Wednesday, March 26, 2014

2000 RAPM: non-prior and prior informed

Background for what RAPM is: +/- was a revolution for the NBA because it allowed for 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 low minute players, 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.) Using a prior set of values, Bayesian analysis, greatly improves the results. 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.

As the league tried to recover from the lockout season, a new dynasty took form. Although it sounds odd now, the Shaq and Kobe duo were once disappointments, but with Phil Jackson on board as a coach and Shaq putting in more work than he ever had before the Lakers had an all-time great season -- 67 wins, a +8.6 point differential, and a championship. It was the dawn of a new era, and while it wasn't technically a new millennium (that's 2001), a number of new stars were surfacing. Garnett was second in MVP voting and did everything for his Minnesota team. Iverson took a step forward scoring 28 a game. Vince Carter reinvigorated the all-star weekend with his epic dunk contest (oh and he played basketball too.) And other young players emerged -- Dirk went from an unknown German into a intriguingly good player, Ray Allen topped 20 points per game for the first time, Kobe did so as well (the first of 14 such seasons), and Elton Brand was rookie of the year.

How does NPI RAPM view the players? Well, just as a reminder, non prior informed RAPM often has wonky results because there's not enough data -- Rodney Rogers tops the list. He was a big forward who had a career year, shooting efficiently and spacing the floor for the 53 win Phoenix Suns, who toppled the Duncan-less Spurs in the playoffs. Simply put, when Rogers was on the floor the Suns outscored their opponents by 9.6 points per 100 possessions, but it dropped to virtually 0 without him. He also won sixth man of the year; the fact that Phoenix plays with the best with him on the court is impressive. And the adjusted +/- rating, RAPM, obviously agrees that the Suns were better with him. Shaq, however, is third, curiously behind Terry Porter (Spurs that season.) Stockton and Vince Carter continue to be plus/minus stars even without the bias of a prior, and Payton looks great again on offense. As for a historically underrated player, Bo Outlaw was fourth overall -- and he was fifth in 1997 (NPI).

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

The preferred form of RAPM, however, is in the spreadsheet below. The top twenty consists of stars and highly respected players with unique skillsets in Sabonis, Rasheed Wallace, Divac, Mutombo, Eddie Jones, and Robert Horry. But Shaq destroys everyone. Playing 40 minutes a game, he would, going purely by the numbers, take an average team to 60 wins.

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

RAPM and MVP voting agree on the first two names, and the rest of the top five in voting are rated well too. The divergence starts with big men who, mainly due to defense, are found to be more valuable from plus/minus, but there are only a couple guys in the top ten in MVP voting who aren't highly rated. Iverson came in 7th, winning the MVP next season, but he had one of the worst defensive plus/minus values. Webber also had fairly mediocre plus/minus stats, but was voted 9th. The all-NBA voting follows a similar path as 11 of the 15 players were in the top 25 in RAPM. The other four names are known for not being rated well in the stats community: the aforementioned Iverson and Webber, Stephon Marbury, and Kobe Bryant, who's actually a significant negative on defense. For the Rookie of the Year results, Elton Brand and Steve Francis shared the trophy, but according to this stat they were two of the worst rookies. Instead the guys who came in third and fourth in the voting, Odom and Andre Miller, should have won -- they were first and second, respectively, in RAPM, where Odom in particular was a very valuable player at +3.4. Rookies are rarely that valuable.

The best offensive player was Shaq -- not surprising because he averaged nearly 30 points a game on great efficiency with almost 4 assists. Karl Malone was second; apparently he slipped on defense but was still a scoring machine. Grant Hill, in his last great season, was third, as he was a point forward who scored 26 a game. One surprise is that Gary Payton's value appears to be more on offense because he's fourth here, matching previous results. Shooting legend Reggie Miller was fifth in offense in his last all-star season. Iverson, criticized for his shot selection, was actually eighth. Defense, of course, is dominated by big men -- Mutombo is first again, the giant Shawn Bradley second, and the underrated Bo Outlaw third (though he did pick one up vote for Defensive Player of the Year.) David Robinson was fourth, as RAPM finds him to be the basis for San Antonio's defense. Rasheed Wallace and Vlade Divac, not known for defense, followed closely. The Defensive Player of the Year was actually Mourning, who was tenth in defensive RAPM -- not a terrible choice according to plus/minus, but I suspect there was some voter fatigue with Mutombo. As a last note, this is believed to be Shaq's best season on defense, but he doesn't show up, and instead the highest rated Laker, and highest rated perimeter player in the league, was actually Derek Fisher.

RAPM, like any metric, isn't perfect, but it can perform as well or better than the popular box score metrics PER and Win Shares. For example, while Kobe's defensive +/- doesn't necessarily mean he was a "bad" defender, you can treat it like robust evidence about what effect his defense had in 2000. But every single metric agrees that Shaquille O'Neal stormed the league and was by far the best player. Plus/minus stats are often used to identify undervalued players, and in this context it's more of a historical retrospective for unheralded guys like Divac, but sometimes it's just fun seeing what legends have done in the past. Shaq owned the NBA that year.

Click here for the link to the spreadsheet.