The Problems with Plus-Minus and How to Fix Them

By Jack Van Deventer • August 12, 2021

More and more teams are using the Plus-Minus (PM) metric, so it’s important to understand the risks and benefits of doing so.  The benefits are obvious:  in theory, one can identify which individuals contribute most to a team’s winning performance. 

Before we discuss the risks, let’s remember what the PM metric is.  If “Joe” is in a game and his PM metric is +5 it means that while Joe is in the game his team outscored the 5-player opposing team by 5 points. 

What are the problems with Plus-Minus?

Problem 1 – High Variability.  The +5 PM score is affected by 10 players.  There’s Joe, his 4 teammates, and the 5 opposing players.  All 10 people impact Joe’s PM score.  Thus, there’s no way to completely isolate Joe’s contribution.

Solution 1:  PM is an inherently erratic metric.  For PM to be truly informative, a large sample size is required to overcome the statistical “noise” (variability) in the data.  I prefer an accumulation of at least 15 games worth of data, and more games for sparsely used players.

Problem 2 – PM needs to be scaled to game length.  If Joe has a +5 Plus-Minus score, what does that mean?  If Joe only plays 5 minutes per game, then Joe’s impact is enormous.  If Joe plays all 40 minutes in a college game, then his impact is more modest. 

Solution 2:  PM stats (and, I would contend, every metric in basketball) needs to be converted based on TIME played, not based on games played, because of differences in the amount of time played can be dramatic.  By calculating based on time played we create a standardized context among players for fairness which avoids the extreme bias toward those who play the most. 

Here’s my simple formula for how PM stats should be calculated:

• PMpoints = the score differential of the TEAM while a player (or players) was in the game. 

• MinPlayed = the number of minutes the player (or combination of players) was in the game.

• MinPerGame = the number of minutes in a regulation game.  So, 32 for high school, 40 for college, and 48 for NBA.

PM per (Minutes in a Full Game) = (PMpoints / MinPlayed) * MinPerGame

Example:  Joe plays 16 minutes in a college game.  Joe’s team outscores the opposing team 17 to 13 (a +4 PM score) during those 16 minutes.  A college game is 40 minutes of play. 

PM per 40 = (4 / 16) * 40  =  10.    So, Joe’s “PM per 40” = +10.    

Problem 3 – PM Results are highly impacted by blow-out games.  The first year my daughter played college ball, she initially struggled with the speed of the game.  And so I was both pleased and surprised when I discovered, early in the season, that she led her team in the Plus-Minus metric.  Upon closer inspection her stellar results were misleading because they were unduly influenced by a 15-0 run against a very weak opponent.  That single game’s +15 PM score disproportionately weighted her overall PM score.    

Solution 3:  Blow-out games need to be filtered out of the PM calculation data.  Emphasize conference games and avoid large wins or losses.

Problem 4 – Individual PM versus Team PM.   The high variability of Plus-Minus data is partly remedied with increased sample size.  Thus, the more games played the clearer the PM contribution is.  But sample size alone is insufficient to filter out the effects of 4 other teammates.  

Solution 4:  Coaches can and should focus on PM scores for multi-player combinations rather than just individual PM scores.  Doing so increases precision (better team insights) while reducing variability.  Ultimately and ideally, we want to look at a groups of 5 players at a time and get their collective PM scores, but this requires a very large sample to be reliable.  If you remember combinations from your “Intro to Stats” class you’ll know that 2- and 3-player combinations have 10X the explanatory power as 5-player combinations in terms of sample size (minutes of evaluation time).  Your advantage as a coach is that you have insights into team synergy such that you can leverage your team’s strengths and exploit your opponent’s weaknesses. 

Conclusion and Summary

There’s much more that needs to be said about the Plus-Minus.  It’s a key metric, but one that needs to be used cautiously and with a healthy sample size.  It has high variability, so interpretive caution is warranted.  Context is key.  Outliers need to be discarded as unrepresentative.  An honest PM will be calculated based on TIME played (scaled to minutes of game length), not based on games played.  Failure to do the latter heavily favors (or penalizes) players with the most playing time.  Team synergy is best evaluated using a multi-player Plus-Minus metric, which has advantages over one-player PM scores.

Coaches, do you want team synergy metrics for every possible team combination? 

Team synergy matters.  Winning matters.  We can help.