# Quantifying Defensive Versatility

I’ve wanted to work on finding a way to quantify defensive versatility for some time now. For teams and lineups there exists some decent solutions, standard deviation of height divided by average height of a lineup, both weighted by minutes if trying to calculating for an entire team, is a decent way to quantify how “switchy” a group is. As has been highly published, defensive statistics are okay at best; which complicates going much further especially at the player level. NBA.com’s new defensive matchup data is a godsend in this regard. Krishna Narsu, @Knarsu3, recently compiled the data and matched it to basketball-reference’s position estimates to find the percent of time each player spends guarding each position, available here.

Using a similar methodology to the one outlined in this post I wrote, it’s possible to quantify defensive versatility. The formula used to calculate versatility is the HHI formula, the sum of the squares of the percentage of time spent guarding each position. The sum of percentages can only add up to 100%, but squaring each percentage introduces variation in the sum. The more versatile the player the smaller rating, and the higher the rating the less versatile. The highest possible versatility rating is 10,000, and the smallest rating(exactly 20% spent at each position) is 2,000. The ranking for the top-20 most versatile players, minimum 500 minutes played, is below.

Absent from the list is Draymond who ranks just outside the top-20 with a rating of 2565. Jeff Green has been a welcome defensive addition to Cavaliers, being the most versatile defender in the league, and their defense gives up almost 5 fewer points per-100 with him on the floor. The list is made entirely of wings and a point guard in the body of a center. Small forward is the most versatile position on defense.

The numbers underneath each positional designation is the average percentage of time the position in each row has spent guarding that position. The distribution of versatility ratings both for the entire league and by each position are displayed below.

The wider and shorter the plot, the more tightly packed the distribution; the longer and skinnier the plot; the more variation. Both point guards and centers have a wider range of versatility than the wing positions, and higher(worse) average ratings. Small forwards have the densest distribution at the most versatile range. I’d prefer to use a ridgeline plot for distribution by position, but I am still learning tableau. I will likely update later.

The versatility rating can be applied to teams as well. This is done simply by taking the average of the versatility rating for each player, weighted by possessions played.

Houston, Cleveland, Golden State, and Boston are exactly where you’d expect. Boston is bolstered by their young wings Jaylen Brown and Jayson Tatum, as well as Marcus Smart and Al Horford. Philadelphia, with two of the most versatile players in the league, are hurt by their big-men, specifically Embiid who spends 78% of his time on the floor guarding centers.

Defensive versatility has some loose correlation to defensive rating. Less versatile teams tend to do worse on defense, but the relationship is not particularly strong.

Data available here.

1. This is really interesting work. Looking forward to seeing more of your stuff in the future!

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2. Curious, but do you have access to the data to provide the versatility ratings for 2016/17?

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• I do not, sorry. I don’t believe NBA.com ever published the matchup data for any previous seasons.

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3. […] his slower feet further away from the basket. Houston has been the switchiest team in the league, per Krishna Narsu’s Defensive Versatility metric, but Nene ranked as the least-versatile player on the Rockets. Houston has sometimes changed up […]

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