NHL Team Power Ratings and Predictions (SRS Algorithm)

[Doctor No]

By way of comparison, this is what an SRS (simple rating system) algorithm develops, with games through December 29:

Team | 2014-15 Strength
Chicago|

1.145​

|
Nashville|

0.745​

|
Pittsburgh|

0.636​

|
Tampa Bay|

0.580​

|
St. Louis|

0.477​

|
NY Rangers|

0.446​

|
Toronto|

0.432​

|
NY Islanders|

0.372​

|
Montreal|

0.367​

|
Detroit|

0.298​

|
Calgary|

0.262​

|
Washington|

0.212​

|
Winnipeg|

0.177​

|
Los Angeles|

0.172​

|
Minnesota|

0.170​

|
Vancouver|

0.096​

|
Anaheim|

0.088​

|
San Jose|

0.015​

|
Boston|

0.001​

|
Ottawa|

-0.021​

|
Philadelphia|

-0.232​

|
Colorado|

-0.305​

|
Florida|

-0.309​

|
Dallas|

-0.401​

|
New Jersey|

-0.571​

|
Columbus|

-0.603​

|
Carolina|

-0.682​

|
Arizona|

-0.902​

|
Buffalo|

-1.173​

|
Edmonton|

-1.378​

|

Click to read more...

 

[charlie1]

By way of comparison, this is what an SRS (simple rating system) algorithm develops, with games through December 29:

Are you using goal differential for the constants?


Also, for those of you (like me) who are unfamiliar with these algorithms, here is a good primer on SRS:

http://www.pro-football-reference.com/blog/?p=37

Essentially it is just a set of N linear equations with N unknowns, where N is the total number of teams. Setting the constants is interesting though.

 

[Doctor No]

Are you using goal differential for the constants?

Precisely - and I definitely should have said that. The intent is that you could predict the expected outcome of a game (goal differential) by taking the home team's power rating, subtracting the visiting team's power rating, and adding in home ice advantage (currently +0.307 goals).

I first saw the basis of this algorithm in Carroll/Palmer/Thorn's "The Hidden Game of Football" (from the 1980s). I have some adjustments that I make if I'm actually using it to predict games, but use this version here since it's just about as good and completely open-source. It's basically goal differential + average schedule strength = power rating. The "average schedule strength" is the average power rating of opponents, which of course is a circular definition, so you have to iterate to a convergent solution (or find eigenvectors in a matrix).

 

[charlie1]

Precisely - and I definitely should have said that. The intent is that you could predict the expected outcome of a game (goal differential) by taking the home team's power rating, subtracting the visiting team's power rating, and adding in home ice advantage (currently +0.307 goals).

Very interesting, thanks. This is new to me so bear with me please:

So for a team that has played 10 games, with 6 home games and a total goal differential of +4, they would be given a constant of (4 - 0.307*6)?

 

[Doctor No]

Very interesting, thanks. This is new to me so bear with me please:

So for a team that has played 10 games, with 6 home games and a total goal differential of +4, they would be given a constant of (4 - 0.307*6)?

That's close, although I prefer to unpack it from the opposite direction.

Their goal differential would be 0.40 (+4 divided by ten games).

Assuming that all ten of their opponents were "average", their schedule strength would be (1/10)*[(6 * -0.307/2) + (4 * +0.307/2)] = -0.03

So their initial power rating would be 0.40 + -0.03 = 0.37.

On the other hand, the other teams' initial power ratings would then be below zero (since this team has an above average goal differential, then the aggregate of the rest of the league would have to be below zero). Since we used the other team's power ratings to develop the initial power rating, this is where things become circular, and why we have to iterate to a convergent solution (basically, you quit iterating when the results don't change appreciably).

 

[charlie1]

That's close, although I prefer to unpack it from the opposite direction.

Their goal differential would be 0.40 (+4 divided by ten games).

Assuming that all ten of their opponents were "average", their schedule strength would be (1/10)*[(6 * -0.307/2) + (4 * +0.307/2)] = -0.03

So their initial power rating would be 0.40 + -0.03 = 0.37.

