The Leafs Team Save Percentage vs. Pythagorean Winning Expectation

by Chemmy on Mar 4, 2010 10:50 AM EST

Long time reader first time caller mf37 is sort of like my muse. If I had to credit him every time he gave me an idea for a post or shoved me in the right direction you'd all probably tell me to save the time and just have him write here. We'll ignore that I dipped my toes into Leaf blogging because of his blog, Ninja's blog, the BoO and PPP's original home at Blogspot and get down to brass tacks.

One day after the trade deadline and as a collective group we're angry. We're frustrated and at wit's end and I think a lot of people are wondering how we ended up here. This season started off with a ton of hope and after a thrilling preseason this team fell off a cliff.

I decided to run some numbers to see where the Leafs would be in the standings if they had a better save percentage as a team. This doesn't place all of the blame on the goaltenders; clearly our defense and forwards hang them out to dry plenty. Clearly the object is to not get scored on as much as we do, but just how much would a better team save percentage change the 09-10 Leafs' fortune?

Exhibit A: Our four goaltender's raw numbers for all to see:

	SA	GA	Saves	SV%
Giguere	137	12	125	0.912
Gustavsson	862	88	774	0.898
Toskala	676	85	591	0.874
MacDonald	157	17	140	0.892
Total	1832	202	1630	0.890

Oof. 0.890 is a horrible number. It would have been fine in the mid 80s but it's abyssmal now. Average NHL starting goaltending is in the .915 range now. We're looking to see how the Leafs would fare with a better team save percentage so we're going to use something called the pythagorean expectation which was popularized in baseball but can be summed up if you don't care about math as: the more a team scores relative to how many points it gives up the better it does. This is obvious.

Quick note: Jonas Gustavsson has allowed 3 more goals on 186 more shots than Toskala. That's how bad Toskala is.

I'm not mc79 or Gabe Desjardins, I'm not presenting the most fundamentally rigorous statistical analysis in the world here, but the first thing I did was using goals for and goals against calculate the pythagorean percentage for all 30 teams in the NHL. Then I compared their pythagorean percentage to their points percentage (Pts / (2 * Games played)) to determine if a correction factor was needed. I averaged a comparision of every team's PYTH% vs. their PTS% and got an average of 1.12 with a standard deviation of 0.05. That's a tight enough spread for me.

Here's a huge table of teams' records, goals for, goals against, etc.:

	GP	PTS	GF	GA	Pyth	Pts %	Correction Factor
Washington	63	92	250	178	0.664	0.730	1.100
Chicago	63	89	207	153	0.647	0.706	1.092
San Jose	63	89	207	157	0.635	0.706	1.113
Los Angeles	62	80	190	167	0.564	0.645	1.144
Vancouver	63	80	204	158	0.625	0.635	1.016
New Jersey	62	79	166	147	0.560	0.637	1.137
Phoenix	64	79	169	163	0.518	0.617	1.191
Pittsburgh	63	78	198	181	0.545	0.619	1.136
Colorado	63	78	184	164	0.557	0.619	1.111
Ottawa	64	76	179	183	0.489	0.594	1.214
Buffalo	62	75	169	158	0.534	0.605	1.134
Nashville	62	73	174	176	0.494	0.589	1.191
Detroit	63	70	165	172	0.479	0.556	1.159
Philadelphia	62	69	190	169	0.558	0.556	0.997
Calgary	63	69	156	160	0.487	0.548	1.124
Dallas	62	68	176	191	0.459	0.548	1.194
Anaheim	63	67	180	193	0.465	0.532	1.143
St. Louis	63	67	168	174	0.482	0.532	1.102
Minnesota	62	66	175	178	0.492	0.532	1.083
Montreal	64	66	168	177	0.474	0.516	1.088
Boston	61	65	150	158	0.474	0.533	1.124
NY Rangers	63	65	165	170	0.485	0.516	1.063
Atlanta	61	64	186	196	0.474	0.525	1.107
Tampa Bay	62	63	162	189	0.424	0.508	1.200
Columbus	64	61	169	207	0.400	0.477	1.192
Islanders	63	60	164	197	0.409	0.476	1.163
Florida	63	60	164	185	0.440	0.476	1.082
Carolina	62	57	173	195	0.440	0.460	1.044
Toronto	62	49	163	213	0.369	0.395	1.070
Edmonton	63	44	158	220	0.340	0.349	1.026

