Adjusted Plus-Minus

Adjusted Plus-Minus, a.k.a. APM, has been considered to be the best player evaluation metric. But it also could be misleading. Let’s dive in!

What is Adjusted Plus-Minus (APM) in brief?

Over a given time period, the basic plus-minus results are getting adjusted to account for both the teammates and the opponents on the court.

What does adjusted plus-minus do?

It reflects the impact of each player on his team’s scoring margin after controlling for the strength of every teammate and every opponent during each minute he’s on the court.

What does adjusted plus-minus incorporate?

Every time segment a player is in a game, adjusted plus-minus tracks:
(1) The other nine players on the floor,
(2) The length of the segment,
(3) The score at the start and at the end of the segment.

How to interpret Adjusted Plus-Minus numbers? Examples

Adjusted +/- ratings indicate how many additional points are contributed to a team’s scoring margin by a given player in comparison to the league-average player whose adjusted +/- value is zero over the span of a typical game. It is assumpted that in a typical game a team has 100 offensive and 100 defensive possessions.

  • If a +6.5 APM player is on the floor with 4 average teammates, his team will average about 6.5 points better per 100 possessions than 5 average players would.
  • MVP Antetokounmpo finished the 2019-20 regular season with a +10.3 APM rating which makes his teammates’ value seem higher than they would be without Greek Freak.

How are the estimates for Adjusted Plus-Minus calculated?

It’s a matter of finding out the estimates of player variables which produces the smallest difference between the expected margin and the actual margin in the matchups. This is how a regression model works, basically. More information about adjusted plus-minus calculation

What are the PROs and CONs for Adjusted Plus-Minus?

PROS::
The biggest advantage of adjusted plus-minus ratings is one of the closest we can come to an unbiased measure of a player’s effectiveness.
CONS:
(1) Adjusted plus-minus ratings have high variance and can change pretty dramatically. The regression tries to find a constant value for a player, but this does not control for out-of-sample lineup-teammate quality effects. A different role, a different coaching scheme, different teammates, different match-ups, or different seasons affect APM big time.
(2) There is noise in the data. For some players, especially when only looking at data over just 1 year, there are some strange results, but that is to be expected. An examination of 239 players revealed that only 7% of the variation in a player’s adjusted plus-minus value in 2008-09 was explained by what he did in 2007-08. Although more data does increase the level of statistical significance, it’s still the case that most players even when five years of data are employed are not found by this method to have a statistically significant impact.
(3) Another issue which adjusted plus-minus technique struggles to address is the multicollinearity issue. Coaches prefer to use some player duos/trios frequently or rarely since all players could not be on the court with every other teammate at the same time.
(4) We find this within a model that accounts for teammate quality changes from season to season. We note that basketball leagues are not natural experiments in which players are randomly paired and resampled. Rather, players are organized into often stable team environments and resampling occurs infrequently such that players have often aged by the time they receive a new set of teammates with whom to play. In such an environment, counterfactuals concerning player value will go largely unobserved. From this estimation, further (out-of-sample) adjustments to the APM estimation methodology can be explored in future work.

History of Adjusted Plus-Minus Development:

Adjusted plus-minus technique is first developed by Wayne Winston and Jeff Sagarin in the form of their WINVAL software system in 2002. For each player, it starts with the team’s average point differential for each possession when they are on the court. This gives a number showing how effective the player’s team was when they were in the game. The problem with using this to evaluate individual players is that it is biased in favor of players who play alongside great teammates and players who play against weak opponents.

Dan Rosenbaum initially outlined his approach in an influential article that analyzed the 2002-2003 and 2003-2004 seasons as a combined dataset. David Lewin then published both 2004-2005 and 2005-2006 ratings.

Likewise, Steve Ilardi determined adjusted +/- ratings for the 2006-2007 season using a similar approach. While the previous analyses were conducted at the conclusion of a season, he presented the first in-season computation of adjusted +/-.
From 2007-08 season to 2011-12 season, daily updates of the APM calculations are available on Aaron Barzilai’s BasketballValue website.