Using Pythagorean Expectation to predict remainder of VHL S66

[DMaximus 1,045]

As we move past the midway point in the VHL season. I thought it would be a good time to use some statistics to help predict the remainder of the season. Pythagorean Expectation is one of the better methods to use to create a predictive model.[1] The Pythagorean Expectation takes our beloved Pythagorean Theorem and translates it to hockey to create an expected win percentage based on Goals For and Goals Against. Researchers found that a more precise model could be created using a different exponent than Pythagoras’ 2. To determine the proper exponent to use, take the totals goals scored per game and raise it to .458[2].

 

For the VHL this year there has been 1282 goals over 218 games equaling 5.88 goals per game. That gives us a Pythagorean exponent of 2.251.

Now we take that exponent that is based on the scoring rate this season and apply it to each team’s goals for and goals against to figure out their expected winning percentage.[3]

 

Here’s our results for the current season:

Team	GP	Wins	Goals For	Goals Against	Expected Winning %	Actual Winning %	Win differential
Helsinki Titans	44	33	148	102	0.698	0.750	2.286
Riga Reign	44	26	123	105	0.588	0.591	0.123
Calgary Wranglers	43	24	124	110	0.567	0.558	-0.382
HC Davos Dynamo	44	22	135	122	0.557	0.500	-2.496
New York Americans	44	23	113	110	0.515	0.523	0.334
Vancouver Wolves	43	23	133	132	0.504	0.535	1.317
Toronto Legion	43	21	129	139	0.458	0.488	1.303
Malmo Nighthawks	43	21	121	120	0.505	0.488	-0.701
Moscow Menace	44	15	153	177	0.419	0.341	-3.424
Seattle Bears	44	10	103	165	0.257	0.227	-1.315

 

A positive win differential means that team has won more games than expected, that team is over-performing. A negative means they won less than expected, they are under-performing.

 

Using the expected winning percentage, we can figure out the expected number of wins each team should get over the remaining games in the season:

Team	Expected wins for remainder of season
Helsinki Titans	19.545
Riga Reign	16.467
Calgary Wranglers	16.443
HC Davos Dynamo	15.589
New York Americans	14.424
Vancouver Wolves	14.623
Toronto Legion	13.284
Malmo Nighthawks	14.635
Moscow Menace	11.724
Seattle Bears	7.201

 

Using that can give us a crude prediction for the final standings. I say crude because we’re not accounting for OT loses, which means we’ll underestimate the total points most teams have at the end of the year.

 

Here’s the final standings prediction using this model:

Team	Wins	Loss	Points
Helsinki Titans	53	19	106
Riga Reign	42	30	84
Calgary Wranglers	40	32	80
HC Davos Dynamo	38	34	76
Vancouver Wolves	38	34	76
New York Americans	37	35	74
Toronto Legion	34	38	68
Malmo Nighthawks	30	42	60
Moscow Menace	27	45	54
Seattle Bears	17	55	34

 

Seeing how close the projected standings are for the makes me wish I took into account overtime loses, because that will make a huge difference in how the actual final standings turn out. But I still think this will be a fairly accurate projection of the actual final results.

 

* I apologize for the table formatting, it didn't copy over nicely and I can't get it to copy with the boarders properly.

 

---

[1] See this paper for an analysis on predictive models in hockey. They conclude that a Poisson model gives the best results. Computing that is well outside my current capabilities. http://www.hockeyanalytics.com/Research_files/Win_Probabilities.pdf

 

[2] Why .458? It was determined to be the optimal rate for the NHL and it’s beyond me to figure out what it should be for the VHL.  http://www.hockeyanalytics.com/Research_files/Win_Probabilities.pdf

 

[3] This website explains it better than I am. https://thehockeywriters.com/analytics-predicting-measuring-nhl-success/

[Beaviss 4,949]

Interesting take but one thing you didn't take into account is STHS being STHS.

[Rayzor_7 741]

58 minutes ago, DMaximus said:

Pythagorean Expectation is one of the better methods to use to create a predictive model

So did you do this all manually? Because this seems like a lot of work.