So to get a team's expected points percentage we use this handy dandy formula:

PTS% = 1.12 * (Goals For)^2 / ( (Goals For)^2 + (Goals Against)^2)

Now we can play with that to see what would happen. If we raise the team's save percentage we lower the number of goals against and our PTS% formula will tell us what percentage of points we'll get.

SV%	GF	GA	Pyth	Pts Pct	82 Gm
0.89	163	213	0.369	0.414	67
0.895	163	192	0.418	0.468	75
0.9	163	183	0.442	0.495	80
0.905	163	174	0.467	0.523	84
0.91	163	165	0.494	0.554	89
0.915	163	156	0.523	0.586	94
0.92	163	147	0.553	0.619	100

We currently get terrible .890 goaltending. If we got .915 goaltending for 60 games from our starter and .905 goaltending for 22 games from our backup we'd be in the .913 range at the end of the year. That probably would have won us the eighth spot in a weak East.

I don't know how to fix our goal against trouble, it's continued despite a defensive overhaul, three goalies and two coaches but I do know that the Leafs should worry more about keeping the puck out of their net than anything else. As a parting note; if the Leafs finished with Vesa Toskala's 0.874 save percentage they'd be on pace for 60 points. Ouch.

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Comments

it's too early for math

I have nothing interesting to say.

by blurr1974 on Mar 4, 2010 10:53 AM EST reply actions

Amazing

This is great work Chemmy. Also, it’s depressing work.

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by PPP on Mar 4, 2010 10:55 AM EST reply actions

This is actually the best cause for optimism I’ve seen yet. Nice work. I feel better.

Come on, Giggy/Monster!

by The '67 Sound on Mar 4, 2010 11:04 AM EST up reply actions

Look Away!

Showing the world our collective goal-tending numbers is akin to finding out your Grandpa was a Nazi-War Criminal.

But seriously, awesome work.

The Guess Who sucked, the Jets were lousy anyway

by Plea From A Cat Named Felix on Mar 4, 2010 10:57 AM EST reply actions

just when I thought I couldn’t hate toskala any more

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by JaredFromLondon on Mar 4, 2010 10:59 AM EST reply actions

Fun stuff

One thing you need to do, however, is strip away points earned in the shootout (the shootout is basically a coin flip, uncorrelated with Goals For/Against ratios). I’ve done something similar in the past.

More fun than a stick to the face!
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by Dirk Hoag on Mar 4, 2010 11:14 AM EST reply actions

We lose every game we play in OT or the SO.

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by Chemmy on Mar 4, 2010 11:38 AM EST up reply actions

RALLY CAPS!

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by JaredFromLondon on Mar 4, 2010 11:39 AM EST up reply actions

Obviously the correction factor being >1 because of the shootout point. What does it say about Philadelphia that they’re the only team that has a factor under 1? They’re just underperforming their Pyth expectation that badly?

by Dr. Ice on Mar 4, 2010 11:16 AM EST reply actions

I bet they do nearly as poorly at OT / shootout as we do

Just from looking at these numbers. Someone should look and see if that’s actually the case. Because otherwise they’re just unlukcy in the distribution of points they got (i.e., they run up lots of points for in wins, and lost a lot of close games, so if you look at their total goals scored, you’d think they should have more points than they do).

Glory glory Man United, AND the other MU, AAAAnd the Leafs. I think I need a drink now.

by Wan Ihite on Mar 4, 2010 12:39 PM EST up reply actions

Good stuff

The only thing I usually do is remove SO and OT points and goals; regulation win % has a better correlation with goals.

