[Miz]

Calculating Home Field/Court/Ice Advantage on a Per Team Basis...

I am tinkering with developing a linear regression model for a competitive league using the first part of 2009-2010 season data. I am not to the point of validating the model yet, just coming up with the format and code to manipulate the data, scrapers, macros, parsing etc.

I am keeping it somwhat simple with respect to the number of independent variables just to get the format and code to work. Then I plan to go back and add more variables/complexity to it, and then evaluate its predictive value via back testing on 2004 - 2008.

The offensive and defensive ratings are calculated first without distinguishing between Home/Road games, to maximize the data set concerning number of events. For simplicity's sake I haven't implemented a diminishing returns function for MOV or anything like that, etc. Just the bare bones ratings for each team's offense and defense.

To illustrate this for the example's purpose, I chose the NHL and here are my offense and defense ratings for each team:

Team Off Def HA
--------------------------------------------------------------------
1 Anaheim 2.7763 0.3256 0.9256
2 Atlanta 2.9639 0.7285 -0.1803
3 Boston 2.4277 -0.2488 -0.1584
4 Buffalo 2.7172 -0.3814 0.1494
5 Calgary 2.7099 -0.2675 -0.935
6 Carolina 2.4296 0.6584 1.131
7 Chicago 3.1716 -0.4488 0.1613
8 Colorado 2.83 0.1111 0.3268
9 Columbus 2.7106 0.4654 0.8182
10 Dallas 2.6815 0.3616 0.5443
11 Detroit 2.562 -0.2299 0.3591
12 Edmonton 2.8043 0.4656 -0.1465
13 Florida 2.624 0.2413 -0.6731
14 Los_Angeles 2.9986 0.0684 0.4598
15 Minnesota 2.6031 0.1433 0.721
16 Montreal 2.3647 -0.0888 0.1815
17 Nashville 2.8597 0.0121 -0.8245
18 New_Jersey 2.7529 -0.6371 -0.4804
19 NY_Islanders 2.4822 0.3683 0.1614
20 NY_Rangers 2.6199 -0.0481 -0.167
21 Ottawa 2.5862 0.2275 0.9764
22 Philadelphia 2.8919 0.1247 0.3491
23 Phoenix 2.564 -0.2973 0.4109
24 Pittsburgh 2.9931 0.2043 2.0231
25 San_Jose 3.1502 -0.1815 0.4196
26 St_Louis 2.68 0.0124 -1.5679
27 Tampa_Bay 2.4449 0.1829 1.2067
28 Toronto 2.8097 0.6841 0.2454
29 Vancouver 3.1678 -0.3977 0.9423
30 Washington 3.5746 0 -0.0095

So to predict the final score of tonight's game between Vancouver and Minnesota...

Off Def HA Predicted Score
------------------------------------------------------------------
Vancouver 3.168 -0.398 0.942 2.840
Minnesota 2.603 0.143 0.721 2.566

So to get the score for Vancouver-----> Score = VanOff + MinDef - (VanHA)/2

So to get the score for Minnesota-----> Score = MinOff + VanDef + (MinHA)/2

So Vancouver's probability to win the game is estimated like this
2.840 / (2.840 + 2.566) = 0.525 and corresponds to a fair moneyline of -111 for Vancouver

It seems to resemble the market price of -115. Most of my other games are pretty close to the line as well, but some are off a bit. That is where the backtesting will
eventually come in.

My question is in the method that I used to calculate Home Ice Advantage. I calculated separate home and away, offensive and defensive ratings for each team. Then took the difference between them to represent the Home versus Away Ice Advantage.

For example if a team was rated say, 0.4 goals better on offense at home and say, 0.3 goals better on defense then that team's HA would be 0.7.

So since Vancouver will be away and Minnesota will be home you subtract half of Vancouver's home advantage from it's projected score and add half of minnesota's to its projected score.

Does anyone have a different way to calculate and implement independent Home Advantages or does this seem reasonable?

There really aren't that many NHL models to compare to, although I found one with somewhat similar numbers.

Again, this sport is just an example, since the number of teams is limited and the numbers are not very cumbersome to work with, as I get the automation process going.

I just wanted to run it by some folks to see if they agree/disagree or do it a different way...

