"Expected Points" per D'ohboy's Theorem

by D'ohboy on Jan 28, 2010 11:19 PM EST

For all three of you who I haven't yet bored to death with Excel and math, after the break will be my breakdown of the current standings according to Expected Points per what I'm calling "D'ohboy's Theorem." I'll also include the same table using my original theorem that used PP, PK and 5v5.

The following table is the current NHL "Expected Points" according to "D'ohboy's Theorem," which is:

Expected Points = (1.1134)*GP + Goal Differential/2.645

2009	-2010
Team	GP	GF	GA	Diff	Pts Expected	Pts Actual
SJS	53	179	128	51	78.29960579	78
CHI	53	174	122	52	78.67781423	76
WSH	53	207	146	61	82.08169014	76
NJD	52	139	115	24	66.97456341	70
BUF	52	147	126	21	65.83993811	69
VAN	53	173	129	44	75.65214675	68
PIT	55	173	156	17	67.66734827	67
COL	51	153	136	17	63.21368974	66
LAK	53	160	147	13	63.92768526	65
PHX	53	144	139	5	60.90201778	65
OTT	55	154	155	-1	60.85959644	64
NSH	52	145	145	0	57.89756098	61
CGY	53	135	138	-3	57.8763503	59
DET	53	137	143	-6	56.741725	59
DAL	53	152	171	-19	51.82501535	57
MIN	53	150	158	-8	55.98530813	56
PHI	51	155	144	11	60.94443913	55
FLA	53	146	154	-8	55.98530813	55
NYR	54	138	150	-12	55.58588902	55
ANA	54	150	171	-21	52.18201311	55
MTL	55	141	149	-8	58.2121374	55
BOS	51	127	131	-4	55.2713126	54
ATL	52	158	167	-9	54.49368506	54
TBL	52	135	157	-22	49.57697541	54
STL	53	139	149	-10	55.22889126	54
NYI	54	142	168	-26	50.29097094	54
CBJ	56	146	186	-40	47.22288211	51
TOR	54	142	187	-45	43.10501067	44
CAR	53	141	174	-33	46.53009726	43
EDM	51	135	176	-41	41.27760051	38

The following is a rating system based on the following equation: (PP+PK)^2+3*(5v5^2):

2009	-2010
Team	Points	PP	PK	ST	5v5
SJS	78	0.216	0.878	1.094	1.37	6.827536
CHI	76	0.213	0.856	1.069	1.28	6.057961
WSH	76	0.261	0.803	1.064	1.56	8.432896
NJD	70	0.192	0.826	1.018	1.08	4.535524
BUF	69	0.183	0.871	1.054	1.09	4.675216
VAN	68	0.22	0.816	1.036	1.39	6.869596
PIT	67	0.162	0.829	0.991	1.15	4.949581
COL	66	0.186	0.817	1.003	1.16	5.042809
PHX	65	0.171	0.825	0.996	1.12	4.755216
LAK	65	0.185	0.796	0.981	1	3.962361
OTT	64	0.149	0.84	0.989	0.93	3.572821
NSH	61	0.158	0.773	0.931	1.01	3.927061
DET	59	0.174	0.804	0.978	0.92	3.495684
CGY	59	0.167	0.832	0.999	0.98	3.879201
DAL	57	0.186	0.753	0.939	0.93	3.476421
MIN	56	0.175	0.828	1.003	0.94	3.656809
ATL	56	0.175	0.802	0.977	0.97	3.777229
MTL	55	0.247	0.842	1.089	0.79	3.058221
NYR	55	0.181	0.845	1.026	0.97	3.875376
ANA	55	0.186	0.801	0.987	0.94	3.624969
FLA	55	0.168	0.805	0.973	0.96	3.711529
PHI	55	0.231	0.798	1.029	1.06	4.429641
NYI	54	0.163	0.75	0.913	0.83	2.900269
STL	53	0.162	0.849	1.011	0.95	3.729621
TBL	54	0.195	0.799	0.994	0.86	3.206836
BOS	54	0.174	0.874	1.048	0.89	3.474604
CBJ	51	0.204	0.821	1.025	0.72	2.605825
TOR	44	0.165	0.694	0.859	0.96	3.502681
CAR	43	0.181	0.794	0.975	0.81	2.918925
EDM	38	0.192	0.739	0.931	0.82	2.883961

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Comments

It definitely does work pretty damn well, despite the kludge. It does make me a little nervous to see that (with the exception of VAN) the teams that are over-performing are the teams that have rocks in net and the teams that are under-performing are the teams that rely on their offense. I don’t know if a team’s ability to win close games is a factor, or if it’s a coincidence, or what. But despite the solid goaltending the Caps have gotten this year I don’t think anyone would put us in the “rock in net” category.