There are some other subtle effects here – if you improve the Leafs save pct, then they don’t trail so much, and their own shooting % should go up, so the improvement is even bigger than you might think.

by Hawerchuk on Mar 4, 2010 11:18 AM EST reply actions

Probably says that they lose a disproportionate amount of close games and win more than their fair share of blowouts.

by unavoidable on Mar 4, 2010 11:32 AM EST up reply actions

The Leafs are something hysterical like 2-18 in one goal games.

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by Chemmy on Mar 4, 2010 11:39 AM EST up reply actions

This same thing, but the opposite,

Is why the Coyotes number is so high but the record is so good. We win a ton of 1 and two goal games, but when we lose, we really go all out.

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by Travis Hair on Mar 4, 2010 11:40 AM EST up reply actions

Which is clearly unsustainable.

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by Chemmy on Mar 4, 2010 11:42 AM EST up reply actions

Clearly.

Except that it might be.

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by Travis Hair on Mar 4, 2010 11:44 AM EST up reply actions

The season is short enough that there might not be enough time for a regression to the mean.

I've always wanted to be a PPP Princess. You see kids, you can be anything you want to be; so long as Jay Leno doesn't also want to be that.

by SkinnyFish on Mar 4, 2010 11:45 AM EST up reply actions

Exactly,

That and if the goal scoring improved with yesterday’s moves then the Pyth would change.

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by Travis Hair on Mar 4, 2010 11:47 AM EST up reply actions

Where would I grab those numbers without trolling through our record to see how we did in every SO game?

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by Chemmy on Mar 4, 2010 11:39 AM EST up reply actions

NHL.com should have them

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by Travis Hair on Mar 4, 2010 11:40 AM EST up reply actions

Leafs OT goals: 0 Goals for, 9 Goals Against.

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by Travis Hair on Mar 4, 2010 11:44 AM EST up reply actions

Shootout “Goals”: 1 for, 2 against

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JaredFromLondon: ...Odin, he's cool.

by Travis Hair on Mar 4, 2010 11:46 AM EST up reply actions

Thanks for the kind words in the intro let me throw some right back at you: this is a fantastic post and the type of stuff that draws so many visitors to this great site. Thanks for doing the math.

Two big “ifs”: if the Leafs can get some scoring support next year and a average goaltending from Toskala and Gustavsson, it should make for a much more enjoyable viewing experience in 2010-11.

Bitter Leaf Fan: because sometimes there's no option but to be bitter...

by mf37 on Mar 4, 2010 11:29 AM EST reply actions

Tos..ka….la?

The Artist Formerly Known as...

by JaredFromLondon on Mar 4, 2010 11:32 AM EST up reply actions

Fail?

mf37 is so bitter he forgot Toskalol is gone?

by unavoidable on Mar 4, 2010 11:33 AM EST up reply actions

D’oh! Talk about a brain cramp, I meant Giguere.

When will SBN/PPP bring me the much needed “edit” button?

Bitter Leaf Fan: because sometimes there's no option but to be bitter...

by mf37 on Mar 4, 2010 11:37 AM EST up reply actions

It’s been in discussion. The big thinkers don’t want people replying to changed comments. Shrug.

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by Chemmy on Mar 4, 2010 11:40 AM EST up reply actions

S’ok, I guess I can live with my general dumb-assery/typos/ brain cramps in the comments.

Bitter Leaf Fan: because sometimes there's no option but to be bitter...

by mf37 on Mar 4, 2010 11:53 AM EST up reply actions

I’ve seen it implemented at another blog with a 5 minute timer… After you post you can make rapid corrections and edits and addendums, but after 5 minutes it’s locked in as a permanent post.

That works pretty well.

Glory glory Man United, AND the other MU, AAAAnd the Leafs. I think I need a drink now.

by Wan Ihite on Mar 4, 2010 12:43 PM EST up reply actions

One suggestion has been the ability to edit until there is a reply to the comment.

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by PPP on Mar 4, 2010 1:15 PM EST up reply actions

or a straight up delete button

There is no "I" in team, but there is an "M" and an "E"

by Matt_Roberts on Mar 4, 2010 11:51 AM EST up reply actions

Problem with that is it would delete every post that replied to it

Maybe have it so you can only delete if no one has replied to it yet? Seems like a fair compromise.