Thanks,

Miz

[Miz]

I forgot to mention that my league average home ice advantage is 0.246, which is consistent with the numbers I've seen of roughly 0.25

[IrishTim]

I've seen breakdowns like this for NFL but never in hockey. Will take a closer look after class, looks like some good stuff.

[Sinister Cat]

Any reason to believe that nhl teams actually do have different home ice advantages? (Maybe younger teams can't handle the pressure, different speeds of ice surfaces, etc.) My hunch is that you'll find when you back test that there's little consistency year-to-year between teams' home ice advantages and that you'll find that your model will have more predictive value using the flat 0.25. Would you feel comfortable having your money at risk where your model is telling you that a team has a significant disadvantage playing at home? Not saying it's impossible for that to be the case but you need to be careful.

[Bsims]

Miz, How did you come up with the approach of dividing the expected score for each by their sum to get the expected percentage for each? Did you compare this to the Bill James Pythagorean formula used in baseball where each of these factors are squared? Another approach would be to use the averages and assume a Poisson distribution to compute the probabilities. Just a couple of thoughts.

[Sinister Cat]

Here's a good thread, which includes a document worth reading for goal distributions in hockey:
http://www.sportsbookreview.com/forum/handicappe...ble-model.html

[Miz]

First, let me say that ratings and HA are calculated for the year in which they are to be applied. This is done via least squares... e.g. accumulating 1-2 months of data first before hypothetically wagering. So, I agree that it would be unwise to apply 2009-2010 HA for a team to the 2003-2004 season. I am definitely not saying that. So far my line is closer to the book's closing line using my calculated HA. I was just curious if anyone else has performed the calculation before, and if so, did they do it in a similar fashion.

I do believe that home ice can vary significantly from team to team just as HFA does in college football. I have seen college teams with large and negligible home field advantages, so i have no problem believing that it could be the case in hockey. BTW, I don't feel comfortable with my money on anything I haven't thoroughly tested and quantified. Also, yes I do believe that a team can play more poorly at home, I just go with the numbers - St. Louis is one of those teams. Thanks for the feedback.

[Miz]

Bsims and sinister, thanks for the feedback. I must've been responding to Sinister's first post while you were posting. I will look a little more deeply into it. I found an empirical relationship that seemed reasonable, but there is always the possibility it could be improved via Root sum squaring etc.

Sinisiter, thanks for the link, I will check it out now.

Cheers

[Sinister Cat]

My point regarding using the home ice advantage season-to-season is that if there were something inherent in the environment you may see consistency season-to-season. The fact that you would expect that you wouldn't see it might make you tend to believe that the results you are seeing are simply due to luck.

Does St. Louis's team or arena have some sort of intrinsic qualities that cause the team to play poorly at home, or have they just happened to have off-nights this season at home, or played a tougher schedule at home? I am just pointing out that these are the types of things that you need to look at. It is one thing for St Louis to have a poor record at home thus far; another for them to have it going forward. In the absence of season-to-season consistency for a given home field think you will find your model will more predictive if there is at least some sort of regression-to-the-mean component to your HFA parameter.

[Miz]

I'm with you now about the season to season. The method of the ratings takes opponent strength into account. When I look at other seasons I will take a look at this parameter for each team over the 2004-2010 time frame. Thanks again for the feedback.

[Sinister Cat]

Interesting that you are closer to the closing lines with your calculated HFA.. especially given that it seems to be so extreme in some cases. Obviously suggests that the market believes that different NHL teams do indeed have varying HFAs.

[Miz]

Honestly the extreme values are exactly why I posted this. I found one other model, and mine correlates pretty well with his, but i still wanted to run it by some other people to see if there is anything I am doing obviously wrong.

I was strongly considering implementing some type of diminishing returns function... but will probably leave it alone for now and see what the data say. Have a good night

[Justin7]

Sinister Cat raises a good point.

I would start with the assumption that all home fields are created equally. One you compute HFAs based on that, you can evaluate whether or not it is a valid assumption.

[DOMINATER]

wow good thread

[dkp]

I agree that strength of schedule has to come into play.

I wonder what these numbers would look like for conference games vs. nonconference games? Does home ice matter more when you know that you are not only getting points but depriving your division opponent from getting a point too?