On the other hand, the other teams' initial power ratings would then be below zero (since this team has an above average goal differential, then the aggregate of the rest of the league would have to be below zero). Since we used the other team's power ratings to develop the initial power rating, this is where things become circular, and why we have to iterate to a convergent solution (basically, you quit iterating when the results don't change appreciably).

Got it. Last question: Why is 0.307 being divided by 2?

 

[Doctor No]

Got it. Last question: Why is 0.307 being divided by 2?

Good question (great question, actually).

Since the home-ice advantage is 0.307 in total, I represent this by lowering the road team's rating by half that amount and raising the home team's rating by half that amount. (The result is that the difference of the two adjustments is the full advantage).

 

[charlie1]

Ah I see, very nice. Thanks for the explanation.

Going in another direction now-- Given what we know about Corsi and it's predictive value for the playoffs, do you think the rating system would better predict playoff win% if it was based on Corsi or Fenwick, instead of Goals?

That's a question for anyone who has played with these things...

 

[Doctor No]

I bet that it would based upon what I've seen, although (1) I haven't actually tried it myself, and (2) if you wanted to predict goal spreads (for gambling) you'd want to convert these back into goals somehow at the end.

 

[Doctor No]

Here's an updated SRS algorithm, data through January 4th:

Team | 2014-15 Strength
Chicago|

1.097​

|
Nashville|

0.747​

|
Pittsburgh|

0.618​

|
NY Rangers|

0.607​

|
Tampa Bay|

0.581​

|
St. Louis|

0.551​

|
Montreal|

0.469​

|
NY Islanders|

0.347​

|
Washington|

0.277​

|
Toronto|

0.274​

|
Calgary|

0.252​

|
Vancouver|

0.249​

|
Detroit|

0.225​

|
Winnipeg|

0.194​

|
Los Angeles|

0.131​

|
Anaheim|

0.074​

|
Minnesota|

-0.012​

|
Ottawa|

-0.051​

|
San Jose|

-0.063​

|
Dallas|

-0.079​

|
Boston|

-0.115​

|
Colorado|

-0.312​

|
Philadelphia|

-0.377​

|
Florida|

-0.402​

|
New Jersey|

-0.529​

|
Carolina|

-0.586​

|
Columbus|

-0.604​

|
Arizona|

-0.922​

|
Edmonton|

-1.154​

|
Buffalo|

-1.363​

|

Congratulations, New Jersey - your team has the toughest schedule so far this year (+0.130).

 

[Doctor No]

SRS algorithm, data through January 8th.

Team | 2014-15 Strength
Chicago|

1.030​

|
St. Louis|

0.760​

|
Nashville|

0.743​

|
NY Rangers|

0.696​

|
Tampa Bay|

0.614​

|
Pittsburgh|

0.578​

|
Montreal|

0.428​

|
Washington|

0.346​

|
NY Islanders|

0.326​

|
Detroit|

0.257​

|
Calgary|

0.219​

|
Vancouver|

0.207​

|
Toronto|

0.183​

|
Los Angeles|

0.113​

|
Winnipeg|

0.065​

|
Anaheim|

0.009​

|
Boston|

-0.031​

|
Minnesota|

-0.073​

|
San Jose|

-0.106​

|
Ottawa|

-0.149​

|
Dallas|

-0.153​

|
Colorado|

-0.155​

|
Philadelphia|

-0.293​

|
Florida|

-0.328​

|
Carolina|

-0.521​

|
New Jersey|

-0.524​

|
Columbus|

-0.533​

|
Arizona|

-0.935​

|
Edmonton|

-1.177​

|
Buffalo|

-1.464​

|

Colorado has eclipsed New Jersey with the toughest schedule thus far.