Leafs Nation: A drinking team with a hockey problem.

by nhlcheapshot on Mar 4, 2010 11:52 AM EST up reply actions

preview

then post

I have nothing interesting to say.

by blurr1974 on Mar 4, 2010 12:00 PM EST up reply actions

The programming for all of the solutions is fairly trivial – it’s more of a user interaction decision. There are pros and cons to allowing people editing posts, especially in threaded comments.

I tend to be in the camp that just indicates in the post if it’s been edited or not, and then allow people to edit, but I know there are plenty that would just rather not allow edits.

Prefers pugnacity to truculence.

by chillin411 on Mar 4, 2010 12:30 PM EST up reply actions

as you know

i love math. well done sir.

Yesterday is dead, but not my memory.

by daoust on Mar 4, 2010 12:14 PM EST reply actions

2010 in review

Vesa Toskala: Traded not once, but twice. To teams in the NHL
Russian Olympic Team: no medal.
Chemmy: Married and doing math problems. Well!

Now, dammit, I’ve seen everything. Nice job and I will cling desperately to this analysis. It’s math-magical proof, isn’t it, that it JUST CAN’T POSSIBLY BE THIS BAD NEXT YEAR AGAIN. Right?

jrwendelman
The Artist Formerly Known as "Junior", who blogs at heroesinrehab.ca/blog

"But if someone so eager to engage into fist talk, we can always meet after season end in Minsk." (Mikhail Grabovski and a well-meaning but not particularly skillful translator)

by jrwendelman on Mar 4, 2010 12:33 PM EST reply actions

I’d bet on it being worse.

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by Chemmy on Mar 4, 2010 12:44 PM EST up reply actions

Math doesn’t lie! you’ll clearly be better unless some catastrophe or Vesa Toskala occurs!

Not even the Toronto Maple Leafs could kill my optimism

Free Tyler Ennis!

by Ubiquitous on Mar 4, 2010 12:56 PM EST up reply actions

Seriously?

Doesn’t your own work refute your point, or am I missing something?

jrwendelman
The Artist Formerly Known as "Junior", who blogs at heroesinrehab.ca/blog

"But if someone so eager to engage into fist talk, we can always meet after season end in Minsk." (Mikhail Grabovski and a well-meaning but not particularly skillful translator)

by jrwendelman on Mar 4, 2010 3:46 PM EST up reply actions

You’re missing that they’re the Toronto Maple Leafs.

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by Chemmy on Mar 4, 2010 4:08 PM EST up reply actions

Oh, right.

Which makes that (checks calendar, does quick figurin’) um…..43 years in a row that I’ve made that mistake.

jrwendelman
The Artist Formerly Known as "Junior", who blogs at heroesinrehab.ca/blog

"But if someone so eager to engage into fist talk, we can always meet after season end in Minsk." (Mikhail Grabovski and a well-meaning but not particularly skillful translator)

by jrwendelman on Mar 4, 2010 4:49 PM EST up reply actions

Let me add to the chorus. Nicely done.

Glory glory Man United, AND the other MU, AAAAnd the Leafs. I think I need a drink now.

by Wan Ihite on Mar 4, 2010 12:44 PM EST reply actions

This shouldn't be necessary Mr. Burke

I have a feeling that Capitals and Sharks fans do a lot less math than Leafs fans. Good work though Chemmy.

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by Another Good Kingston Boy on Mar 4, 2010 1:15 PM EST reply actions

No one does math when you’re winning games. Why bother? The only math you need to know is making sure Goals for > Goals against each game.

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by nhlcheapshot on Mar 4, 2010 1:51 PM EST up reply actions

No one does math when you’re winning games. Why bother?

To see if you’re breaking records, if you’re really really good.

