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Using Numbers to Talk About Offense and Defense

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Or also, how not to use numbers to talk about offense and defense

NBA: Philadelphia 76ers at Boston Celtics Greg M. Cooper-USA TODAY Sports

I’m going to start this article with the motivating tweet.

I think we can all agree that Joel Embiid is one of the very best defensive players in the league. It’s not a particularly debatable point. What I want to do is add some clarity on ways to use or not use common advanced-ish stats.

Defensive Rating

I’ll be using the official NBA.com definition of defensive rating (DRTG), which is “[t]he number of points allowed per 100 possessions by a team. For a player, it is the number of points per 100 possessions that the team allows while that individual player is on the court”.

I hate to assign homework, but check out this table for context, which is the league leaders in DRTG by players. You’ll note that there are two Milwaukee Bucks players in the top five, both of whom are not Brook Lopez or Giannis Antetokounmpo. This gets at precisely the problem with assigning an individual player a DRTG - it’s a lineup based statistic. The proper way to cite a DRTG is “lineups with Joel Embiid have a DRTG of 95.3” or “Joel Embiid has an on-court DRTG of 95.3”. This might sound like meaningless pedantry, but it’s important to be clear about what exactly a statistic you are citing measures. The lineup effect is huge, as Sterling Brown and Donte DiVincenzo are likely benefiting from time playing alongside Milwaukee’s pair of DPOY candidates.

More directly applicable to the Sixers is that last year, JJ Redick had a better DRTG (104.7) than Joel Embiid (104.8). Considering that they were heavily platooned because Redick needed a defensive stopper behind him (also the DHO), you can see how the improving phrasing of “lineups with player X had a DRTG of Y” is better. Also, without any context to the shared minutes, it can be incredibly misleading.

Offensive Rating

Exactly the same as DRTG, but offense.

Net Rating

Net Rating is the combination of offense and defense into one rating, which “[m]easures a team’s point differential per 100 possessions. On player level this statistic is the team’s point differential per 100 possessions while he is on court”.

Essentially the primary issue with net rating, and in particular five man lineup net rating, (this all goes 100% the case for DRTG as well), is that it is incredibly unstable. Ryan Davis (@rd11490) just wrote a very nice explainer on this concept, but I’m going to summarize here as well. Also, go follow him on Twitter and explore his website.

Five man net rating requires a huge sample size of possessions in order to become stable enough to be useful. Let’s walk through the below figure, provided courtesy of Ryan Davis. Moving to 100 on the x-axis we can see that the orange line has the lowest net rating. This means that if a lineup has played 100 possessions (offense and defense each), giving up a single three and not scoring on the 101st possession pair reduces net rating by almost three full points. The reverse is true, where making a three and getting a stop increases net rating by almost three full points. Even moving out towards 250 possessions, a single 3/0 or 0/3 possession pair is about a +/- 1.5 net rating swing.

Figure 1: Net rating and single possession changes by total number of possessions
Ryan Davis (@rd11490)

You should be very judicious to use net rating below 250 possessions (provide further context if you do), and just flat out don’t do it less than 100. Ryan again provides a great graphic for the Sixers’ most played lineup (prior to last game) that shows how their net rating would change based on giving up a run or going on a run.

Figure 2: Effect of runs on Sixers net rating
Ryan Davis (@rd11490)

If this lineup started a game at approximately a +15 net rating, just one run against of 0-15 would reduce their net rating by eight. That’s a greater than 50% reduction in net rating based on a bad couple of minutes. The converse is also true, with a nearly 50% increase in net rating with a few hot possessions.

Keep in mind that over the course of the entire season last year, only 40 out of 15297 lineups played more than 500 possessions (~10 games of possessions), and only 15 lineups played more than 1000 possessions (~21 games of possessions).

Individual Advanced Metrics

This is where we get into the RAPM, RPM, and PIPMs of the world. Explaining exactly how they are calculated is far outside the scope of this article, but I’ll focus on PIPM and it’s usage. PIPM is provided by Jacob Goldstein and The BBall Index.

First, here is the public display of PIPM that you can and should explore. Like other single value advanced metrics a larger value is “better” and a smaller value is “worse”. The important part is what comes next. PIPM is explicitly not a tool to rank players by how good they are. It is a tool to measure impact, which obviously relates to quality. However, impact is devoid of context related to how a player is used in a scheme and similar strategic decisions.

Secondly, it’s important to note that the output of these type of models are estimates with error bars, analogous(ish) to the standard deviation of a mean of values. At this point in the season, single year PIPM has approximately +/- 1.0-1.2 around each estimate. If Player A is +3.00 and Player B is +3.08, you absolutely should not say that Player B is obviously better because they have a larger PIPM. The confidence interval for Player B’s PIPM would range from approximately +4.08 to +2.08 and Player A’s would be between +4.00 and +2.00. Use these single value metrics as ways to make tiers. Rote rankings as absolute truth of quality is both factually incorrect and against the intent of the model.

Wrap Up

  1. Don’t use five man ratings unless you have an extremely good reason to do so or have a large sample size (>500 ideally).
  2. Don’t say “Joel Embiid’s DRTG is 100”, but do say “lineups with Joel Embiid on the floor have a DRTG of 100”. Again, only if there is a large enough possession total to indicate that as a good idea (>500 ideally).
  3. When using single value advanced stats like PIPM or RAPM, don’t use them as absolute barometers of a player’s quality or goodness, but as a measure of impact. Also, understand that there are fairly large error bars associated with single year models (especially early in season), and use multi-year when possible to reduce those.
  4. Understand that there might not be a perfect numerical way to describe what you want, so use the best option, provide context, and note the limitations.