Statistical +/-

by trk on Apr 22, 2009 11:47 PM PDT

Statistical +/- is a metric originally created by Dr. Dan Rosenbaum in 2004 that is intended to predict a player's adjusted +/- ratings based on box score data. He used a regression of box score stats vs. adjusted +/- to determine the coefficients of different variables in the formula. Neil Paine at Basketball-Reference.com has tweaked and updated the statistical +/- formulas by including data for the last couple years, as well as adding new variables for a player's height and age. Statistical +/- is not perfect, and I am not completely convinced that Rosenbaum & Paine selected the correct variables to use in the regression (the "versatility index" especially seems like it could be improved upon), but it is still an intriguing approach to the problem of creating a way to evaluate players and I believe that it is superior to the more commonly used metrics like PER and Win Score.   Although it is called statistical +/-, this metric is box score based and does not actually use any +/- data (although there is a team adjustment to make sure that a weighted sum of a team's players' statistical +/- will equal the team's +/-).

How do the Blazers do in Paine's new statistical +/- ratings?

Roy            +6.13

Rudy          +2.57

Oden         +1.67

Blake         +1.55

Aldridge    +1.32

Batum       +0.99

Przybilla    +0.48

Sergio       -0.49

Outlaw      -0.70

Frye           -4.44

Bayless    -5.05

Roy is 9th in the NBA (behind LeBron, CP3, Wade, Ginobili, Howard, Kobe, Duncan, and Kidd). He is a stud, and pretty much all metrics agree on that at this point.

Rudy did better than I would have expected, since although adjusted +/- loves him most box score based metrics don't.   Statistical +/- likes 3-point shooters. Rudy is the #1 rookie in the NBA (if you don't count people like Hamed Haddadi who have barely played any minutes).

Oden has had a pretty good rookie season when he has been able to stay on the court.

Blake has had a good season, his statistical +/- rating is close to being the same as his adjusted +/- rating.

Aldridge is lower that I would have expected, but is still considered an above average player.

Batum does pretty well in statistical +/-, which is a bit surprising. He also does very well in adjusted +/-, but most people looking at his box score stats would not think he is that good and the formula shouldn't have any way of figuring out that he is a lock-down defender.

Przybilla helps the team a little more on defense than he hurts them on offense.

Sergio is rated as a slightly below average player, but that is still much better than how he is rated by adjusted +/-.

Outlaw normally does fairly well in box score-based metrics, but statistical +/- doesn't like him very much. Adjusted +/- doesn't like him much either.

Frye and Bayless have obviously both had terrible years this season.

I was actually a bit surprised by how closely the statistical +/- ratings matched the adjusted +/- ratings for a lot of players. Considering that the two metrics use completely different types of data to rate players, it would not be surprising to see a bunch of major disagreements between the two metrics. The fact that the correlation is as strong as it is suggests that statistical +/- is doing a good job of what it is intended to do.

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interesting stuff, rec

I’m not a huge fan of this metric, personally. Adjusted plus/minus is nice because it tries to capture things that don’t show up in the boxscore (ie stops, deflections, secondary assists, etc). I understand the desire to correlate this with boxscore stats, but statistical plus/minus suffers from some of the same problems as stats like PER— they don’t include things outside the boxscore.

I kind of prefer to look at both PER and adjusted plus/minus and then use those two along with qualitative observations of the player’s defense to get an idea of the player.

by jksnake99 on Apr 23, 2009 12:01 AM PDT reply actions

i dont like this metric as well

but over the course of the year it sometimes helps paint a clearer picture.

I got 6 years of playoff blue balls going on, and I'm ready to release. GO BLAZERS. ~Mortimer

by Philthyanimal on Apr 23, 2009 12:09 AM PDT up reply actions

Obviously it isn't perfect

I think it is better than PER though. With PER, it seems like Hollinger just sort of made it up as he went along without using any real process to determine what the weights of different terms in his formula should be. Statistical +/- at least uses a semi-scientific approach to determine what the coefficients should be.

