In working on my offensive wins above average stat, I realized that one of the key missing pieces to the formula was a function that adjusted for the player’s offensive possessions per minute. The offensive-possessions-per-minute statistic is just what it says: the player’s offensive possessions per game, divided by his minutes per game. It seems logical then, that if a player were to increase his offensive possessions per minute (taking more shots in the same amount of time) that his efficiency would decrease due to a lower minimum in his shot selection and increased attention from defenses. Conversely, were a player to decrease his offensive possessions per minute, it seems logical that his offensive efficiency would increase, due to a higher minimum in selecting shots and less attention from defenses. Below is a graph of all players in the NBA to have played at least 20 games and 15mpg. When looking at the graph, two trends are immediately noticeable, as illustrated by the red and blue lines.
The top red line illustrates exactly the theory I mentioned before: as offensive possessions per minute increase, offensive efficiency falls. This would explain why the highest offensive efficiencies fall to the left of the graph, and all of the numbers at the far right of the graph are somewhere near the middle of the y-axis. However, the blue line seems to violate this theory. What it illustrates is that the bottom of the efficiency spectrum increases as OP/M (offensive possessions per minute) increases. The expectation however, would be that all of the data points would follow a general trend from upper left to lower right, as shown by the graph below:
Quite clearly, however, this is not the case. So why is the bottom end of the spectrum increasing? The answer is simple: coaches won’t allow a player with a very low efficiency to take many shots. What this does then, is shifts most of the players that would be in the bottom right portion of the graph up and left, as shown in the graph below:
This is why there are large clusters of players along the bottom edge of the efficiency spectrum where one would expect a more even distribution, as seen along the top edge.
So, what then does this mean? It means that for a basic estimation of a player’s “true efficiency,” one should adjust by the slope of the line in the graph. The slope of the line in the graph as shown is ~ -1/3, though it is something of a subjective choice. The average player’s OP/M in the NBA is about .379. With the slope and the player’s OP/M and OE known, it is possible to calculate the OE for any OP/M using the point slope formula Y1 – Y2 = m (X1 – X2). So, to adjust a player’s efficiency to see what it would be at the average OP/M, use the following formula:
True efficiency = 1/3[OP/MP – OP/MA] + OEP
OP/MP is the offensive possessions per minute of the player
OP/MA is the offensive possessions per minute of the average player, or .379
OEP is the offensive efficiency of the player
Example: Shaq has an OP/M of about .495, and an OE of 1.179. His true efficiency then is 1/3[.495-.379] + 1.179 = 1.218
Example 2: Brent Barry has an OP/M of about .261, and an OE of 1.357. His true efficiency then is 1/3[.261-.379] + 1.357 = 1.318
