Is +/- the Real Key to Player Value?

For those that don’t know, I’m doing a series of blogs about advanced basketball stats, and last week I talked about John Hollinger’s Player Efficiency Rating (PER) stat.

This week I’ll look at the plus-minus (+/-) stat, as it has become popular enough to be included in the and box scores of each game.

Unlike PER, which is based entirely upon the individual numbers that a player produces, the +/- stat is based wholly upon how the team performs when the player is on the court. Whether a player scores 5 points or 50 is irrelevant to +/-, it’s all about team results. Thus, to many +/- has become the key stat to try to gauge a player’s impact on winning.

What is it: The basic +/- stat is similar to the one used in hockey: how many points did the team score vs. how many did the opposing team score with a certain player was playing vs. how the team did when that player was not playing. A positive +/- value indicates that the team was better with that player on the court, while a negative value indicates that the team played worse. Simple and easy. (There are ways to use math to try to improve on the basic +/- stat, as several “adjusted +/-“ stats are out there. I may eventually do a separate blog on that, but for the sake of keeping this simple I won’t go into it much here. For those who would want more on adjusted +/- now, here is how calculated adjusted +/- for the 2007-08 season.)

Strengths: The basic +/- stat is very easy to understand, so there is no complex math necessary. Now that it is being carried in many boxscores, one can tell from game-to-game whether a player has improved or hurt their current +/- for the season. And it is a very intuitive measure: you would expect a team to play better when better players are on the court, so you would expect better players to have higher +/- values.

Finally, there are many parts of a game that aren’t measured by traditional stats (i.e. setting a good pick, strong man-to-man defense, good help defense, communication, “willing” a team to win, leadership, etc.). But presumably, if these intangibles really lead to winning basketball, they should show up in a catch-all stat like +/-.

Weaknesses: The biggest weakness of +/- is establishing causation. In other words, does the team play better because a certain player is out there? Or does that player just happen to be part of a unit that is successful without contributing much himself? The best way to counter that weakness is through large numbers. Over five games the +/- stat may not tell you much, but over 80 games it becomes at least strongly suggestive of player impact, as no one player is on the court with exactly the same group of players every time. And over several seasons a player’s impact becomes even clearer as he plays with different groups of teammates. This weakness is also addressed by several of the adjusted +/- calculations that are out there, that attempt to correct for quality of teammates.

Another weakness is that +/- does not correct for team role. For instance, in Minnesota last season Al Jefferson had a much worse +/- than Rashad McCants did. Clearly Jefferson is better than McCants, but Jefferson was the focal point of opposing defenses on a weak starting unit while McCants was often the free-lance scorer on the second team. Thus, if you went purely by +/- in this situation you may have come to the incorrect conclusion. But that doesn’t mean that this data is useless. McCants was the only effective perimeter scorer/slasher on the Wolves last season, so perhaps his better +/- score indicates that the team really needed someone to fill that role and that McCants did it adequately. Another possible interpretation is that though Jefferson is a much better player than McCants, perhaps last season he wasn’t as good at being a team No. 1 option as McCants was at being the 6th man/scorer.

Usage: As seen in the Jefferson/McCants example, you can’t simply say “player X has a higher +/- than player Y so he is better”. Instead, you can use +/- to say how important a particular player's production and role are to a particular team, and how well that player fulfills that roll. After that, you have to apply your own reasoning to it with regards to how useful it is to whatever you're comparing. Corroborate it with other data and good-ol' common sense, and make your determination from there. In other words, the best way to use +/- is as a part of the argument in conjunction with other back-up support, not as the whole argument. As for some specific examples where I think +/- is useful:

1) Gauging the impact of a stud player across teams. For instance, Boozer and Duncan were both 20/10-type big men centerpieces for 50-win teams last season. But Duncan’s +/- was among the best in the league whereas Boozer barely broke even. Similarly, LeBron and Melo were both primary offensive weapons on their respective teams and Melo’s Nuggets had a better record than LeBron’s Cavs, but LeBron’s +/- numbers were near the league lead but Melo’s were negative. The +/- in these examples captures the intuition that LeBron and Duncan were more valuable than Melo and Boozer, respectively, regardless of what their traditional numbers or team records might say.

2) Identifying good role players. Role player defender-types like Shane Battier or Bruce Bowen don't seem to have much value using production-based stats, but players like them always tend to have good +/- numbers which indicate that they perform important duties on winning teams.

3) Gauging "empty" numbers vs. good player on bad team syndrome. Every year there are players that put up big traditional numbers on bad teams, and you never know if they're stat-padding or if it would translate to a good team (many's the team with buyer's remorse for signing/trading for one of those empty stats guys, only to not see it translate). Then you look at someone like Kevin Garnett, who tied Tim Duncan for the league in on-court/off-court +/- in 2007 on a 32-win team which would suggest his numbers weren't empty. This was supported by the way his team performed in 2008 when he got some talent around him.


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