If this is your first interaction with XPPS, it’s important to remember a few things. The XPPS numbers for a team a rough evaluation of a team’s shot selection. But since it relies on league average values, it isn’t a perfect fit. Teams over and under perform the league average values and so when looking at XPPS it’s also important to compare it to Actual Points Per Shot and Shot Making Difference (the difference between XPPS and Actual PPS–how well a team actually performed compared to what we expected). Although my analysis showed that variations in XPPS could explain about 19% of the variations in a team’s overall offensive efficiency, it’s just one factor for evaluating how effective a team is at implementing an offensive or defensive game plan. For a more nuanced look at shot selection, you can check out this “What We Know” piece from last week.

Ian Levy

Ian Levy (@HickoryHigh) writes about basketball from the wilds of Southern Vermont. In addition to his work for Hardwood Paroxysm, he is the man behind the curtain at Hickory-High and a contributor to Indy Cornrows, The Two Man Game and HoopChalk.