Regularized Adjusted Plus-Minus


Regularized Adjusted Plus-Minus (RAPM)

  • Stint-level weighted ridge regression. The target variable is a per 60 rate (separate regressions are run using GF60, CF60, and xGF60 as the target variable), the weights are the length of each stint (stint is defined as a period of play where no player substitutions occur), and the predictor variables are:
Variable Definition
All Skaters – Offense boolean variable: 1 = skater was on the ice for the stint, 0 = skater was not on the ice for the stint
All Skaters – Defense boolean variable: 1 = skater was on the ice for the stint, 0 = skater was not on the ice for the stint
All Goalies – Defense boolean variable: 1 = goalie was on the ice for the stint, 0 = goalie was not on the ice for the stint
Score State 7-level factor variable for CF (home lead of -3 through +3), and 3-level factor variable for GF and xGF (trailing, tied, leading)
Strength State factor variable equal to the applicable strength states in the regression
Offensive “Zone Start” boolean variable: 1 = stint included at least one faceoff in the offensive team’s offensive zone, 0 = no faceoff in offensive zone
Neutral “Zone Start” boolean variable: 1 = stint included at least one faceoff in the offensive team’s neutral zone, 0 = no faceoff in neutral zone
Defensive “Zone Start” boolean variable: 1 = stint included at least one faceoff in the offensive team’s defensive zone, 0 = no faceoff in defensive zone
Back-to-Back boolean variable: 1 = offensive team had one night of rest, 0 = offensive team had more than one night of rest

 

  • The skater ratings are the coefficients that result from the regression. These are interpreted as a skater’s offensive and defensive contribution (per 60 minutes) to the league scoring rate (Goals, xG, or Corsi).
  • Please reference our full explainer found on Hockey-Graphs for more information about this metric.

 

RAPM Charts

The RAPM Charts use the RAPM metrics we feel are most reliable for skater evaluation. These include:

  • Offense:
    • Goals For per 60
    • xG For per 60
    • Corsi For per 60
  • Defense:
    • xG Against per 60
    • Corsi Against per 60

The respective RAPM ratings used in the RAPM Charts are centered and scaled around the positional mean (Forwards/Defensemen) of the selected timeframe using Z-Scores. This is done so each RAPM rating can be viewed on the same “level” as the others. Using Z-Scores we can look at how a player has performed relative to all other players at the same position over the selected timeframe.

Note: The GA/60 ratings that result from the Goals RAPM regressions are inherently influenced by the goaltender behind the skater and are problematic for defensive evaluation. They are not included in these charts for this reason.

Image Source

 

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