Raptors Cage

The newest player efficiency statistic: EPCPM

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Oakland Athletics’ general manager Billy Beane was famously quoted saying, “Adapt or die”, several times in Oscar nominated movie, Moneyball, in reference to the idea that the ideologies around team building in professional sports were changing drastically.

Paul DePodesta, played by Jonah Hill in the movie, entered the Athletics’ organization as a data junkie who had an eye for looking at sports through a different perspective. Rather than looking for the sexiest swings, the swiftest runners, or the fastest pitchers in baseball, DePodesta developed statistical models to infer which players were being undervalued according to their true efficiency. His outlook ultimately helped a bottom-of-the-barrel Oakland team with a payroll one third as high as their competitors manage to win an American League West title, generating one of the most cultivating storylines in sports history.

Not only did this new approach of team-building and data analysis spread throughout the baseball world to give organizations a competitive edge, but also throughout the world of sports. In the video below, Rajiv Maheswaran outlines just how incredible and in-depth basketball analytics can be. Note that this TED Talk is nearly five years old, and the world of data science in sports has only evolved further since that time.

The usage of analytics in the NBA has been evident in recent years. One can point to the Golden State Warriors’ dynastic run from 2015-2019, which existed vicariously through their small-ball “death lineup” consisting of a frontcourt filled with forwards, and no traditional centres. This ideology of preferring skill to size enforced by Steve Kerr, and with the help of talent such as Stephen Curry and Kevin Durant, has helped shape the modern game of basketball. If you can’t shoot the three (which is worth more than a two), your value as a player diminishes exponentially.

Of course, there’s more analysis that goes into the game than a three point shot being worth more than a layup, but the ways in which it is enforced, and the ways in which the game has changed around such simple theories is obvious. In Houston, Daryl Morey has opted to build his Rockets squad without any traditional centres – attempting to maximize the expected value of every shot, and make his team’s offensive possessions even quicker than they already are. In Detroit, Ed Stefanski traded Andre Drummond – whom was thought to be the franchise’s cornerstone for the better part of the 2010’s – to the Cleveland Cavaliers for a penny, a potato chip, and an IOU.

Change is always a process, but numbers in the game of basketball have a track record that leads to championships. They’re more prevalent than ever, and there can never be enough analysis or data involved in making a decision.

Currently, there is a wide array of player efficiency measures available to the public, and even more are used by NBA executives. These stats range from true shooting percentage, to Player Efficiency Rating, to Real Plus-Minus, and there are plenty more. Most of the stats either calculate a player’s efficiency based on their own statistics, or attempt to depict one player’s true efficiency devoid of the other guys on the floor with them. While statisticians have done an incredible job of finding ways to describe such intangible subjects to an extent that makes sense to average basketball fans, it can’t be dismissed that none of these computations are perfect. Nor are mine, but here we go again.

Having previously developed the Scoring Balance Coefficient – a figure that attempts to describe how balanced, or unbalanced, a teams offense is, I decided to tackle the issue of tracking a players efficiency, taking all aspects into account.

I decided to look at the issue from two sides: a player can be efficient within the offense – as one of the five guys on the floor, and they can be efficient as an individual – essentially based on what the player does with the ball in their hands.

Thus, these are two separate measures to efficiency, one of which I used an existing stat to track – the true shooting percentage of a player, which accumulates and effectively weights a player’s shooting percentages from the three-point line, the free throw line, and within the arc. As for a measure that depicts how efficient a player is within the offense, I chose to develop my own. I wanted to see who was able to create the most points for their team while using up as few possessions as possible, per each minute they were on the floor.

To elaborate, the Effective Points Created Per Minute (EPCPM) was developed as follows:

((points + assists*average value of team’s basket)*(1 – usage rate)) / minutes per game

The first part of the bracket serves to identify how many points a player creates for their team in a game – obviously first accounting for the points that they score themselves, and then adding the points that they create off of assists, by taking their assists per game, and multiplying it by the average value of their team’s basket.

This figure is then multiplied by one minus the player’s usage rate (percentage of the team’s possessions that are used by that player) as a method to penalize players with a higher usage rate, and level players with a lower usage rate.

Finally, to account for the fact that some players play longer minutes than others, which would expectedly lead to them creating more points for their team, the final number is divided by said players minutes per game. This ultimately spits out the EPCPM.

For example,

Kyle Lowry averages 19.6 points per game, and 7.6 assists per game, the average Raptors basket is worth 2.334817 points, he has a usage rate of 23.0%, and he plays 36.5 minutes per game.

This means that Lowry creates approximately 39.85 points per game for his team, leaves 77% of the team’s possessions up his teammates when he’s on the floor, all throughout 36.5 minutes per game, which gives him an EPCPM of approximately 0.79. This ranks him 26th in the league (including unqualified players).

The EPCPM does not account for any shooting percentages of the player, because that factors into the player’s individual efficiency, rather than their efficiency within the team’s offense.

By comparing these two variables, EPCPM, and true shooting percentage, I was able to generate the following matrix, which indicates how efficient a player is within the offense, and how efficient they are as an individual, if either. Each corner of the matrix is labeled based on what that segment represents, and how players stack up against league averages.

Each point on the chart represents an individual player. Higher points on the matrix represent players with better true shooting percentages (more efficient individuals), and points on the chart further to the right represent players with a higher EPCPM (players more efficient within the offense)

In order to validate the EPCPM as an effective measure of player efficiency, I also graphed each player’s EPCPM against their turnover percentage. Rightfully so, the two variables had a negative relationship, meaning a higher turnover percentage, implying an inefficient player, would have a lower EPCPM, also implying an inefficient player, and vice versa. The regression analysis, with EPCPM as the independent variable and turnover percentage as the dependent variable is shown below.

Additionally, I have provided a list of the top 50 EPCPM’s in the league:

Admittedly, the caveat of this stat lies in the fact that it does not account for a team’s pace, the player’s turnovers, the quality of the players competition or his teammates surrounding, or offensive rebounds, amidst other nitty gritty details, however it does provide reliable insight as to how effective a player is as a piece of his team’s offense.


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