Now let's say you and I go toe to toe on bird law and see who comes out the victor.

by Rob Parker on Jan 28, 2010 11:35 PM EST reply actions

Agreed

One of the criticisms of Bill James’ original Pythagorean Theorem for baseball was that it undervalued teams that could repeatedly win close games – like teams with exceptional bullpens for example.

I think we’re seeing something similar – teams like NJ and BUF that win close games on the back of their goaltending get penalized here, whereas teams like the Caps, Sharks and ’Hawks get a lift.

I’m going to fiddle with the second equation, perhaps add in Penalties For/Against and I’ll use it as a “Power Ranking.”

This is not a game of who the f*ck are you...

by D'ohboy on Jan 28, 2010 11:43 PM EST up reply actions

Qualifying the special teams percentages by how often they are on those specials teams might be a start.

Now let's say you and I go toe to toe on bird law and see who comes out the victor.

by Rob Parker on Jan 29, 2010 12:13 AM EST up reply actions

See the equation below!

This is not a game of who the f*ck are you...

by D'ohboy on Jan 29, 2010 12:38 AM EST up reply actions

Now we’re talking business! One point: you’ve probably noticed that the average factor of 2.645 actually monotonically decreases over last four seasons — 2.85, 2.78, 2.62, 2.32. Maybe it would be reasonable to take the previous season number as it might better reflect the CURRENT state of affairs.

I’m still not too comfortable with (PP+PK)^2. This parameter is almost constant for all teams and therefore the ratings difference is in fact just the difference between 3*5v5.

In any case, excellent job. Both “this” and “rec’d”.

by fnralch on Jan 28, 2010 11:43 PM EST reply actions

I actually didn’t notice that. Why do you think that is? I wonder if more games are going to OT/SO and this is affecting it…

Hmm. I squared the numbers to “reward” those teams that managed to get over 1, while punishing those under 1. I thought that this would further differentiate between good teams and bad teams and lead to a greater spread in the curve.

As I develop it more, I’m going to figure out exactly what the post-lockout ratio of PP goals to EV goals is league-wide, then I’ll use that as the multiplier “X” for the 5v5 number.

Actually, here’s the equation I’m thinking of doing as a “Power Rating:” (Minor Penalties Drawn/Minor Penalties Against * (PP+PK))^2 + "X"*(5v5^2)

This is not a game of who the f*ck are you...

by D'ohboy on Jan 28, 2010 11:57 PM EST up reply actions

Why do you think that is? I wonder if more games are going to OT/SO and this is affecting it…

I think as scoring has gone down since the lockout each goal has been more valuable so a smaller goal differential makes a bigger difference.

Now let's say you and I go toe to toe on bird law and see who comes out the victor.

by Rob Parker on Jan 29, 2010 12:15 AM EST up reply actions

Makes sense – points are relatively constant but overall goals are down so the goals/point would likewise go down. Don’t know why I didn’t see that.

This is not a game of who the f*ck are you...

by D'ohboy on Jan 29, 2010 12:41 AM EST up reply actions

You can actually rewrite the formula as the following:

Points Percentage = (1/2)((1.1134) + (Goals For Avg – Goals Against Avg)/2.645)

What’s interesting about writing it this way is that it means that points percentage should scale linearly with the difference between the average goals for and average goals against, or your average goal differential. If you’re blowing a lot of teams out of the water, but losing a significant number of one goal games, then your team is probably underperforming according to this formula. Likewise, if you’re squeaking by on getting a lot of OT losses (which are by definition one-goal games) and a handful of one goal wins, but losing in blowouts every other night, your team is probably overperforming.

GUTEN TAAAAAAAAAAAAG!

by Wheeler on Jan 29, 2010 8:12 AM EST reply actions

I’m not being flippant or defensive, but why would you want to know points percentage? Ultimately, the important thing is to know the value in points of a given goal for or goal against.

Is the preference for points percentage because that’s how James’ formula works?

I guess I’m just trying to understand why you’d want to do it this way and it’s not coming to me… could you elaborate a bit?

(Again, remember that I’m somewhat obtuse when it comes to statistics – I have no training whatsoever, so whatever I’m doing I’m not standing on the shoulders of giants, I’m burrowing around with the moles.)

This is not a game of who the f*ck are you...

by D'ohboy on Jan 29, 2010 9:36 AM EST up reply actions

Well, it’s another way of analyzing the data. Dividing through by the number of games played normalizes the points for each team across the standings regardless of the number of games they’ve played. If you’re interested in whether a team is under- or over-performing despite their great/horrible offense/defense, . Using the total number of points is kind of a problematic yardstick in the middle of the regular season because it doesn’t account for the number of games-in-hand.

Another useful metric would be Expected Points Per Game, which would just be total points divided by number of games played. Rewriting the formula in this fashion gives the following:

If you’re trying to know the value in points of a given goal for or goal against, then I suppose the best way to write the formula would be as follows:

Expected Points Per Game = 1.1134 + (Goals For – Goals Against)/(GP*2.645) = 1.1134 + (Goals For Avg – Goals Against Avg)/2.645

This gives the value of a particular goal for or goal against in terms of standing points. The only problem is that it highly overvalues goals early in the season and devalues them late in the season.

