NBA Lineup Evaluator: Diversity

In most sports and at most skill levels, if you are unpredictable in your movements and actions you will have a better chance at being successful; you’ll have a better chance of beating your defender if he doesn’t know what you’re going to do. Granted, at the end of the day, high-performance level always wins out, but one can give themselves a better chance of winning a battle by being unpredictable or diverse.

One component in our measuring of a basketball lineup (NBA Lineup Evaluator), is the predictability of what a lineup will do offensively. Using’s play type statistics, which Cranjis McBasketball outlines well in this article, we can measure how frequently a player uses a specific play type. If you aren’t familiar with the play types, we recommend you check out Cranjis’s article, but here is a quick list:

  • Pick and Roll Ball Handler
  • Pick and Roll Roll Man
  • Transition
  • Off-screen
  • Spot-up
  • Isolation
  • Hand-offs
  • Cuts
  • Putbacks
  • Post-ups
  • Miscellaneous

It is important to note that these frequencies are generated from how often a player shoots out of those play types. It is also important to note that these play types are heavily influenced by the coach. The offense implemented and the freedom given to players will determine which play types are most often used. Additionally, the type and skill level of teammates will also affect which types of play type a player shoots out of. For example, Kevin Durant’s play types changed from OKC to GSW. He shot in isolation 14.9% of the time in OKC and 11.5% in GSW.

So, in order to get a measure of diversity from play types for a specific player, we calculate the overall diversity from the individual play type frequencies using this formula (where i = playtype):

\displaystyle PlayerDiversity = 1 - \sum_{i = 1}^{11} Freq_{i}^{2}

To roll up to the lineup level, we simply weight each player’s individual diversity score by his usage (where i = playtype and j = player):

\displaystyle LineupDiversity = 1 - \sum_{i = 1}^{11} \sum_{j = 1}^{5} Freq_{i,j}^{2} * Usage_{j}^{2}

So, what do these diversity scores look like? Well, they look fairly normally distributed around a mean of 0.135, as seen in this distribution of diversity scores for 2016-2017 lineups:

Here are the most diverse lineups from 2016-2017:

And the bottom 20 (least) diverse lineups from 2016-2017:

How does Diversity compare to Offensive Rating?

While it’s difficult to directly tie diversity to offensive or defensive performance, there may be a number of additional factors affecting the apparent lack of relationship (as plotted above). Furthermore, are some play types more efficient? Most likely. If that’s the case, you probably want to use those play types more. Seth Partnow did a dive into synergy playtypes early in his career, found here, and Nick Restifo with the Minnesota Timberwolves did some further work on Playtypes Varying Importances. Next, how much influence do coaches have on the play types used? Probably a decent amount, and thus at least part of this measurement can be attributed to coaching. Even though there may not be a direct relationship with offensive lineup performance, this at least serves as an interesting study and something to expand on going forward.

For a complete list of 2016-2017 Lineup Diversity Scores, see this link.

Written by  Marc Richards and Jack Werner.

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