Freelance Friday: Evaluating Composite Values of Different Shots
By Guest Post
May 2, 2014; Portland, OR, USA; Houston Rockets guard James Harden (13) shoots over Portland Trail Blazers 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
Freelance Friday is a project that lets us share our platform with the multitude of talented writers and basketball analysts who aren’t part of our regular staff of contributors. As part of that series we’re proud to present this guest post from Josh Mazlish. John is a high school student who proves that you don’t need advanced math skills to love, understand, or even create “advanced” stats. Follow John @thecorner3john to hear his basketball thoughts and random thoughts, and if you want to get in touch feel free to email him at thecorner3john@gmail.com to talk about basketball or whatever else.
In a post a few weeks ago on Nylon Calculus, Andrew Johnson used the idea of expected points per shot to show why free throws are more valuable than three-pointers or two-pointers. In his post, he noted the added chances of getting an offensive rebound may make field goal attempts slightly more valuable in comparison to free throws, but also mentioned that since field goal attempts are much lower percentage shots than free throws they will yield the opposing team more opportunities against an unset defense.
In two prior articles of his on his blog Andrew had examined differing offensive rebound chances based on shot type/location, and adjusted the overall eFG% of the shot from that; and also average team eFG% based on the prior result (i.e. offensive rebound vs made shot). I thought it would be an interesting idea to combine his two works and try and find a total average value for different shot types. For example, we know a 75% free throw shooter shooting two shots will yield an average of 1.5 points per shot (PPS), while a 40% shooter taking three-point shots produces 1.2 PPS, but that doesn’t take into account the likeliness of an offensive rebound, or how the shot affects your team defense. Using the data tables from Andrew’s site, and additional data from Basketball-Reference and NBAWowy, I was able to try and find a true expected composite value PPP for different shot types. In order to make this work you need to know the chances of getting an offensive rebound based on the shot type. Using NBAWowy data, Andrew was able to figure out these different offensive rebound probabilities:
Though NBAWowy data is very informative, because it only breaks down these five categories we cannot evaluate the expected value of a floater vs. an elbow 18-footer, vs. a corner three because they do not have unique offensive rebound numbers available. Also, because NBAWowy does not provide league-wide shooting percentages based on shot type, I used Basketball-Reference’s shot data to determine league averages. However, Basketball-Reference does not separate into shot type, but instead into shot distance, so the only categories where I had both OREB% and FG% averages were three-point shots and free throws. I decided to evaluate everything in terms of PPP, in order to make it easier to compare relative values of shots. Here are the comparative values of taking a league average three-point shot, and two league average free throws:
In order to get these numbers I had to figure out the expected PPP off of an offensive rebound, defensive rebound, or made shot, because Andrew only had the eFG% after these outcomes. I figured out the average number of shots per possession (0.88) and used the eFG% based on prior event as compared to the league average eFG% to find how much of an increase or decrease in PPP there was based on prior results. I found that PPP after an OREB is 1.12, after a DREB is 1.063, and after a made shot is 1.016, while the league average PPP is 1.067. In this analysis I did not take into account any events past the first offensive rebound, so the small but existent probability of two offensive rebounds in a row, or getting an offensive rebound, but then turning the ball over and putting the opposing team in an advantageous situation is not taken into account.
What is interesting about these numbers is that despite the much higher frequency of getting an offensive rebound, a three-point shot is still only half as valuable as two free throws, in terms of net value. Additionally, what these numbers represent is a way to judge any type of shot, if we can just figure out the FG% or FT% of that specific shot, and the OREB% from that location. For example, we could figure out the net PPP of a Kyle Korver 3, a Dwight Howard FT, a Kyrie Irving layup, or even a Dirk Nowitzki 16-23 footer, if we estimate OREB%. Also, you can further refine the accuracy of this analysis when you are looking at just one player, because instead of using league average PPP off of DREB/OREB/Made FG we can use specific teams, and what they allow, thus enabling us to examine the value of any shot within a team context.
This analysis still has it’s flaws; for example: are offensive rebounds off three-point attempts less valuable because they are usually farther away from the hoop, and defensive rebound off three-point attempts more valuable because they more easily start breaks? I have not seen numbers on specific shot locations effecting eFG% of offensive rebound possessions or possessions from defensive rebounds, but my guess is they may slightly bring down the value of the three in relation to closer rim attempts. Overall, the key conclusion from this article is that three pointers are really good shots for an offense, but still pale in comparison to getting to the line. Using this analysis one could further examine the merits of different Hack-a-Shaq strategies by team and player. As the amount of data for specific events continues to increase in coming seasons the ability to estimate the two way impact of any one shot will become more and more accurate, and our understanding of shot efficiency will continue to grow.