WNBA Rotations and Rotation Indices

In my post called Worst Coach in the W?, Q from Rethinking Basketball semi-challenged me to take two metrics and apply them to the WNBA:

a) The John Hollinger index of measuring coaches by performance vs. expected wins, and
b) The David Sparks metric called "Rotation Index" which measures how much of a rotation each team has.

I've already completed a). The work is at home, and will show up on the blog later. As for b)....

Sparks writes:

One difficulty with identifying team rotations is that it isn't as simple as counting then number of players who appear in any given game. There is a subtle difference between identifying the number of players who might be used in a game versus the number of players in a rotation, and that difference mainly has to do with playing time.

As such, it is common to see a threshold of playing minutes employed to identify where the rotation ends. Perhaps the rotation is all players who see more than 10 minutes of playing time in a game... but perhaps the number should be eight minutes. Regardless of the cutoff employed, this method will give an authoritative-sounding answer, but using a minutes cutoff only means that rotation size is a function of the threshold chosen, which is a telltale sign of arbitrariness.

Sparks solves this problem by using something called the Herfindahl index, which is used to determine how much competition there is among firms in an industry. Sparks simply took the same idea and used it to determine the competition among players for minutes.

For example, here are the minutes played for all members of the Dream so far:

Holdsclaw 708
Castro Marques 656
Lyttle 699
McCoughtry 488
de Souza 703
Snow 377
Miller 330
Latta 221
Lehning 510
Lacy 285
Teasley 234
Young 72
Price 16


This adds up to 5,299 minutes. (Really, 5,300 but the missing minute is a rounding error.) We are now going to determine the percentage of total minutes played by each player. This is expressed as a decimal number and is the second number following each player's name.

Holdsclaw 708 0.13
Castro Marques 656 0.12
Lyttle 699 0.13
McCoughtry 488 0.09
de Souza 703 0.13
Snow 377 0.07
Miller 330 0.06
Latta 221 0.04
Lehning 510 0.10
Lacy 285 0.05
Teasley 234 0.04
Young 72 0.01
Price 16 0.00

What we do is add up the squares of the second numbers. In the end, we get the value 0.1016. We could take numbers like this for each team, and see which one has the biggest Herfindahl index. To use the example in economics, we find out which of the businesses (players) are closest to a monopoly (in minutes).

However, there's no easy intuitive grasp of 0.1016. Sparks created the "Rotation Index" by taking the inverse of this number, or 1/0.1016. The number you get is 9.8388. To quote Sparks again:

I think that you will agree that these numbers look very much like what you would subjectively conclude after viewing the above minute distributions.

In short, you should conclude that Meadors has a 9 to 10 player rotation - she's playing almost with two full units of players. This is a subjective measure - it doesn't really spit out the number of players in a rotation, but you can imagine it as such.

Here are the numbers for the entire WNBA before the games of August 24, 2009:

Seattle 7.44
Washington 8.11
Detroit 8.55
Indiana 8.60
Phoenix 8.61
New York 8.83
Los Angeles 8.98
San Antonio 9.27
Minnesota 9.34
Chicago 9.48
Atlanta 9.84
Sacramento 10.23
Connecticut 10.43


We can see that the Storm depend strongly on certain players who eat up the bulk of the teams minutes - if you want an imaginary number of players in the Storm rotation, why not choose "7" or "8" as suggested by the Rotation Index? Whereas Sacramento and Connecticut practically use everyone they can find.

Q suggested this might be a way of looking at whether coaches were strong coaches or weak coaches. A weak coach has an inconsistent rotation and is always flipping players in and out, whereas a strong coach identifies her best players and sticks with them. Theoretically, a high Rotation Index should equal a good coach? Right?

Sparks disagrees.

Based solely on these results, it is difficult to discern whether smaller or larger rotations correlate with success. Many good teams appear to have small rotations, but many other good teams appear to have large rotations.

Furthermore, these results can be skewed by trades or injuries. Each of these events break up the distribution of minutes. Connecticut and Sacramento might simply have had a lot of injuries - or trades - or maybe it's just Mike Thibault's style to use up a lot of players.

So if you're the fan of a particular team, you can ask yourself: "does my team's place in the Rotation Index list say more about my coach's style of play, or does it say more about external circumstances, or does it say something about my coach's inability to play players consistently?" I'll let the reader be the judge.