Measuring the Relationship Between Players and their Lineup’s Effective FG%

In my last post I presented a method for measuring the relationship between players and their lineup’s shot distribution.

This, however, is only part of the picture. We also need to know the relationship between players and their lineup’s shooting percentages from those locations on the court to determine if a player has a positive or negative relationship with their lineup.

To measure this relationship, we can combine the shooting percentage and shot distribution relationships to calculate the relationship between a player and their lineup’s effective field goal % (eFG%). This measure takes into account the fact that 3pt shots are worth more points, so it has a direct relationship to points per field goal attempt.

The Shot Distributions

While putting this data together I realized I needed to re-define the areas on the court. This is because some of the areas like the high paint and the corner 3pt shot are associated with small samples that do not provide a very good link between lineups when rating FG%. Thus the FG% ratings using 5 areas is filled with a bunch of noise.

To resolve this, I decided to use these three areas:

• Low Paint – Shots in the paint within 6 feet of the basket
• Mid-Range – All other 2pt shots
• All 3pt Shots

It would be nice to separate the high paint from the mid-range shots and the corner 3pt shots from the other 3pt shots, but it doesn’t appear as if the method for rating FG% would handle these small samples well.

To see the relationship between players and their lineup’s shot distribution with respect to these three areas of the court, see the following spreadsheet:

http://spreadsheets.google.com/ccc?key=pLJimPjd7oquK5TB7tWIDNQ

This should match up well with the results from my last post, as the high paint shots have been merged with mid-range shots, and corner 3pt and other 3pt shots have been combined to simply be all 3pt shots.

As before, a number of 1.5 indicates this player is associated with an increase of 1.5% more shots from this location on the court compared with the league average player at that position.

The Shooting Percentages

I’ve already looked at the low paint, but now I need to present the results from the other two locations.

You can see these results in the following spreadsheet:

http://spreadsheets.google.com/ccc?key=pLJimPjd7oqvrsxuJnpI3Kg

This spreadsheet shows how a player is associated with shooting percentages on the three locations of the court when compared the league average player at that position.

As an example, here is how you would interpret Chris Paul’s numbers (line 20):

On Offense: Chris Paul is associated with a 0.1% FG% increase from the low paint; a 0.7% FG% increase from mid-range; and a 1.3% FG% increase from 3pt range.

On Defense: Chris Paul is associated with a 2.8% FG% decrease from the low paint; a 2.3% FG% increase from mid-range; and a 11.7% FG% increase from 3pt range.

I think it’s fair to say that this relationship between Chris Paul and defensive 3pt FG% played a major role in his ’07-’08 defensive adjusted +/- rating last year.

Combining Shot Distributions and Shooting Percentages

Using the shot distribution and shooting percentage data, I can calculate an offensive and defensive eFG% for each player.

These ratings can be found in the following spreadsheet:

http://spreadsheets.google.com/ccc?key=pLJimPjd7oqsrV5hEIH36NA

As an example, here is how you would interpret Manu Ginobili’s rating (line 6):

On Offense: When facing a league average defense and surrounded by an offensive lineup consisting of a league average PG, SF, PF, and C, Manu is associated with a 50.6% offensive eFG%.

On Defense: When facing a league average offense and surrounded by a defensive lineup consisting of a league average PG, SF, PF, and C, Manu is associated with a 43.5% defensive eFG%.

Net eFG% Rating: Subtracting the defensive eFG% from the offensive eFG% provides the net eFG%. Based on this ’07-’08 data, Dwight Howard is rated as the best in net eFG%.

Lineup Combinations

In my last post I presented a hypothetical loaning of Yao Ming to the ’07-’08 Celtics. Under this scenario, Yao Ming would replace Kendrick Perkins and would be paired up with Rajon Rondo, Ray Allen, Paul Pierce, Kevin Garnett.

With Perkins, the ’07-’08 Celtics offensive eFG% would be 54.7%, while the defensive eFG% would be 42.8%. This equates to a difference of 11.9%.

With Ming, we would estimate that this lineup would have an offensive eFG% of 53.7%, while the defensive eFG% would be 43%. This equates to a difference of 10.7%.

So strictly in terms of eFG%, the Celtics would prefer to keep Perkins over Ming. This advantage is very small, though. In terms of points, this equates to an advantage of 2.4 points per 100 shots for the ’07-’08 Celtics lineup with Perkins over Ming.

Summary

These are fun to look at, and I believe they provide an interesting look at the game that we’ve never had before. That being said, we need to know how these ratings vary from year to year. Can we create aging curves for these offensive and defensive eFG% (or for specific areas of the court)? How well do these predict future results?

In addition, while important, shooting does not explain everything. Turnovers, rebounding, and free throw shooting all play an important role in winning games. So these are the areas for future investigation when comparing players.