Obviously I haven’t been updating this blog at all, but with some recent work I’ve done, now is definitely the time to re-visit this place.
One of my favorite statistics to use to evaluate a basketball player is something called “Regularized Adjusted Plus-Minus,” or RAPM for short. Joe Sill wrote a paper about this statistic for the Sloan Sports Analytics Conference, and the statistic itself has been developed by Jeremias Engelmann, who has maintained RAPM ratings on his website here.
If you’re like over 99 percent of NBA fans out there, you’re probably wondering – what in the world is RAPM?
I can write 3000 words explaining just what RAPM is, but here’s the very short version. RAPM is an estimate of a player’s on-court impact. If a player has an RAPM of +2, that means the player improves his team’s performance by two points per 48 minutes, compared to an average NBA player. Check out Engelmann’s ratings for the 2011-12 season, and you’ll see LeBron James at the top of the list, with an RAPM of +9.5. That means if James was replaced by a league-average player, the Miami Heat would be an estimated 9.5 points worse per 48 minutes because of it.
What you’ll notice is that Engelmann doesn’t have ratings up for the current NBA season. I wish I could say why (and I hope it’s because an NBA team hired him, he deserves it), but the honest truth is that I don’t know. And as long as there are no RAPM ratings to go by, it’s difficult for me to keep track of how well each NBA player is doing.
Until now. Recently, I stumbled across an article written by Dan Rosenbaum, one of the pioneers of the adjusted plus-minus rating, in 2004. In the article, Rosenbaum writes at length about the adjusted plus-minus rating, but also includes information on an alternative to APM, which he called “statistical plus-minus,” or SPM.
SPM worked to estimate what a player’s APM would be by looking at the player’s box score statistics. By running a regression analysis, Rosenbaum was able to determine the relationship between box score statistics, such as points, rebounds, and assists, and APM, the actual estimate of a player’s on-court impact. The resulting formula provided a means by which Rosenbaum could estimate a player’s APM by using only statistics that would be found in the box score.
Back then, all Rosenbaum had to work with was an early model of adjusted plus-minus ratings, which was very insightful but also very flawed. This led me to wonder – what would happen if I duplicated Rosenbaum’s approach with Engelmann’s refined version of APM?
The results are nothing short of remarkable. As it turns out, there is a very strong relationship between a player’s box score statistics and his RAPM. For you stat nerds out there, the “r” value is .893 and the “r-squared” value is .798, which is consistent with a very strong correlation. (By contrast, the “r-squared” value of Rosenbaum’s study was just .4397, which I believe is reflective of a less sophisticated model of APM.) By using a formula with such a strong correlation to RAPM, I can often get very close to what a player’s RAPM would be with box score statistics alone.
Here is the very lengthy formula for a statistic I’m calling “RSPM,” or “Regularized Statistical Plus-Minus.” All statistics are per 36 minutes, except for minutes per game:
RSPM = (PTS/36 * 1.295) – (FG/36 * 1.571) – (FGA/36 * .551) – (FT/36 * 1.336) + (FTA/36 * .694) + (ORB/36 * .548) + (DRB/36 * .47) + (AST/36 * .704) + (STL/36 * 1.438) + (BLK/36 * 1.396) – (TOV/36 * 1.281) – (PF/36 * .179) + (MIN/G * .094) – (9.949)
I know what you’re thinking… this sounds good, but let’s see some results. I’m going to start with what I call the “LeBron James test”. The LeBron James test is simple – if a rating system doesn’t think LeBron James is a great player, it deserves to be thrown right in the trash can.
LeBron James 2012-13 RSPM: +8.48
Fortunately, this formula passes the LeBron James test, estimating him to be 8.48 points better than average. This is also the single-highest RSPM any NBA player (minimum 1000 minutes) has this season.
Here are the top 20 (as of March 29th):
- LeBron James +8.48
- Dwight Howard +7.79
- Chris Paul +7.04
- Kevin Durant +6.57
- Tim Duncan +5.81
- James Harden +5.36
- Larry Sanders +5.10
- Joakim Noah +4.27
- Blake Griffin +4.07
- Tyson Chandler +3.94
- JaVale McGee +3.70
- Kyle Lowry +3.68
- Dwyane Wade +3.61
- Russell Westbrook +3.51
- Josh Smith +3.39
- Paul Millsap +3.31
- Anthony Davis +3.22
- Stephen Curry +3.11
- Kenneth Faried +3.06
- DeAndre Jordan +2.97
For the most part, the names on the above list make a lot of sense. Many of them are players universally recognized as stars in the NBA, such as James, Howard, Paul, Durant, Duncan, and Harden. So far, I think this system passes the “smell test.”
Here are the bottom ten:
- Richard Hamilton -6.03
- Kevin Seraphin -5.55
- Norris Cole -4.89
- Austin Rivers -4.83
- Michael Beasley -4.74
- Keith Bogans -3.90
- Gary Neal -3.73
- Terrence Ross -3.73
- Willie Green -3.65
- Andrew Nicholson -3.64
While I didn’t expect to see “Rip” Hamilton at the top of a “worst players” list, there’s an argument to be made for it. Hamilton has never been known for lock-down perimeter defense, and he hasn’t been a particularly efficient shooter either. Imagine Kevin Martin without the scoring efficiency – that’s not good.
Otherwise, this list again mostly makes sense – it includes Norris Cole, Austin Rivers, and Michael Beasley, who have all been identified as particularly lousy players by a lot of the “smart” NBA community.
I’m very enthusiastic about this statistic, to the extent that I’m willing to publish these numbers on this blog. They’re not RAPM numbers, but they’re the next best thing. Look for RSPM numbers to go up here very soon.
And I’m sorry, but they’re way better than PER.