# Defense: Performance, Consistency, and Trends

Click for a full-sized interactive version

Measuring individual defense is tricky. Even our primary defensive measure, points allowed per 100 possessions (defensive rating), is arguably more dependent upon what other people do than what the player of interest does or does not do. For instance, I am confident that a lineup consisting of Francisco Garcia, me, my fat neighbor, and his two obnoxious little children could achieve pretty good individual defensive ratings if we were on the floor while JR Smith decided to go on one of his epic three-point chucking expeditions. Garcia would just stand still in front of Smith while the rest of us eat nachos in the corner. A defensive rating of  no more than 70 would be guaranteed for all of us.

For this reason, I created a new defensive measure, called net defensive rating. It is calculated by subtracting the team’s defensive rating for one game from an individual player’s defensive rating for that same game (player’s defensive rating – team defensive rating). Basically it compares a player’s defensive rating to his team’s defensive rating in order to better separate individual performance from team performance. The above charts show the net defensive ratings for each game for nine Houston Rockets players, their average net defensive ratings for the season, and the standard deviations for their net defensive ratings (as a measure of consistency).

Technical information

The line graph shows every player’s net defensive rating for every game. The players can be filtered using the check boxes on the right. The thickness of each player’s line represents how many minutes he played each game. On the x-axis are dates of games. On the y-axis is net defensive rating. You can mouse over a player’s line to find more information about a game on a specific date. Remember, since this is defense, lower numbers are better. Each player also has his own trend line (the straight dotted line).

The left bar graph shows players’ average net defensive ratings . Again, lower numbers are better. The right bar graph shows players’ standard deviations. Standard deviation is a measure of variance; think of it as average distance away from an average value. So if I have two numbers, say 20 and 10, my average is 15 and my standard deviation is 5 because 20 and 10 are both 5 away from 15. In comparison, I can have two numbers, 16 and 14, and my average is still 15 but my standard deviation is 1. Back to the bar chart, a high standard deviation indicates a player is usually far away from his own average net defensive rating, and therefore is defensively inconsistent. A low standard deviation indicates that a player’s performance is consistent from one game to the next.

Important limitations

All values are unweighted. That means a player’s net defensive ratings for his games are considered equally when computing averages, regardless of how many minutes that player might have played in those games.

Observations

Let’s start with the bar chart of averages. Dwight Howard is by far and away the Houston Rockets best defensive player, while Aaron Brooks is the worst. In fact, Howard is the only player whose average net defensive rating is negative, meaning he’s usually defending better than the team as a whole. Not much surprise here.

The consistency measure is a bit more interesting. In addition to being the worst defender, Aaron Brooks is also the least consistent, not a good combination. Jeremy Lin and James Harden are the two most consistent defenders, with the lowest standard deviations on the team. But since those two are also two of the worst defenders on the team, that just means they’re consistently not very good. And for all the acclaim that Patrick Beverley’s defense receives, it’s pretty much on par with Harden’s and Lin’s, but much less consistent.

The best news comes from looking at the line graph. The volatility of measuring defense definitely shows, with each player’s line looking like the Dow Jones Industrial Average. However, despite the volatility, some trends are developing. First, some players are strongly trending downward, meaning their net defensive ratings are improving over time (Howard, Terrence Jones, and Chandler Parsons).

Brooks, Harden, Lin, Garcia, and Beverley (injury shortened) have flat trend lines, or at least flat enough that one can’t really make any conclusions. Omri Casspi is the only player who could be argued is trending upward, though it’s not a very steep climb.

Philosophical thought of this post

Defensive performance seems to correlate with size. The Rockets biggest guys have the best net defensive ratings, and the smaller the player the higher his net defensive rating seems to be. Maybe all the talking head babble about length and wingspan has some truth to it.

Conversely, if the above is true, then some of the worst defenders might be those who are worse than their size would predict, and vice versa for those who are better than their size would predict. The Harden/Garcia and Parsons/Casspi comparisons are worth mentioning here. Both pairs are similarly sized players who play the same positions and guard the same opponents, but one is playing better defense than the other.

About the author: Richard Li is an independent researcher and consultant. He likes numbers and pictures.

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