## Universal Measures of Player Value: THoR

Christopher Pasatieri

Analytics has tried to find a universal currency for player values. “Total Hockey Rating” is another attempt.

Michael Schuckers is an Associate Professor of Statistics at St. Lawrence University and a co-founder of Statistical Sports Consulting, LLC.  Over the years, Professor Shuckers has done a lot of the work on shot location and shooting percentage/save percentage adjustments.

THoR was developed in 2013 by Shuckers and James Curro.  Like APM, THoR uses ridge regression to determine coefficients.  Unlike APM, THoR uses all events, including Hits, Faceoffs, etc.  THoR also only looks at the probability of scoring in the 20 seconds after an event.  “We refer to this as the net probability after 20 seconds or NP20. Twenty seconds was chosen after an analysis of the changes in these probabilities in the seconds after each event. Changes after 20 seconds were not significant.”  THoR also includes a home-ice advantage component.  THoR only looks at ES play, although it could easily be extended to all play.  THoR corrects shots for location and type of shot (forehand, backhand, etc.)  It then adjusts shooting percentage accordingly.

Each player has a THoR value.  This is probability of scoring a goal in the 20 seconds after an event.  This is multiplied by 80 to get expected goals per game.  This is multiplied by 82 to get expected goals per season.  Expected goals per season is then divided by 6 to get expected wins per season.

Output:  estimated goals created per full season or estimated wins created per full season.
Input: All ES Events.
Zero-point: league average.
Slope:  The impact of events vary from location to location.
Symmetry:  THoR is symmetric.
Comparability:  Goalies don't have a THoR value.
Complexity:  Like APM, running the regressions is actually pretty straight-forward.  Correcting the shots for quality adds a layer of complexity.

One thing I do like about THoR.  Over 2010-11 and 2011-12, it comes up with Alex Steen as the best player in the NHL.  The top 15 defensemen and the top 15 forwards:

 Team Player Position Wins Created Philadelphia Flyers Kimmo Timonen D 5.73 Los Angeles Kings Drew Doughty D 4.07 Edmonton Oilers Tom Gilbert* D 3.32 Columbus Blue Jackets Fedor Tyutin D 3.13 Calgary Flames Mark Giordano D 3.08 Philadelphia Flyers Andrej Meszaros D 2.82 Chicago Blackhawks Brent Seabrook D 2.63 New York Rangers Ryan McDonagh D 2.5 Detroit Red Wings Niklas Kronwall D 2.48 Anaheim Ducks Lubomir Visnovsky* D 2.48 Pittsburgh Penguins Paul Martin D 2.27 Winnipeg Jets Tobias Enstrom D 2.23 Ottawa Senators Erik Karlsson D 2.22 Boston Bruins Zdeno Chara D 2.18 New York Rangers Michael Sauer D 1.95

 Team Player Position Wins Created St. Louis Blues Alexander Steen C 6.72 Detroit Red Wings Pavel Datsyuk C 6.32 Pittsburgh Penguins Tyler Kennedy C 6.05 Boston Bruins Patrice Bergeron C 5.95 Nashville Predators Patric Hornqvist R 5.88 Phoenix Coyotes Ray Whitney+ L 5.62 Pittsburgh Penguins Evgeni Malkin C 5.57 Vancouver Canucks Ryan Kesler C 5.53 Chicago Blackhawks Jonathan Toews C 5.5 Vancouver Canucks Daniel Sedin L 5.47 San Jose Sharks Joe Pavelski C 5.42 Toronto Maple Leafs Mikhail Grabovski C 5.13 Carolina Hurricanes Jeff Skinner C 5.07 Los Angeles Kings Anze Kopitar C 4.93 Pittsburgh Penguins Sidney Crosby C 4.92

I have to say that some of these players seem wildly out of place.  Kimmo Timonen the best defensemen in the league?  Tyler Kennedy above Malkin and Crosby???  They do note that Crosby missed a lot of games over these two seasons which drives down his value.

I have several concerns about THoR.   I'm not sure about the use of 20 seconds.  Tyler Dellow has shown that the effect of some faceoffs persists up to 37 seconds (http://www.mc79hockey.com/?p=6338), and my own data shows a faceoff effect through at least 30 seconds.  THoR seems to treat all events as equal.  I'm not sure that makes sense.  I would think some events (faceoffs, shots) are more likely to lead to goals than others.  Shuckers does say they have an improved version of THoR (ODiN?).  One of the improvements may well be weighting different events differently.  The use of shot location concerns me.   If Delta was Corsi plus shot location, the shot location piece made it function worse than Corsi alone.  On the other hand, Shuckers probably has the most experience with shot location adjustments and if anybody is going to do it right it would seem to be him.

One of the benefits of THoR is the number of events.  By including the additional events, THoR seems to have enough data to give a reliable number based on only one season of data.  Hopefully, down the road, more THoR data will be out there to analyze.

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