The plus-minus statistic is often reviled by NHL fans as a useless statistic.
This is not without reason, as the stat produces numbers that are often inexplicable. Most importantly, a player’s team is a major factor in his plus-minus.
However, the plus-minus stat is not without merit. Most importantly, it aims to measure the most important part of winning – outscoring the other team. The only thing that matters in winning hockey games is outscoring the other team, whether by scoring goals or preventing them. Evaluating players based on scoring stats alone will more directly measure a player’s contribution to scoring, but will fail to capture other aspects of the game, especially defensive play. Plus-minus aims to capture the full impact of a player’s game, but it is a more indirect measure that can be influenced by a number of factors out of the player’s control.
The most important of these is the quality of the team on which the player plays. My adjusted even-strength plus-minus statistic
attempts to remove this bias from the numbers and present a number that can compare players from bad teams and good teams on an equal footing. Specifically, the method of adjusting for team is to compare the team’s goals for and against while the player is on the ice to the team’s goals and against while the player is off the ice. Additionally, plus-minus includes shorthanded goals scored by both teams. This introduces a bias against players who play on the power play and in favor of players who play on the penalty kill. My adjusted plus-minus
estimates on-ice shorthanded goals based on on-ice power play goals, as on-ice shorthanded goals for individuals are not available for most years, and removes them from the player’s record.
To calculate the adjusted plus-minus, I take the player’s on-ice total goals for and against as given.
I calculate an expected plus-minus for the player, based on his team’s off-ice performance. The expected plus-minus is calculated using the off-ice performance regressed partially to even, as a player should be expected to play somewhat better than a set of bad teammates or worse than a set of good teammates. I then calculate an actual plus-minus, which differs from official NHL plus-minus in that it is normalized to a scoring environment of 200 even-strength goal per season and does not include shorthanded goals. I subtract the “expected plus-minus” from the “actual plus-minus” to generate an adjusted plus-minus number.
While this method removes many of the biases from raw plus-minus,
it is still an imperfect method of rating players. First, most importantly, it is for even-strength play only. Second, a player’s linemates or defence partner may exert a major influence on a player’s numbers – see Milan Hedjuk for a prime example. Third, the on-ice/off-ice method of adjusting for team implicitly compares a player to the other players on his team who play the same position but on another line or D-pairing. If a player is on the same team as a great player, the off-ice baseline may not be a fair comparison. For example, Ted Green’s 1971 season has one of the lowest adjusted plus-minus ratings ever. When you realize that much of his off-ice baseline was set by Bobby Orr, the reason for the low rating becomes clear. Also, some players play more difficult opposition than others, facing the other team’s best players and taking more defensive zone faceoffs. These differences can also skew the numbers.
For the above reasons, please keep the following in mind when using these numbers to evaluate players
- Adjusted plus-minus is best used to compare players who played in a similar role. For example, compare #1 defensemen who played the toughest ice-time on the team to other #1 defensemen, not to #6 defensemen who were sheltered by their coaches from the best players. For example, take Tom Preissing’s rating with a huge grain of salt.
- Adjusted plus-minus is measured against a baseline of average, so it will tend to underrate players with a long decline phase or several poor years at the start of their career (Mark Messier) and give high ratings to players who retired young and didn’t play a lot past their prime(Bobby Orr, Eric Lindros).
- Adjusted plus-minus is measured against a baseline of average, so it will tend to underrate players with a long decline phase or several poor years at the start of their career (Mark Messier) and give high ratings to players who retired young and didn’t play a lot past their prime(Bobby Orr, Eric Lindros).
- Check to see who the player’s linemates were. Did he have a great player on his line? Charlie Simmer and Dave Taylor both have very high ratings, and likely owe much of it to Marcel Dionne.
- Did the player play on a team with another great player who was on another line/D-pairing? If so, his adjusted plus-minus may be too low. Mark Messier in his Edmonton years is an example here, along with Ted Green. I don’t think there are too many cases of this kind, but there are certainly a few.
- There may be a significant amount of random variation in a single-year result. For that reason, I would look at multiple years when measuring a player’s peak, and would not use this stat as definite proof that one player was better than another in a given year.
There are a lot of disclaimers there, but I still believe there is a lot of good information in adjusted plus-minus when evaluating a player’s career. Even after taking the above possible biases into account, there are still some very interesting results.