 

[Doctor No]

Here's an updated NHL SRS through games of January 14:

Team | 2014-15 Strength
Chicago|

+0.959​

|
Nashville|

+0.848​

|
St. Louis|

+0.772​

|
Pittsburgh|

+0.693​

|
NY Rangers|

+0.646​

|
NY Islanders|

+0.458​

|
Tampa Bay|

+0.453​

|
Montreal|

+0.405​

|
Washington|

+0.394​

|
Detroit|

+0.218​

|
Calgary|

+0.200​

|
Winnipeg|

+0.194​

|
Anaheim|

+0.117​

|
Vancouver|

+0.108​

|
Toronto|

+0.092​

|
Los Angeles|

+0.079​

|
Boston|

+0.049​

|
Ottawa|

-0.104​

|
San Jose|

-0.125​

|
Colorado|

-0.168​

|
Dallas|

-0.170​

|
Philadelphia|

-0.243​

|
Minnesota|

-0.246​

|
Florida|

-0.393​

|
New Jersey|

-0.458​

|
Carolina|

-0.473​

|
Columbus|

-0.640​

|
Arizona|

-1.006​

|
Edmonton|

-1.094​

|
Buffalo|

-1.454​

|

Home-ice advantage is currently estimated at 0.308 goals.

I'll be tweaking the algorithm slightly over the next few days, so there may be some more movement in the next edition.

 

[charlie1]

Here's an updated NHL SRS through games of January 14:

Team | 2014-15 Strength
Chicago|

+0.959​

|
Nashville|

+0.848​

|
St. Louis|

+0.772​

|
Pittsburgh|

+0.693​

|
NY Rangers|

+0.646​

|
NY Islanders|

+0.458​

|
Tampa Bay|

+0.453​

|
Montreal|

+0.405​

|
Washington|

+0.394​

|
Detroit|

+0.218​

|
Calgary|

+0.200​

|
Winnipeg|

+0.194​

|
Anaheim|

+0.117​

|
Vancouver|

+0.108​

|
Toronto|

+0.092​

|
Los Angeles|

+0.079​

|
Boston|

+0.049​

|
Ottawa|

-0.104​

|
San Jose|

-0.125​

|
Colorado|

-0.168​

|
Dallas|

-0.170​

|
Philadelphia|

-0.243​

|
Minnesota|

-0.246​

|
Florida|

-0.393​

|
New Jersey|

-0.458​

|
Carolina|

-0.473​

|
Columbus|

-0.640​

|
Arizona|

-1.006​

|
Edmonton|

-1.094​

|
Buffalo|

-1.454​

|

Home-ice advantage is currently estimated at 0.308 goals.

I'll be tweaking the algorithm slightly over the next few days, so there may be some more movement in the next edition.

Please tweak so that Islanders are higher. Thanks so much.

 

[Doctor No]

Please tweak so that Islanders are higher. Thanks so much.

Tell the Islanders to score more goals, and allow fewer.

 

[hatterson]

Interesting to see the team tied for the league lead in the middle of the pack. Although I guess that's what you get with that type of algorithm when the goal differential is so close to zero.

 

[Doctor No]

Interesting to see the team tied for the league lead in the middle of the pack. Although I guess that's what you get with that type of algorithm when the goal differential is so close to zero.

Exactly - it will be interesting to see what comes of that. Based on what else I've seen, I'd be surprised if their differential didn't improve over the second half.

 

[Doctor No]

My SRS algorithm using games through February 8th:

Team | 2014-15 Strength
Chicago|

0.829​

|
Nashville|

0.685​

|
St. Louis|

0.683​

|
NY Rangers|

0.567​

|
Tampa Bay|

0.525​

|
Montreal|

0.436​

|
NY Islanders|

0.384​

|
Detroit|

0.370​

|
Washington|

0.369​

|
Pittsburgh|

0.353​

|
Anaheim|

0.246​

|
Calgary|

0.222​

|
Boston|

0.146​

|
Vancouver|

0.143​

|
Winnipeg|

0.122​

|
San Jose|

0.003​

|
Minnesota|

-0.009​

|
Los Angeles|

-0.058​

|
Dallas|

-0.066​

|
Ottawa|

-0.112​

|
Colorado|

-0.127​

|
Philadelphia|

-0.177​

|
Toronto|

-0.197​

|
New Jersey|

-0.366​

|
Carolina|

-0.379​

|
Florida|

-0.440​

|
Columbus|

-0.441​

|
Arizona|

-1.031​

|
Edmonton|

-1.039​

|
Buffalo|

-1.521​

|

Home-ice advantage is now at +0.302 goals.

These are the values used in my goalie strength of schedule, which I will update next.

 

[Taze em]

Wow. So the Hawks are just the wire to wire runaway best team in this model?

