A Primer on the NBA’s Plus-Minus Statistics

Modern basketball analysis contains a plethora of advanced statistics and metrics to help us better understand and parse what’s going on out there on the floor. We can go beyond simple measures like points, rebounds and assists to contextualize the game more effectively – from metrics like true shooting percentage that help track the value of shots to advances like SportVU data that help us dig into the granular level of every pass, shot and rebound.

Growing in popularity within the analytics community over the last several years has been another metric: Plus-minus. The term sounds simple enough, but what exactly is it? Let’s break it down in simple terms even the casual fan can understand.

What is Plus-Minus?

In its simplest form, plus-minus is exactly what it sounds like – when a given player is on the floor, be it for a single game, group of games or a season, does his team get outscored or does it outscore the opponent? This very simple metric is housed in most common single-game box scores, and is the rawest way of determining what sort of effect a player has on his team (and the opponent) while on the court.

The results of such a simple statistic can often have tons of noise involved, however, and those in the statistical community have derived more advanced measures to help add detail and context. This process, and the resulting outputs, are most commonly referred to as Adjusted Plus-Minus (APM).

There are a number of different well-known types of APM metrics, each of which uses slightly different techniques to reach their final output. The most basic goal is to account for the other players on the floor when establishing a guy’s total, and this can be done by adjusting a number of different variables. The statistician can control for such elements as coaching, opponent, time in between games and more. They can also use longer stretches of prior games to “inform” the model (the process of setting a concrete statistical baseline with which to compare subsequent players). There are also formats known as Statistical Plus-Minus, which include elements of standard box scores as well.

What Can We Learn From Plus-Minus?

The answer here will vary somewhat depending on which version we’re viewing, but the general goal remains to contextualize the effect a player has on his team and opponents while accounting for as many situations and player combinations as possible. Rather than tracking what a player accomplishes individually, the idea is to determine what each individual player’s cumulative contribution has meant to what their team does while they’re on the floor.

Beyond this, the details will depend on the model. ESPN’s Real Plus-Minus, for instance, factors in both teammate and opponent context for each individual player, and also has an element of box score statistics involved – it’s among the more complex measures out there, and generally considered one of the more “accurate,” so far as such a term confirms what we already can glean about players.

Let’s look at a simple example of how this sort of thing can be useful even for the casual observer:

Quantifying a player’s defensive abilities has always been one of the toughest areas within analytics. Anyone with a keen eye and experience can get a good rough idea by watching players, and one can use NBA.com’s advanced on/off court logs to determine that a team tends to suffer defensively when one particular player steps on or off the court. There are a few other tracking services (such as Synergy Sports and SportVU cameras) that can assist us here.

These are helpful things to know, but they’re limited. What if, for instance, a guy has bad on/off numbers which would indicate that he’s a defensive liability, but in reality he simply plays a huge portion of his minutes with at least one other bad defensive player? That’s where APM metrics come in. By aggregating figures neither our brains nor simple on/off measures could ever keep track of over long periods of time, they can do a much better job of separating the true causes of a team’s positive or negative play on an individual level.

Now, none of these metrics are perfect by any means – it’s why there are so many variations favoring slightly different approaches. No stat can track how well a guy contests a shot, or whether he pushes himself to 100 percent to get around every single screen set against him. But because these metrics touch so many individual data points that help smooth out incongruities, the guys who make these sorts of “non-trackable” plays will almost always eventually show through in APM outputs.

Who Are Some Plus-Minus Outliers?

Part of what helps indicate the effectiveness of a metric like Real Plus-Minus is the fact that a look at the top of the rankings typically reveals all the guys we’d think of as the best players in the league. Last season’s top five for RPM, in order, were: Stephen Curry, LeBron James, James Harden, Anthony Davis and Kawhi Leonard – or in other words, the top three MVP vote-getters, the Defensive Player of the Year, and the best under-22 player since LeBron at that age.

That said, each iteration of APM will highlight several outliers on both ends of the spectrum: guys who the models either like or dislike in stark contrast with what consensus opinions of them tend to be.

Last year’s prime example here would be Milwaukee’s Khris Middleton, who finished 10th overall for RPM despite coming into the year as a relatively unknown player. A large factor was the way his impact on the court for the Bucks was consistently felt even when he wasn’t putting up traditional numbers.

His versatility defensively is a huge plus – Middleton’s capability to guard up to four positions in the right situations made him a plug-and-play piece who could fit with plenty of different lineup combinations. In the long run, these elements plus Middleton’s ability to stay within his role on both ends of the floor made him a Plus-Minus All-Star, and there’s no question the rise in prevalence of these measures at the front office level contributed to him receiving a hefty pay day last offseason.

There are several others as well – Kyle Korver has always rated very well, and guys like Draymond Green and Tony Allen can look to APM metrics as some of the greatest representations of their value on the floor. Michael Kidd-Gilchrist is another who sees his defensive contributions accurately reflected even when traditional stats are unable to do so. In general, while we do see examples of big positive outliers offensively, the majority of them tend to come on the defensive end where aggregating counting stats has always been more difficult.

On the other side of the coin, traditional stats have inflated certain players’ reputations to a point that APM metrics disagree with, sometimes strongly. Enes Kanter is one example – he was 45th of 55 centers for total RPM last season, and was dead last among these same 55 for isolated Defensive RPM. And yet, Kanter still managed to ink a gigantic deal in restricted free agency. Carmelo Anthony is another, finishing just 400th of 474 total players last season mainly due to a big negative figure defensively – confirming to many the prevalent opinion that he’s a one-way player and short of a true superstar for that reason.

A word of caution, one that could be applied to any single-number metric out there: This is not an end-all statistic. A simple look at RPM rankings, or those of any other APM derivative, is not a surefire way of determining which players are “better” than others in any sort of concrete sense. These metrics have error margins, and even their creators would acknowledge that there will always be parts of the game they struggle to pick up entirely. They also don’t do a good job at all of telling us why certain guys rate so highly, a determination that can be tough at times.

Still, APM and plus-minus in general have a number of very effective uses. The ability to contextualize the effect a guy is having on his team over the long run, with a keen eye to certain situations or combinations that may be leaning heavily on his overall production, is a valuable one. Plus-minus metrics aren’t going anywhere, and will only become more useful as our best statisticians figure out ways to make them even more reliable and less prone to error.