Friday, December 6, 2013

1997-98 RAPM: Non-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.

Continuing my work on breaking down the new play-by-play data from, here's the non-prior informed (NPI) version of RAPM. This version is less predictive as an informed RAPM set, and it often has some wonky results, but it's another tool to use in evaluating NBA players. 1998 was an intriguing season historically as it was the last for the Jordan on the Bulls, preceded the destructive lockout that delayed the '99 season, and was perhaps the last hurrah for a generation of stars who gave way to Duncan, Shaq, Kobe, et al. Going by his stats, it wasn't Jordan's best season during their six-peat, but he still nailed a crucial shot over the Jazz for a championship. It was the second straight year they met in the finals with Jordan also taking back the MVP trophy after Malone stole it in 1997. However, by RAPM and considering minutes, Karl Malone was the most valuable player.

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

Although Jordan and Malone got all the MVP attention, Shaq was an absolute monster -- a +6 RAPM on non-prior informed is enormous (all players, including Shaq, were regressed to 0 as a prior, so a high value is impressive.) Alas, he only played 2000 minutes as he missed many games with injuries. The iron-man Stockton was actually the same: he only played 1800+ minutes with nearly 20 missed games. If you scoff at these two leading the league, refer to's raw +/- for 1998 where both players lead the league. Jordan is only 6th here and near teammate Kukoc. Strangely, Kukoc's defensive RAPM is one of the highest for the season; there's perhaps a weird interaction between those two and Pippen's missed games. This is where a prior-informed version would excel: assume Jordan has a superstar impact, Harper and Kukoc with more modest impacts, and crunch the numbers from there.

As for the leaders for each category, Barkley was nearly +5 just on offense, while interestingly Olajuwon was a paltry -0.8. This is likely a one-year hiccup due to limited data, but it's an intriguing note. Shaq was second, as that was one of his many seasons destroying the league: a 58.7 TS% with a 33 usage. Reggie Miller's shooting brings him in at number three, and MVP Malone is a close fourth. Detlef Schrempf was fifth, as the Sonics survived the loss of Kemp.

On defense, there were a few bizarre players in the top spots, but there were also the usual suspects. Mutombo won the DPOTY award, and RAPM agrees: he has the top spot. Yet Ben Wallace, and David Robinson were third, and fifth, respectively, while Kukoc and Jaren Jackson were second and fourth. As for an unheralded guy, Aaron McKie was a close sixth. He's known for being a tough defender, but not Defensive Player of the Year worthy. He was traded midseason (Pistons to the 76ers), but both teams were not enormously better with him; both actually only slightly improved on defense when he was on the team. Also, Duncan won Rookie of the Year in one of the best rookie seasons ever; RAPM agrees.

With two consecutive season files completed for RAPM, a prior-informed version can now be created for this season. Hopefully, some of the strange results like Kukoc a +4 on defense will be eliminated or reduced. Look for a prior-informed version to be posted soon along with a version of RAPM informed by a statistical plus/minus. The great MVP debates for Jordan and Malone now have more information, and it's exciting to have these advanced metrics for legends including those two players and young, explosive Shaq.

Click here for the link to the spreadsheet.

Edit: I fixed a problem in the matchup file producing better results for version 2.0.