All boxscore based metrics are going to share a lot of the same weaknesses, so it still makes sense to supplement these metrics with first-hand observations and non-boxscore data.

by trk on Apr 23, 2009 12:18 AM PDT up reply actions

I don't think that's a fair portrayal of Hollinger's methodology in creating PER, but I don't have a link to said methodology to back up my point.

by jksnake99 on Apr 23, 2009 12:20 AM PDT up reply actions

Perhaps my assessment of PER was a bit harsh

Every part of the formula for PER has a purpose, and there is some logic backing up everything Hollinger does. The problem is that often it is a naive sort of logic which relies on a bunch of untested assumptions. For example, Hollinger reasons that an assist is worth 1/3 as much as a made FG because of the 3 acts of creating a basket (getting open, making the pass, making the shot) the passer does one. However, I don’t think he did any research to test whether the different parts of creating a shot are equally difficult or to test how much easier an assisted shot is than an unassisted one.

Hollinger’s PER is a good metric relative to what was available at the time that it was created. However, APBRmerics has advanced significantly since then and better metrics are being developed.

by trk on Apr 23, 2009 1:02 AM PDT up reply actions

With regards to +/- statistical metrics, ...

I’m sticking with Roland Beech at www.82games.com and the more basic Net Points Per 100 Possessions.

by AK1984 on Apr 23, 2009 1:21 AM PDT reply actions

Negative for Travis?

NO WAY I AM SO SURPRISED…not…..

Every time Outlaw fades away in a shot, a kitten dies. Save the Kittens, don't fade!

by Przy4Prez on Apr 23, 2009 10:17 AM PDT reply actions

Aw snap!

by PunkBroc on Apr 23, 2009 10:19 AM PDT up reply actions

I wonder what the correlation between adjusted plus/minus and statistical plus/minus is

Can someone find that info?

by jksnake99 on Apr 23, 2009 10:45 AM PDT reply actions

I don't know what the correlation is for the current version

But Rosenbaum’s original version of the stat had an R^2 of .4397 which corresponds to a correlation coefficient of .663. In comparison, PER had a correlation coefficient of .492 and Berri’s Wins Produced had a correlation coefficient of .372.

by trk on Apr 23, 2009 11:05 AM PDT up reply actions

all those are correlated with adjusted plus/minus?

I’m sure someone has done this, but what happens if you correlate a weighted average team PER, team wins produced and team statistical plus/minus with point differential? What stat wins then? Or is that what you are talking about?

by jksnake99 on Apr 23, 2009 11:07 AM PDT up reply actions

That is the correlation vs adjusted +/-

If you correlated vs team wins it might be different, and I wouldn’t be surprised if Wins Produced won then since it was created by regressing box score stats vs team wins. The big flaw in Wins Produced is that it does not take into account diminishing returns in scoring or rebounding, but if you are looking at team stats instead of individual stats that ceases to be a problem.

by trk on Apr 23, 2009 11:15 AM PDT up reply actions

plus minus is no recent invention

it has been used in hockey for decades.

by soci on Apr 23, 2009 11:38 AM PDT reply actions

Keep in mind that "statistical +/-" isn't the same as actual +/-

Statistical +/- is intended to predict +/- using boxscore stats. The name is a bit misleading, but there is a big difference between statistical +/- and +/-.

by trk on Apr 23, 2009 12:24 PM PDT up reply actions

BTW

I would love to see Damon Stoudamire’s +/- was back in the day in the playoffs. It was like clock work. Blazers up 10. Damon checks in/out Blazers down 5. Blazers go up 12, Damon checks in, Blazers in race to win game at end with him on the floor.

Same syndrome when Travis is not hitting most of his jumpers.

If only then and now we didnt have to do all that theyd be up 20 by the end of the game.

"Both Anthony Carter and Jameer Nelson were downright jubilant in the Magic locker room postgame. Carter said to no one in particular, "Brandon Roy, that man is unstoppable, it's like he's playing NBA Live" and Nelson was cracking on his teammates for not being able to guard Brandon. The kinds of jokes you can make when you win."

by loyal_blazer on Apr 23, 2009 11:57 AM PDT reply actions

Neil Paine did a seiries of articles where he identified the all-time top 10 players (career wise) at each position using statistical +/-

Terry Porter made the top 10 at PG, Clyde Drexler was in the top 10 at SG, and Scottie Pippen was a top 10 player at SF. Rasheed Wallace and Cliff Robinson were listed as just missing the cut at PF, and Bill Walton probably would have made it at center but missed out due to insufficient playing time. There was no mention of Damon Stoudamire though.

by trk on Apr 23, 2009 12:38 PM PDT up reply actions