For statisticians....
I have put together a spread sheet which compares all teams league wide with a Bradley-Terry comparison model. Details of the model can be found here:
http://sites.stat.psu.edu/~drh20/papers/bt.pdf
or, less mathematical rigor on either USCHO or Collegehockeynews.com, where the model is called KRACH, and some math is explained on the site.
Basically, it works like this:
Assume every team has a Power#. We will this P(1) - P(31) for all the teams. These number are such that the odds of Team(1) beating Team(2) on neutral ice are found by:
P(1)/(P(1) + P(2)).
If it were possible to find such numbers, then one could simply replay the entire year's schedule using these number, and add up all those odds for every game, and one would get the current standings.
There are 2 problems with applying this to NHL:
1- The OT system
2- Home ice.
In the first link, above, there is a mathematical discussion of extending the model to home-ice, which I have done. And, about the OT system, my technique in dealing with this matter is to normalize each teams point total so that the sum of standings points over the whole league equals 2 pts/game.
Results (as of games played 2/26)
[TBODY]
[/TBODY]Home ice advantage = 1.21
In one way, there is not much new information here this late in the season. The west shows teams 5-11 covered by a very small margin.
One thing that jumps at you is Philly's lower ranking. They have a brutal schedule left, with lots of BOS games, VEG and WPG as well, etc.
The interesting part of this analysis is the home-ice number. Something like 20%. As an example of what this means.....
If 2 absolutely equal teams played on neutral ice, the odds would be 50/50. Play on someone's home ice, and the odds move to: 1.20*50/(1.20*50 + 50). or 60/110 or....55/45. I found it interesting to find a model to quantify that. Obviously, this method is not perfect in its rankings. Hockey players are very streaky, there are injuries, etc. But I do think the Home-ice advantage portion would squash out correctly over time.
I have put together a spread sheet which compares all teams league wide with a Bradley-Terry comparison model. Details of the model can be found here:
http://sites.stat.psu.edu/~drh20/papers/bt.pdf
or, less mathematical rigor on either USCHO or Collegehockeynews.com, where the model is called KRACH, and some math is explained on the site.
Basically, it works like this:
Assume every team has a Power#. We will this P(1) - P(31) for all the teams. These number are such that the odds of Team(1) beating Team(2) on neutral ice are found by:
P(1)/(P(1) + P(2)).
If it were possible to find such numbers, then one could simply replay the entire year's schedule using these number, and add up all those odds for every game, and one would get the current standings.
There are 2 problems with applying this to NHL:
1- The OT system
2- Home ice.
In the first link, above, there is a mathematical discussion of extending the model to home-ice, which I have done. And, about the OT system, my technique in dealing with this matter is to normalize each teams point total so that the sum of standings points over the whole league equals 2 pts/game.
Results (as of games played 2/26)
| WEST | EAST | |||
| VGK | 160.75 | TBL | 162.78 | |
| NAS | 156.83 | BOS | 141.25 | |
| WPG | 142.55 | TOR | 129.27 | |
| MINN | 120.26 | PHL | 112.62 | |
| SJS | 107.25 | WAS | 110.96 | |
| DAL | 107.01 | PIT | 110.58 | |
| LAK | 103.98 | NJD | 96.3 | |
| ANA | 103.11 | CMB | 89.25 | |
| CGY | 102.86 | FLO | 85.52 | |
| STL | 101.21 | NYI | 81.66 | |
| COL | 99.89 | CAR | 79.76 | |
| CHI | 75.48 | DET | 72.9 | |
| EDM | 69.31 | NYR | 67.82 | |
| VAN | 62.96 | MTL | 61.21 | |
| ARZ | 48.29 | OTT | 57.75 | |
| BUF | 49.68 |
In one way, there is not much new information here this late in the season. The west shows teams 5-11 covered by a very small margin.
One thing that jumps at you is Philly's lower ranking. They have a brutal schedule left, with lots of BOS games, VEG and WPG as well, etc.
The interesting part of this analysis is the home-ice number. Something like 20%. As an example of what this means.....
If 2 absolutely equal teams played on neutral ice, the odds would be 50/50. Play on someone's home ice, and the odds move to: 1.20*50/(1.20*50 + 50). or 60/110 or....55/45. I found it interesting to find a model to quantify that. Obviously, this method is not perfect in its rankings. Hockey players are very streaky, there are injuries, etc. But I do think the Home-ice advantage portion would squash out correctly over time.
