Here it is, my long-awaited advanced stats breakdown regarding Plus Minus (+/-). This is the second in a two part advanced states breakdown, the first explained Wins Produced per 48 Minutes (WP48) and Player Efficiency Rating (PER).
If you have no interest in advanced NBA stats…skip this post because there’s no way you’ll like me more after you read it.
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Plus Minus is an attempt to measure an individual player’s overall impact on offense and defense by tracking the score of the game while said player is on the floor. The stat, which was first used in hockey, has become popular enough that ESPN.com and Cleveland.com put it in their box scores.
It looks like this:
JJ Hickson +12
LeBron James +12
Mo Williams +7
Shaquille O’Neal -9
And on it goes for every player who got off the bench and entered the game.
Just thinking logically, paying attention to +/- makes a lot of sense. We can talk about shooting percentages and turnovers and rebounds and steals and blocks until all of the Earth’s natural resources dry up and basketball no longer matters, but the only thing that actually counts is the score to the game.
Let’s say Player A is shooting 40.8% and 31.3% from 3P. Let’s also just call him Rasheed Wallace for the hell of it. We can all assume that at some point I will author a post complaining about how poor of a shooting 5 he is and what a negative impact that has on his team, especially when he’s only averaging 6.1 rebounds per 36 minutes (3.6 rebounds per game).
However, let’s also assume that although Rasheed Wallace only makes about 4 out of every 10 shots, he is a good enough individual and team defender that when he’s on the floor, the opponent only makes 3 out of every 10 shot attempts.
Technically then, this is a player I should want to have on my team because over the course of 10 back and forth possessions, he’ll help his team increase its lead at least 2 points - and probably 3 since 1 of out of every 4 of his made baskets will likely be a 3P.
As a result, this hypothetical Rasheed Wallace will have a positive +/- number and will contribute to his team winning games.
This is the essence of the +/- statistics you see in the box score: they represent a team’s offensive and defensive efficiency while an individual player is in the game.
Unlike WP48 and PER, +/- is supposed to account for a player’s ability to defend in ways that don’t show up in the box score and, to a lesser extent, measure how much of a positive impact he has doing things like setting screens and moving without the ball, since good plays within the flow of the offense should contribute to the production of points over time.
Of course, the problem with looking at +/- is that there’s never just one player on the floor at a time. If Hickson, for example, is always on the floor with LeBron, is it fair to look at his +12 the same way we look at LeBron’s? What if the Cavs are playing the Warriors one night and, for some reason, Don Nelson decides he’s going to bench all of his starters and start all of his bench players and Hickson and LeBron go against second-teamers the entire night? What if Darnell Jackson comes in in garbage time, when the game’s already over, is sick with the flu and barely trying and gets a +2?
In other words, the straight +/- stats you read in the box score are only slightly useful because they don’t account for the other 9 players on the floor at the same time: Player A’s four teammates and five opponents.
This is where Adjusted Plus Minus (APM) comes in.
APM adjusts the raw +/- stat to account for opponents and teammates (you can read about how that adjustment is made by clicking on the above link).
APM has been utilized some time by the Dallas Mavericks, who paid APM forebearer Wayne Winston as a consultant for the past 9 years, up until the start of this season.
The issue, however, with APM is that although it’s more accurate than normal +/- it’s still not all that precise, as the statisticians who created the model are willing to admit. APM is a “noisy” statistic. Attempts at mitigating its inaccuracies by collecting data over multiple seasons have only been moderately effective.
Like the Mavs, many other NBA teams employ statisticians, some with their own models that those of us who don’t work inside the building can’t know a whole lot about. As far as the Cavs are concerned, they hired Dan Rosenbaum in 2004. Rosenbaum created a variation of +/- called Statistical Plus Minus (SPM) that looks at +/- through the lens of box score statistics, measuring the impact each field goal, defensive rebound, assist, turnover, etc. has on a player’s APM. Rosenbaum’s technique then is a kind of hybrid of WP48 and APM.
Notably, his model comes to a series of conclusions about the effect various box score statistics have on the team game, offensively and defensively. The link takes you to Rosenbaum’s complete APBR forum post on the topic, but here’s a brief rundown:
- A player with a true shooting percentage above 37% tends to increase offensive efficiency. This is a pretty low number - Rosenbaum interprets this to mean that players who create shots are valuable.
- Players with more three point attempts have higher APM ratings on the offensive end, even when accounting for the added points that come with making three point baskets. This suggests that spreading the floor is the important.
- Players who get to the free throw line more tend to be more effective on offense and defense - and the impact is greater on defense.
- Players who turn the ball over frequently contribute to less effective offense and defense - turnovers kill shot attempts and lead to transition baskets by the opponent.
- Steals are almost as important to effective offense as they are to effective defense - again, transition equates to easy baskets.
- Players that foul often tend to be more effective defenders.
- Players who play extended minutes tend to be more effective on offense and defense.
Although what’s available online from Rosenbaum’s SPM model pre-dates his hiring with the Cavs (they lock that shit away), and therefore some of his thinking has likely evolved over the past 5 years, it’s interesting to think about these conclusions in relation to how the team evaluates talent.
Finally, there is a brand new, enhanced version of APM called Regularized Adjusted Plus Minus (RAPM) that purports to be twice as accurate as APM and is worth tracking for this reason. In the future, whenever I refer to +/- on this blog, it will be in the form of RAPM.
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To anyone who’s been brave enough to get this far, my purpose in looking at advanced statistics, from +/- in its all incarnations to WP48 and PER, is to expand my knowledge of the game beyond simply what I see with my own eyes…although that’s pretty important too.
Really, the key to all of this is to observe, read, and react. We have multiple advanced statistics to look at when analyzing players - as well as what we see on TV - and sometimes these different measures even conflict with one another.
For grins, let’s breakdown the advances stats on the aforementioned Rasheed Wallace.
*Numbers based on ‘08-‘09
PER WP48 RAPM
14.1 .073 +3.322
Statistical +/- is unfortunately under lock and key thanks to the cash the Cavs are paying Rosenbaum.
You’ll notice that Sheed was below average last year in PER and WP48, but where did he rank in RAPM?
Sheed was the 17th highest rated player in the NBA in RAPM (Lamar Odom was first at 7.351 and LeBron was second at 6.700)
So, which is it - is Sheed above or below average? How much of an impact does he have on winning basketball?
The debate we could all have on that topic, using stats and observation, is very similar, I’m sure, to the one that went around the offices of numerous GM’s this summer when Sheed was a free agent. We know which end Danny Ainge came out on…
Food for thought.
Either Tim, me, or Dad.com will be back tomorrow with something more fun.