GUTEN TAAAAAAAAAAAAG!

by Wheeler on Jan 29, 2010 10:56 AM EST up reply actions

Ok. I’ve got it now. I think what was confusing me was that you multiplied the 1.1134 by .5, which threw me.

I guess I went for Expected Points because it translates well to what we already know, but I can see how your method would have value in other applications.

This is not a game of who the f*ck are you...

by D'ohboy on Jan 29, 2010 11:22 AM EST up reply actions

Oh, yeah. It’s not 0.5 times the 1.1134, but instead it’s 0.5 times the entire right side of the equation. I can see how that would be confusing.

GUTEN TAAAAAAAAAAAAG!

by Wheeler on Jan 29, 2010 11:55 AM EST up reply actions

Great job!

I was charting out much of the same teams information from BTN. The thing that I struggled with and wondered if it was an X-factor that could serve as a pulse and trending stat was penalties drawn-penalties taken.

The penalties calculation and blocked shots help the most in the post season and I was trying to figure out how to fit them all together, any ideas from the more statistically inclined?

Promote the game, it's the NHL, not SCHL

by kurlNdrag on Jan 29, 2010 9:12 AM EST reply actions

Just eyeballing the comparison between PE and actual points it looks like you have an very high correlation. I’d be curious to know exactly what the correlation coefficient is (you should be able to get that pretty easily in Excel).

Knowing the exact strength of the correlation will be useful as you attempt to fine-tune the formula (keeping in mind that very small changes in correlation strength are probably not meaningful).

by LSF76 on Jan 29, 2010 2:04 PM EST reply actions

Yeah. It looks like I’ll need to figure out how to use Excel a little better.

This is not a game of who the f*ck are you...

by D'ohboy on Jan 29, 2010 3:47 PM EST up reply actions

The correlation between the two is .9439. Pretty damn good.

Of all our iniquities ignorance may be the worst

by Killer_Carlson on Jan 29, 2010 4:05 PM EST up reply actions

That’s so high that I’d almost be afraid to try and get it higher. After all, if the correlation was a perfect 1.0, it would tell us nothing we didn’t already know. Anyone can look at the actual standings. The point of an exercise such as this is to indicate teams which are perhaps over- or under-rated by the actual standings, to give a measure of “true” team strength and to predict performance in the future.

The best measure of how good this formula is would not be to see how well it compares to standings points over the same period, it would be to see how well the formula’s prediction based on the first-half stats compares to the actual standings from the second half. If the formula is better than actual first-half standings points at predicting second-half standings points, then you know you accomplished something. You can determine how well it predicts future performance using correlation coefficients.

by LSF76 on Jan 30, 2010 7:08 PM EST up reply actions

Very Minor Quibble: SJS have 79 pts on account they got a charity point for taking the Hawks to overtime last night. Thanks, Gary!

IS KEPTIN NOW

by EmilyB on Jan 29, 2010 2:42 PM EST reply actions

This was done with last night’s info as of 11pm, so the points won’t be current. I should’ve made that clear.

This is not a game of who the f*ck are you...

by D'ohboy on Jan 29, 2010 3:45 PM EST up reply actions

This is very impressive. Very impressive.

The only thing I might add is a variable for very strong defensive systems or goalie play – perhaps a save pct modifier? It might help account for the performance of BUF and NJD. But I think you’ve got the basic parameters nailed down.

The rest of the hockey world ought to be sitting up and taking notice – this is not insignificant.

"You're gonna eat that g**d**n Koho, three!"

by fat_daddyo on Jan 29, 2010 5:01 PM EST reply actions

Thanks!

This has taken longer than I thought, but it’s been a labor of love.

Here’s the thing about NJD and BUF – I think that it’s up to the reader/analyst/whomever to understand that teams that can repeatedly win close games are going to appear to overperform. Baseball has the same issue with teams that have exceptional bullpens – they have an ability to repeatedly win games by a run or two, but if they get blown out the bullpen never really factors.

In the process of doing this, I’ve also developed a pretty sweet “Power Ranking” that I’ll debut sometime next week. But what’s really cool is what this equation can allow us to do in the future for player evaluation. Are you following me?

;)

This is not a game of who the f*ck are you...

by D'ohboy on Jan 31, 2010 2:49 AM EST up reply actions

Doh, I just wanted to say that I dig your past three FanPosts and the effort you put in. I spent the whole weekend sick and hopped up on various cold medicines, so I wasn’t able to contribute in any intelligent way, but I just want to let you know I appreciate the work. Keep ’em coming.

"Dozens of people spontaneously combust each year. It's just not really widely reported."

by Laich It Or Lump It on Feb 2, 2010 12:15 PM EST reply actions