Monday, March 3, 2014

1999 RAPM: non-prior and prior informed

Background for what RAPM is: +/- was a revolution for the NBA because it allowed a completely new method at evaluating players. You look at how a team scores and defends with you on the court and without you. When you set players as variables, you can use regression to calculate player impact. It's a full scope view of what matters in a game: outscoring your opponent. However, it's noisy for a number of reasons. One is that some player combinations are rare (this is known as collinearity.) Another is that the models don't deal well with players with low minutes, as they don't have enough of a sample for an accurate estimate and will often produce a ludicrous result just to "fit" the data better. 

In simple terms, RAPM deals with this by introducing a heavy dose of regression to the mean. While traditional adjusted +/- creates a model by minimizing error (the difference between the actual points per possession scored/allowed and the expected), RAPM also minimizes the coefficients in the model using a lambda term. The coefficients are reduced toward the "prior," which can be set as zero or as a set of prior values (like the previous season's result.) Players with few possessions/minutes will have results close to their priors because their sample size isn't big enough to prove to the model they're more or less valuable.

The NBA lockout that delayed the 1999 season put a serious dent in the league and wasn't aided by the retirement of Michael Jordan and the dismantling of the Bulls. It was a transition year, with the old guard dropping off with the exception of iron-man Karl Malone, while the next generation was still developing and coming into their own. With a shortened season opening in February, games jammed together with too many back-to-back's, a team known for professionalism, led by a second year Duncan and a 33 year-old David Robinson, won the championship. This was Shaq pre-Phil Jackson but post-Jordan; it's a truly lost season.

Nevertheless, the games were played, and we can't ignore what happened. Surprisingly, by NPI RAPM, the best player in 1999 was ... David Robinson, who had a monster defensive impact. Just a season before Duncan and Robinson were neck-and-neck on a per possession basis, but the Admiral leaps ahead here. Though with a 24.9 PER and a league-leading 0.261 Win Shares per 48 minutes, and stats that did not drop in the postseason, perhaps it shouldn't be surprising. However, he only played 31.7 minutes in the regular season, lending credence to an argument for another candidate like Alonzo Mourning. Jaren Jackson is probably the oddest name near the top of the list. He was a Spurs teammate but only scored 6.4 points per game. And he's why we turn to prior-informed versions....

 *When you reference the spreadsheet, try to include the version number. This will reduce future discrepancies.

With two seasons as seed data behind it, RPI RAPM (an adjusted ridge-regression model given prior information) is a more powerful tool. After a dominating 1998, Shaq loses the top spot due to poorer defense. This was probably Alonzo's greatest season with award-caliber defense coupled with potent scoring (20 points in a slow-paced league and a 56 TS%.) He was second in MVP voting -- justified here. As for some surprising results, Blaylock continues to be a plus/minus star, and Rasheed Wallace rockets to the top on the deep but strong Blazers team that nearly defeated the Lakers in 2000. Charles Barkley also continues his one-sided results: his offensive RAPM rises to 6.16 but his defense slips to -2.64.

 *When you reference the spreadsheet, try to include the version number. This will reduce future discrepancies.

Fourth in MVP voting was Iverson. He's 75th here with good offensive value despite his poor shooting efficiency, but that's submarined by his porous defense, according to RAPM. Duncan was third, and he's backed-up by a very strong +5.2 mark. Rookie of the year Vince Carter, however, climbs from the rookie prior of -2 (given to all rookies) to +3.21 overall. He heads a pretty strong rookie class including Pierce, Brad Miller, and Dirk Nowitzki. Jason Williams received some rookie love, but by this method he was a significantly negative player. For validation of the model, 16 of the top 24 players were on all-NBA teams -- or perhaps that's validation of the all-NBA teams. The lowest rated all-NBA player was the young Kobe Bryant at -1.2 and it wasn't close: he was ranked 267th and the next lowest all-NBA player was McDyess at 117.

The aforementioned Barkley was the best offensive player, according to RPI RAPM, and that's not just because of his past heroics: his non-prior informed RAPM was second. Shaq's stats were muted by fewer minutes and the slogging pace of the lockout season, but, with the first of his strong of 30+ PER seasons, he's second in RPI RAPM on offense, barely trailing Barkley. Malone rounds out the top three, and the next highest players are more intriguing: Reggie's three-point bombing is probably underrated by most box score metrics at fourth here, Grant Hill's fifth, and Jeff Hornacek, again, has a strong showing at sixth followed by Blaylock. Both Hornacek and Blaylock are players that appear to be underrated by a method that wasn't available in the 90's. Mutombo, David Robinson, and Mourning were top three by defense. Mourning won the Defensive Player of the Year award, which wasn't a bad choice, necessarily, but Mutombo has a huge lead in RAPM. Rasheed was fourth, and his value was demonstrated later when he was traded to the Pistons to complete one of the greatest defensive teams ever. Jaren Jackson appears to be an anomalous result, ranking fifth, but he was San Antonio's first "three-and-D" player. He concentrated on defense, and his value does not show up in box scores. His NPI RAPM wasn't entirely misleading. Trailing him were Shawn Bradley, Olajuwon, and Garnett. Gigantic size might actually be underrated because Yao Ming's defense looked better under the RAPM microscope and Bradley joins Gheorghe Muresan as another 7' 7" player with strong defensive results.

With three seasons of data, outliers can be weeded out and patterns emerge. We can reevaluate past legends like David Robinson and Stockton who rate well, but sub-stars should receive more discussion. Mookie Blaylock, by NPI RAPM, was 8th in 1997, 11th in 1998, and 36th in 1999. By prior-informed regression, he was fifth in 1999. Blaylock played in the shadows of point guards like Stockton and Kidd, but he may have been better than we thought. Defense is notoriously tricky to judge by basic stats, and this is where RAPM can be most illuminating. Bo Outlaw stands out as a defensive force who wasn't heralded. Divac fares well as a two-way center, often better than his famous teammate Chris Webber. And, again, we shouldn't completely toss aside Jaren Jackson's RAPM results. He was a forgotten role player and not highly regarded, but like Shane Batter we should look beyond the box score.

Click here for the link to the spreadsheet.


  1. Justin, does Robinson's injured 1997 affect his RAPM on this list? I would imagine that season is lowering his 1999 RAPM. How would his 1999 RAPM look if 1998 was his only prior (though 98 is dragged down by 97 too)? I wouldn't be surprised if he would have been #1 in RAPM in 98 and 99 if his prior was his last full season.

    1. Well, first of all, all guys who were rookies in '97 or later have that same bias, but it's worse: rookies are assumed to be negative players.

      Robinson was also had a pretty good +/- in '97 despite the limited time, so it's not an awful limit. But for guys like Olajuwon who peaked before '97, they're probably being underrated.

  2. Great stuff, thanks for your hard work. Looking forward to your 2000 results!