9 standings points off the President's trophy and only 2 goals ahead in GD.

I just wonder what the model loves so much about the Hawks to be 140 points clear of the league.

 

[Doctor No]

Wow. So the Hawks are just the wire to wire runaway best team in this model? What about the model favors the Hawks so much? Very interesting.

It's scheduled adjusted goal differential, so most of what's driving it is that (relatively) the Hawks score more goals, and allow fewer goals.

With that said, they dropped behind St. Louis midweek, but regained their position by Sunday (right now, it's Chicago/Nashville/St. Louis in that order).

Totaling the components (Goal Differential + Schedule = Power Rating):
Chicago: 0.722 + 0.055 = 0.777
Nashville: 0.648 + 0.051 = 0.699
St. Louis: 0.685 + -0.020 = 0.666
NY Rangers: 0.577 + -0.004 = 0.573

 

[hatterson]

It's scheduled adjusted goal differential, so most of what's driving it is that (relatively) the Hawks score more goals, and allow fewer goals.

With that said, they dropped behind St. Louis midweek, but regained their position by Sunday (right now, it's Chicago/Nashville/St. Louis in that order).

Totaling the components (Goal Differential + Schedule = Power Rating):
Chicago: 0.722 + 0.055 = 0.777
Nashville: 0.648 + 0.051 = 0.699
St. Louis: 0.685 + -0.020 = 0.666
NY Rangers: 0.577 + -0.004 = 0.573

Can you post the individual breakdowns of Differential and Schedule at your next update?

Also, I can't recall if it was mentioned earlier and a cursory view didn't reveal it, is the strength of schedule based on opponent goal differential or is it based on opponent power rating?

I was thinking it was power rating and that there was some iteration involved to find convergent values since I recall you mentioning something about that, but couldn't remember if that was this rating or another one of yours

 

[Doctor No]

Absolutely! That's an easy adjustment - I've been doing these on Mondays, so that I don't annoy everyone as much , but I can add that.

For the two components - the first is straight up goal differential per game.

The second is the average power rating of a team's opponents.

The sum of those is a team's power rating, and that's where the iteration comes in (since you need this to get the second term, which you need to get this). It complicates matters that opponent matrices are almost always singular, so you can't just find the matrix inverse and plug.

 

[Doctor No]

NHL Simple Rating System, games through February 15, 2015:

Team | 2014-15 Goal Diff | 2014-15 Schedule | 2014-15 Strength
Chicago|

0.719​

|

0.051​

|

0.770​

|
Nashville|

0.696​

|

0.041​

|

0.737​

|
St. Louis|

0.732​

|

-0.010​

|

0.722​

|
NY Rangers|

0.685​

|

-0.025​

|

0.660​

|
Tampa Bay|

0.569​

|

-0.059​

|

0.510​

|
NY Islanders|

0.411​

|

0.000​

|

0.410​

|
Pittsburgh|

0.357​

|

0.052​

|

0.410​

|
Montreal|

0.455​

|

-0.056​

|

0.399​

|
Washington|

0.404​

|

-0.031​

|

0.372​

|
Detroit|

0.389​

|

-0.096​

|

0.293​

|
Calgary|

0.321​

|

-0.073​

|

0.249​

|
Vancouver|

0.182​

|

-0.008​

|

0.174​

|
Anaheim|

0.158​

|

-0.014​

|

0.143​

|
Winnipeg|

0.121​

|

0.013​

|

0.134​

|
Minnesota|

0.074​

|

-0.010​

|

0.065​

|
Boston|

0.091​

|

-0.039​

|

0.052​

|
Los Angeles|

0.073​

|

-0.042​

|

0.031​

|
Dallas|

-0.071​

|

0.029​

|

-0.043​

|
Ottawa|

-0.037​

|

-0.025​

|

-0.062​

|
San Jose|

-0.035​

|

-0.051​

|

-0.086​

|
Colorado|

-0.250​

|

0.135​

|

-0.115​

|
Philadelphia|

-0.196​

|

-0.010​

|

-0.206​

|
Toronto|

-0.263​

|

0.045​

|

-0.218​

|
Florida|

-0.327​

|

-0.064​

|

-0.391​

|
New Jersey|

-0.536​

|

0.111​

|

-0.424​

|
Carolina|

-0.500​

|

0.072​

|

-0.428​

|
Columbus|

-0.519​

|

0.047​

|

-0.471​

|
Edmonton|

-1.053​

|

0.036​

|

-1.017​

|
Arizona|

-1.053​

|

0.030​

|

-1.022​

|
Buffalo|

-1.589​

|

0.071​

|

-1.519​

|

Home-ice advantage is currently valued at 0.302 goals/game (which I add half of to the home team, and remove half of to the away team).

