In my last post, I introduced the idea of a “convex hull” for the usage vs. efficiency relationship. If we agree that the upper-right edge of that relationship represents “greatness” (in terms of scoring), then it is a simple matter to quantify the relative greatness of all other player-seasons by measuring the distance from each point to that edge (see the plot below).
The equation for the fitted line (black) was determined to be:
$$ TS\% = 90\%-0.89*USG\%$$
Using this equation we can find the distance from each point to that line (a few examples are highlighted by the red “drop down” lines). We can use the distance right away to rank the players, but the values don’t have much meaning. To put the measurement in some context, I am reporting the distance as 1.0 minus the ratio of the distance to that of a hypothetical average player (54% TS, 20% USG). Therefore, a player that is very close to the line will have a measurement of close to 1. A player close to average will be around 0. Here is a list of the players since the 3-pt rule took effect that have had TS%>55% and USG%>25% (as you can see, all players who were used to create the “greatness” line were given the same rank):
Go to Google Spreadsheet
From the current season, we have: