Efficere: A Measure of Shot Efficiency

Efficere (Latin): To effect, bring about, do.

There is no single more important skill in the NBA in my opinion than the ability to make shots.  Woah!  Groundbreaking ideas over here!  Because of this, efficiency has become a hot button issue for the league.  The best commonly used measure of shooting efficiency is True Shooting %.  It is calculated by looking at how many points a player scores relative to the number of “true” shot attempts, a combination of field goal attempts and free throws, a player has.

Generally speaking, players are compared to league average TS% in order to view how they are doing compared to everyone else.  While this is a fine way of looking at it, comparing to a generic league average leads to plenty of pitfalls.  For instance, all players do not shoot the same shots, or the same number of shots, from the same places.  If they did, measuring the most efficient players would be a piece of cake: player 1 is greater than player 2, we’re done here.

Unfortunately for us, none of those things are really true.  Players all take different shots, different amounts of shots, different shot locations.  Players create shots for themselves at different rates, shoot threes at different rates, have different skills.  So the question I want to answer changes from “how efficient is a player relative to everyone else” to “how efficient is a player relative to an average player who took all the same shots they did, the same ways they did”.

How good is a player in their offensive role?

Here is where we reach Efficere, my new measure of scoring efficiency.  Efficere, beyond just being a fancy sounding word (yes, that I will italicize every chance I get because it looks extra fancy that way), attempts to control for everything from shot location to difficulty, to give a better view at how efficient a player actually was.

So how is Efficere calculated?  Well, I started off by running a regression of every regular season from 1979-80 to 2016-17 with TS% as the target variable.  The variables I used to predict Expected TS% were:

Offensive Rebound % (ORB%), Free Throw Rate (FTr), 3-Point Attempt Rate (3PAr), % of Made Field Goals that were Assisted (Ast’d%), Usage %, Self-Created Usage % (SCUSG%), and Self-Created Usage % Squared.

A few of these terms might be surprising to people.  FTr and 3PAr make sense because those are key components within TS%.  Usage % is straight forward as well, simply a measure of how any possessions a player is responsible for using while on the court.

ORB% is a term I often use to help explain where a player is on the court when their team shoots.  Players with high ORB% (think Andre Drummond) spend more time near the rim, while low ORB% (think Kyle Korver) very rarely go anywhere near the paint.

Ast’d% is a useful term for quantifying how much a player is being fed by teammates versus creating their own shots.  High Ast’d% players (think Kyle Korver or Bismack Biyombo) are known for either spotting up behind the arc or finishing passes around the rim, while low Ast’d% players (think Russell Westbrook or John Wall) are often charged with creating shots for everyone and themselves.  It’s much harder to create shots than just finish shots.  Real Ast’d% is available going back to the 2000-01 season and an estimate is used for prior seasons.

The final term to explain is Self-Created Usage % and the squared version of the same.  Self-Created Usage % is an interaction term between Usage % and (100%-Ast’d%), a straight multiplication.  It helps to reward guys who often creates for themselves and takes a lot of shots, and squaring it leads to further rewarding the truly elite players who do everything and do it themselves.

Now that we have a baseline for what makes up expected TS%, the formula is as follows:

Expected TS% = 
ORB% * (0.000517) + FTr * (0.172) + 3PAr * (0.0671) - Ast'd% * (0.0354) + USG% * (0.00132) - SCUSG% * (0.00320) + SCUSG%^2 * (6.29x10^-11) + 0.495

These raw expected TS% values are converted to Efficere per 48 minutes and Efficere using the following equations:

Efficere/48 = 
(Actual TS% - Expected TS%) * 2 * Usage% * (100%-TOV%)

Efficere = 
(Efficere/48) *  Minutes Player/48

The general form for calculating Efficere is a standard way of looking at TS% compared to average; however, using the calculated Expected TS% leads to more accurately valuing the quality of a player’s shots instead of a general league average.

Every player is assigned a raw Efficere score, which is than adjusted so the season long sum is equal to zero.  I adjust in this manner because efficiency matters relative to everyone else of the same era.  While looking at the non-adjusted season averages is interesting for seeing how efficiency has changed in the league over time, it serves no practical use for comparing players.

Before moving on to an example, I would like to remind everyone that Efficere measure how efficient a player is IN THEIR ROLE.  Great role men are rated in the 99th percentile of Efficere in the same way great isolation scorers are.  If you want to use this statistic for comparing players, make sure you take account of a player’s context.  If DeAndre Jordan has a larger Efficere score than DeMar DeRozan, it does not mean that DeAndre Jordan would be more efficient than DeMar DeRozan if they switched roles.

A  great example for the use of Efficere is Russell Westbrook’s insane 2016-17 season.  Westbrook’s TS% of 55.4% was just about league average for 2016-17.  But no one in their right mind would think an average player could have a TS% of 55.4% while using literally all of the possessions and creating literally all of his own shots.

Using Efficere, Westbrook’s season looks as follows:

Screen Shot 2017-08-22 at 3.51.56 PM
Russell Westbrook’s 2016-17 Season

The Expected TS% is much lower than league average for 2016-17 at 53.7%.  Westbrook’s high 3PAr and high FTr hurt him, especially given that he’s a below average three point shooter, but the amount of shots he created for himself on such crazy volume led to him being in the 83.8th %ile on a per minute basis and 89.3rd %ile after accounting for minutes played.  So Efficere says that, while Westbrook still had room to improve his efficiency, he was really freaking good when you consider the shots he was actually being asked to take.

In terms of the complete list of Efficere, the top & bottom 25 career scores are as follows:

Screen Shot 2017-08-22 at 4.02.22 PM
Top 25 Careers by Efficere
Screen Shot 2017-08-22 at 4.02.30 PM
Bottom 25 Careers by Efficere

The way Efficere values careers is lin line with the way most of these players are perceived.  All of the top 25 are renowned for their efficiency and volume, while the bottom are commonly known as in-efficient, volume scorers.

This is Efficere, a better way of looking at how efficient a player really is.

Complete season-by-season and career total database: Database


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