Goal Diff is exactly equal to goals scored, less goals allowed, divided by games played. "Goals scored" and "goals allowed" include the "bonus goal" given to a team winning a shootout (so a team winning a shootout, 5-4, would receive five "goals scored").

Schedule is the average opponent strength (so the average of the last column, after the adjustment made for home-ice advantage above is implemented).

The last column, Strength, is the sum of Goal Diff and Schedule. Since Schedule is the average of Strength, and you need Schedule to compute Strength, the solution is arrived at iteratively.

 

[Doctor No]

NHL games through February 22, 2015:

Team | 2014-15 Goal Diff | 2014-15 Schedule | 2014-15 Strength
Nashville|

0.667​

|

0.006​

|

0.673​

|
St. Louis|

0.678​

|

-0.012​

|

0.666​

|
NY Rangers|

0.690​

|

-0.039​

|

0.651​

|
Chicago|

0.550​

|

0.046​

|

0.596​

|
Tampa Bay|

0.581​

|

-0.050​

|

0.531​

|
Washington|

0.475​

|

-0.017​

|

0.459​

|
Pittsburgh|

0.383​

|

0.054​

|

0.437​

|
NY Islanders|

0.377​

|

0.030​

|

0.407​

|
Montreal|

0.441​

|

-0.055​

|

0.386​

|
Detroit|

0.368​

|

-0.064​

|

0.304​

|
Vancouver|

0.237​

|

0.007​

|

0.244​

|
Calgary|

0.254​

|

-0.070​

|

0.184​

|
Minnesota|

0.207​

|

-0.033​

|

0.174​

|
Anaheim|

0.167​

|

-0.024​

|

0.143​

|
Los Angeles|

0.155​

|

-0.042​

|

0.113​

|
Winnipeg|

0.049​

|

-0.002​

|

0.047​

|
Boston|

0.051​

|

-0.011​

|

0.040​

|
Ottawa|

0.000​

|

-0.035​

|

-0.035​

|
Colorado|

-0.167​

|

0.108​

|

-0.058​

|
San Jose|

-0.067​

|

-0.037​

|

-0.103​

|
Dallas|

-0.150​

|

0.043​

|

-0.107​

|
Philadelphia|

-0.217​

|

-0.017​

|

-0.233​

|
Toronto|

-0.267​

|

0.032​

|

-0.235​

|
New Jersey|

-0.424​

|

0.068​

|

-0.356​

|
Columbus|

-0.466​

|

0.076​

|

-0.389​

|
Carolina|

-0.483​

|

0.067​

|

-0.415​

|
Florida|

-0.390​

|

-0.027​

|

-0.417​

|
Edmonton|

-1.066​

|

0.028​

|

-1.037​

|
Arizona|

-1.102​

|

0.029​

|

-1.073​

|
Buffalo|

-1.533​

|

0.079​

|

-1.454​

|

Home ice advantage is now estimated at +0.272 goals/game.

See post #35 for the definitions that I use.

 

[Doctor No]

NHL games through March 1, 2015:

