# New adjusted +/- numbers from HoopNumbers

HoopNumbers has recently updated its adjusted +/- statistics for the current season (for games up to February 25th).  Details on their method, called Regularized Adjusted +/- or RAPM, as well as links to statistics for each of the past 4 seasons, can be found on the site’s commentary page. The numbers they provide are interesting because  they use a special technique to significantly reduce standard errors and they provide adjusted +/- for both the offensive and defensive end. In this post, we’ll take a look at some of their results for the entire league, and also specific to the Houston Rockets this season.

For those readers that are unfamiliar with what adjusted +/- is measuring, think of it this way. Suppose you have a particular 5 on 5 matchup, and you want to know what the expected point differential would be after some number of possessions. The idea is to come up with a number which describes each player’s +/- impact, such that if you add up all these numbers for one side and subtract all the numbers from the other side you’ll arrive at this expected point differential. Now in reality basketball isn’t so simple, and sometimes certain player combinations works better together or certain matchup are more favorable than others. And there are many other variables to consider. Still, if we knew for each player what those numbers were on average, that could be valuable input in deciding which players to pursue in an acquisition or which players to give more playing time to.

Alright, so what is offensive adjusted +/- and defensive adjusted +/-? Think of offensive adjusted +/- as the number of points a player is expected to add to his team’s score (per 100 possessions) by being on the floor, relative to a “league average player.” Similarly, defensive adjusted +/- would correspond to the number of points a player is expected to add to the opponent’s score (per 100 possessions) by being on the floor, relative to a “league average player”.  So, the higher the offensive APM the better, and the lower the defensive APM the better. Note that when I say “points a player is expected to add”, I’m not simply referring to the number of points he scores individually or the number of points the opponent he matches up against scores individually.

I’ll give the usual “stathead” disclaimer: these are interesting to look at, but are not by any means the end-all, be-all player rating. For most players, the ratings makes some sense and can serve as a sort of validation of our subjective opinions or what other methods (e.g. PER) might say. For some players, especially when only looking at data over just 1 year, there are some strange results, but that is to be expected. The model is not perfect, and there is noise in the data. It is interesting to look at nevertheless.

Below, we’ll take a look at some of the results. Again, refer to HoopNumbers for all the raw data.

# League-Wide Trends

I want to start by looking at some league-wide trends. HoopNumbers provides RAPM, Offensive RAPM, and Defensive RAPM for each of the last 4 seasons, as well as combined numbers over all the 4 seasons (“equal weighting”), and combined numbers that are weighted more heavily to recent seasons (“time-weighted”). Consider the following scatter charts, relating RAPM results to PER for the last 4 seasons:

Average over last 4 seasons, minimum of 1000 total minutes played

PER is referring to Hollinger’s Player Efficiency Rating. For those that are unfamiliar with it,  it is essentially a per-possession summary metric that adds the good things a player does and subtracts the bad things a player does, according to the boxscore. We see that PER has almost no relationship whatsoever to Defensive RAPM, but there is a clear relationship to Offensive RAPM.  This makes sense. The boxscore, as you probably know, is heavily offense-centric. That isn’t to say you can’t do any better than PER at explaining defense with the boxscore, but there are obvious limitations.

Now, let’s look at the same charts, focusing on the current season:

Minimum 1000 played this season.

And here is the chart focusing again on current season, but the RAPM is stabilized by taking into account data from previous 3 seasons (these are the “time-weighted” RAPM stats):

Minimum of 1000 minutes played; RAPM stabilized using data from prior 3 seasons.

We see a similar pattern, as expected. Out of curiosity, I wanted to take a closer look at the “top 30 players” according to PER. What sort of RAPM do they have?

RAPM (4 year time-weighted) vs PER for top 30 PER players (yes, top 30, chart has typo).

I labeled the points with each player’s name. This type of presentation is interesting to me, because I see RAPM and PER as mutually validating eachother. RAPM is based purely on how a team’s performance changes with the player on the floor, while PER is based purely on the numbers the player puts up individually in the boxscore. If a player rates highly in both, and many of the above players do, that gives me more confidence in affirming their status as an elite performer. Here is another chart, again for the top 30 PER players, showing Offensive and Defensive RAPM (4 year, time-weighted):

Offense-Defense RAPM Map (4 year, time-weighted) for top 30 PER players; minumum 1000 minutes played (yes, top 30, chart has typo).

Again, note that the lower the Defensive APM the better. So players falling in the lower right quadrant have an “above-average” offensive and defensive RAPM. Players falling the upper-right quadrant are above average in offense, below average in defense according to RAPM analysis.

# RAPM Stats for 09/10 Houston Rockets (the important ones)

Below are some charts for the Houston Rockets players that have played significant minutes this year (I include Kevin Martin):

The ratings for just this season are not so reliable, so I wouldn’t make so much out of Andersen’s good defensive rating, or Martin’s poor offensive rating. I’d consider these anomalies. By HoopNumber’s +/- analysis, Chuck Hayes rates as one of the top defensive player over the last 4 years in the league, and even for this season, in a starting role, he has the best defensive rating on the team, closely followed by Kyle Lowry. Some may doubt that a 6’6 center can rate so well defensively. I would ask those people to just take a look at Chuck’s performance against Toronto last night.

Interestingly, this analysis finds Battier to be a below average defender this season, and only slightly above average over the last 4 years. In fact, it gives more credit to Battier’s offense than defense, which is hard for me to rationalize so I don’t think I’ll bother.

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