[Peace 1,518]

55 minutes ago, Beaviss said:

Interesting take but one thing you didn't take into account is STHS being STHS.

This is kinda sad. 

What was the results of the internal testing for FHM5 as a sim engine again? lol

[Beaviss 4,949]

2 minutes ago, Peace said:

This is kinda sad. 

What was the results of the internal testing for FHM5 as a sim engine again? lol

 

never did FHM5

[Rayzor_7 741]

3 minutes ago, Peace said:

This is kinda sad. 

What was the results of the internal testing for FHM5 as a sim engine again? lol

 

Just now, Beaviss said:

 

never did FHM5

 

Would EHM (Eastside Hockey Manager) have been tested? It is older but better I know some of us play it and enjoy it.

[DMaximus 1,045]

9 minutes ago, Rayzor_7 said:

So did you do this all manually? Because this seems like a lot of work.

 

The formulas are already established and used by many statisticians across many sports. I took their formulas, threw in the VHL numbers and spit out the results.

[Peace 1,518]

5 minutes ago, Rayzor_7 said:

 

 

It is older but better I know some of us play it and enjoy it.

 

I disagree. 

EHM's user interface is better - much better - but FHM5's sim engine is superior to EHMs. I honestly think there a lot of people wear rose tinted glasses when comparing EHM to FHM5, but if we were talking about FHM4 I'd be leaning towards EHM as well. FHM5 brought a lot of significant upgrades to the series and beyond the user interface it's a treat to play. Now obviously I can only base my opinion on observation, but I've put in over five hundred hours on both titles over their release and I honestly believe FHM5's sim engine is the better choice if VHL went down that route. 

[Enorama 1,980]

38 minutes ago, Rayzor_7 said:

 

 

Would EHM (Eastside Hockey Manager) have been tested? It is older but better I know some of us play it and enjoy it.

 

It was attempted just recently in the NSHL. Player import and stat exports are difficult, to say the least. And because player attributes change on a daily basis, you basically have to re-upload the player file each day. Add to that the difficulties with modifying schedules and adding/removing teams and the crash-happiness of EHM as a whole and the league was a mess.

[Peace 1,518]

37 minutes ago, Enorama said:

 

It was attempted just recently in the NSHL. Player import and stat exports are difficult, to say the least. And because player attributes change on a daily basis, you basically have to re-upload the player file each day. Add to that the difficulties with modifying schedules and adding/removing teams and the crash-happiness of EHM as a whole and the league was a mess.

This is why I think building a FHM5 test would be beneficial - you can do all of that using the build in commissioner mode.

[CowboyinAmerica 2,705]

(Hi still here stalking the VHL)

 

I really liked this piece, always appreciate people applying statistical analysis to sim leagues. Have played around with it in crude fashion myself as well, and was curious - is there any sort of strength of schedule component in what you ran? That's one thing I've run into with STHS in particular - scheduling can be really wonky at times, with Riga playing Seattle 8 of its first 10 games or something like that, which I feel like would make limited sample size projections difficult. (Also asking without actually looking at the index, it may be more balanced with 10 teams for all I know.)

[DMaximus 1,045]

20 minutes ago, CowboyinAmerica said:

(Hi still here stalking the VHL)

 

I really liked this piece, always appreciate people applying statistical analysis to sim leagues. Have played around with it in crude fashion myself as well, and was curious - is there any sort of strength of schedule component in what you ran? That's one thing I've run into with STHS in particular - scheduling can be really wonky at times, with Riga playing Seattle 8 of its first 10 games or something like that, which I feel like would make limited sample size projections difficult. (Also asking without actually looking at the index, it may be more balanced with 10 teams for all I know.)

 

Thank you for the kind words. For what I posted here, I used the basic Pythagorean Expectation to calculate the expected win ratio. That is just using Goals For and Goals Against. It does not take anything else into account.

 

You're correct that using strength of schedule would create a more precise model. In fact, sabermetricians use 2nd order (which uses expected runs scored and allowed) and 3rd order (which factors in strength of schedule) to more accurately predict future wins in baseball. https://en.wikipedia.org/wiki/Pythagorean_expectation#"Second-order"_and_"third-order"_wins

 

[Victor 10,533]