## Universal Measures of Player Value: APM

Christopher Pasatieri

Analytics has tried to find a universal currency for player values. “Adjusted Plus-Minus” is another attempt.

Brian MacDonald is an assistant professor at West Point.  His website looks like Robb gone wild.  (Robb Gone Wild videos coming soon!)  One of his projects looks at travel considerations of different league realignments.  Here's a sample:

APM or "Adjusted Plus-Minus" was developed in 2011 and 2012.  APM uses a technique called ridge regression to determine coefficients for each player's performance.  "The purpose of these statistics is to provide an estimate of each player’s contribution to his team, independent of the strength of his teammates, the strength of his opponents, and other variables that are out of his control."

APM includes offensive and defensive contribution.  It includes ES, PP, and PK pieces.  Adjustments are made for zone starts as well.  One of the benefits of ridge regression is that players with little playing time wind up with estimates closer to 0 than players with more playing time.

Output:  estimated goals per 60 minutes on ice.  ES, PP, and PK each have their own output.
Input: Can be Goals, Shots, Fenwick Events, or Corsi Events.
Zero-point: league average.
Slope:  Consistent.  Each goal, whether for or against, has the same impact as any other goal scored under the same circumstance.
Symmetry:  APM is symmetric.
Comparability:  Goalies don't have a APM value.
Complexity:  Although APM sounds complicated, running the regressions is actually pretty straight-forward.  Once you have the coefficients, you can compare them directly or you can multiply by TOI to get a season value.

Ridge regression results seem to have an advantage over ordinary regression when comparing estimates from year to year.  MacDonald says if you compute APM using ordinary regression with goals as the input, year-to-year correlation is only 0.28.  With ridge regression, it is 0.36.  With ridge regression and Corsi as the input, correlation is a fairly impressive 0.63.

Over 2007-2011, APM seems to get reasonable results.  The top 5 players in total net goals are Datsyuk, Toews, Ovechkin, D. Sedin, and Crosby.  The top two defensemen in total net goals, Chara and Lidstrom, are well ahead of the rest of the pack.  Then again, four years of any metric ought to get pretty good results.  Hopefully, down the road, more APM data will be out there to analyze.

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