Team | 2014-15 Goal Diff | 2014-15 Schedule | 2014-15 Strength
Nashville|

0.635​

|

-0.002​

|

0.633​

|
NY Rangers|

0.656​

|

-0.050​

|

0.606​

|
St. Louis|

0.603​

|

-0.017​

|

0.586​

|
Tampa Bay|

0.609​

|

-0.040​

|

0.569​

|
Chicago|

0.524​

|

0.035​

|

0.559​

|
Montreal|

0.581​

|

-0.047​

|

0.534​

|
Pittsburgh|

0.419​

|

0.062​

|

0.481​

|
Washington|

0.453​

|

-0.021​

|

0.432​

|
NY Islanders|

0.406​

|

0.010​

|

0.417​

|
Detroit|

0.344​

|

-0.032​

|

0.312​

|
Vancouver|

0.210​

|

0.002​

|

0.212​

|
Minnesota|

0.246​

|

-0.045​

|

0.201​

|
Calgary|

0.242​

|

-0.052​

|

0.190​

|
Anaheim|

0.188​

|

-0.031​

|

0.157​

|
Winnipeg|

0.109​

|

-0.011​

|

0.098​

|
Ottawa|

0.100​

|

-0.023​

|

0.077​

|
Boston|

0.097​

|

-0.027​

|

0.070​

|
Los Angeles|

0.065​

|

-0.036​

|

0.029​

|
Colorado|

-0.222​

|

0.111​

|

-0.111​

|
San Jose|

-0.113​

|

-0.043​

|

-0.156​

|
Dallas|

-0.222​

|

0.033​

|

-0.189​

|
Philadelphia|

-0.238​

|

-0.011​

|

-0.250​

|
Carolina|

-0.328​

|

0.067​

|

-0.261​

|
Toronto|

-0.365​

|

0.052​

|

-0.313​

|
New Jersey|

-0.365​

|

0.046​

|

-0.319​

|
Florida|

-0.381​

|

-0.022​

|

-0.403​

|
Columbus|

-0.581​

|

0.061​

|

-0.520​

|
Edmonton|

-1.032​

|

0.035​

|

-0.997​

|
Arizona|

-1.206​

|

0.041​

|

-1.165​

|
Buffalo|

-1.413​

|

0.080​

|

-1.332​

|

Home-ice advantage is currently estimated at +0.277 goals/game.

 

[Doctor No]

Simple Rating System, NHL games through March 8, 2015:

Team | 2014-15 Goal Diff | 2014-15 Schedule | 2014-15 Strength
NY Rangers|

0.672​

|

-0.032​

|

0.640​

|
St. Louis|

0.631​

|

-0.019​

|

0.612​

|
Tampa Bay|

0.672​

|

-0.075​

|

0.596​

|
Chicago|

0.545​

|

0.023​

|

0.568​

|
Nashville|

0.478​

|

0.021​

|

0.499​

|
Pittsburgh|

0.431​

|

0.061​

|

0.492​

|
Washington|

0.522​

|

-0.051​

|

0.471​

|
Montreal|

0.470​

|

-0.053​

|

0.417​

|
NY Islanders|

0.373​

|

0.018​

|

0.391​

|
Calgary|

0.288​

|

-0.035​

|

0.252​

|
Detroit|

0.266​

|

-0.024​

|

0.242​

|
Minnesota|

0.277​

|

-0.037​

|

0.239​

|
Anaheim|

0.209​

|

-0.030​

|

0.179​

|
Vancouver|

0.138​

|

-0.006​

|

0.132​

|
Winnipeg|

0.106​

|

0.002​

|

0.108​

|
Ottawa|

0.141​

|

-0.041​

|

0.099​

|
Boston|

0.123​

|

-0.037​

|

0.086​

|
Los Angeles|

0.108​

|

-0.033​

|

0.075​

|
Colorado|

-0.106​

|

0.106​

|

0.000​

|
San Jose|

0.000​

|

-0.030​

|

-0.030​

|
Dallas|

-0.197​

|

0.048​

|

-0.149​

|
New Jersey|

-0.288​

|

0.029​

|

-0.259​

|
Philadelphia|

-0.269​

|

-0.007​

|

-0.275​

|
Carolina|

-0.344​

|

0.060​

|

-0.284​

|
Toronto|

-0.439​

|

0.060​

|

-0.379​

|
Florida|

-0.379​

|

-0.034​

|

-0.412​

|
Columbus|

-0.631​

|

0.060​

|

-0.571​

|
Edmonton|

-1.091​

|

0.047​

|

-1.044​

|
Arizona|

-1.212​

|

0.052​

|

-1.160​

|
Buffalo|

-1.485​

|

0.096​

|

-1.389​

|

Home-ice advantage is currently measured at +0.265 goals/game.

Good representation by the East at/near the top, for really the first time this season.