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by Cornelius Hardenbergh on Mar 4, 2010 2:06 PM EST up reply actions

the last “winning” record someone leaf affiliated won was raycroft tying the games won in a season record, we don’t like those now

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by JaredFromLondon on Mar 4, 2010 2:11 PM EST up reply actions

Breaking records

You can also break all time bad records. Like the Leafs PK was destined to do before Giggy arrived.

by unavoidable on Mar 4, 2010 2:24 PM EST up reply actions

Cujo

Record losses by a goalie!!!

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by nhlcheapshot on Mar 4, 2010 2:25 PM EST up reply actions

Tied with Gump -not Forrest

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Albert Einstein

by Say *plan the parade one more time*... on Mar 4, 2010 5:11 PM EST up reply actions

Obviously you’ve never been over to Japers’ Rink.

No Alex, no ratings. Know Alex, know ratings.

by gotsparkly on Mar 4, 2010 3:12 PM EST up reply actions

you mean Jaspers rink right?

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by JaredFromLondon on Mar 4, 2010 3:17 PM EST up reply actions

i see what you did there

"I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones."

Albert Einstein

by Say *plan the parade one more time*... on Mar 4, 2010 5:11 PM EST up reply actions

Off-topic, but

John Tavares since Dec 14:

GP:31
G:2
A:5
PTS:7
+/-: -19

Someone must have decided to cover him at the post.

Leaf, the universe and everything.

by 1967ers on Mar 4, 2010 2:22 PM EST reply actions

Pulling a Stamkos, maybe. I’ll be scared of him next year. :(

by unavoidable on Mar 4, 2010 2:25 PM EST up reply actions

But Stamkos got hot at the end of the year.

Not that I expect him to bust, but just imagine if Burke had traded heaven and earth for him and he went into a slump like this.

Leaf, the universe and everything.

by 1967ers on Mar 4, 2010 2:30 PM EST up reply actions

People would be yelling that they should have traded for Kessel instead.

Oh. Wait.

by unavoidable on Mar 4, 2010 3:01 PM EST up reply actions

I still like him.

Not 2 1sts and a 2nd like him, but I still like him.

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by nhlcheapshot on Mar 4, 2010 2:25 PM EST up reply actions

It’s my fault I bought a John Tavares tshirt and everything I like turns into shit.

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by Chemmy on Mar 4, 2010 2:38 PM EST up reply actions

We’ll chip in for the Hall/Seguin/whatever shirt….

Leaf, the universe and everything.

by 1967ers on Mar 4, 2010 2:50 PM EST up reply actions

please

go root for Pittsburgh

I have nothing interesting to say.

by blurr1974 on Mar 4, 2010 4:05 PM EST up reply actions

Giguere

People were saying in another thread that J.S. has been sub-par for the last two years, but his sub-par is still a .900 SV%, which if I’m reading this correctly is good for about 13 extra points. What can Monster do? Is it realistic to suggest he might get up to that range as well? I would think so, and he can probably hit at least league average and still be considered a bust by many (because he’s not Lundquist). I’m cautiously optimistic.

The other thing is, while stats are interesting and all, it is hard to account for things like the deflation factor of having Toskala let in bad goals (not all GA are equal), as someone else mentioned, the benefit of having a lead (not all GF are equal) and the benefit of a timely save (not all SV are equal).

Seems like the bottom line is: our goaltending has sucked hard, and if we improve it, we can get better. Will be interesting to see how our offense goes for the rest of the year, but you know, I don’t think we’ll have trouble scoring goals. Young guys love to score. It’s playing defence they don’t like.

by Leaf in Habland on Mar 4, 2010 2:51 PM EST reply actions

That’s the problem with being a goalie in Toronto… you’re not just expected to be average – you’re expected to be the man. Now, there are maybe only 5 goalies in the league like that, but we silly Leafs fans expect every single one of our goalies to turn into one of those.

by unavoidable on Mar 4, 2010 3:03 PM EST up reply actions

None of the past few have even been average….

Leaf, the universe and everything.

by 1967ers on Mar 4, 2010 3:21 PM EST up reply actions

I don’t expect anyone to be “the man” and haven’t expected that since before the lockout. At this point I’d be ecstatic with league average.

by The '67 Sound on Mar 4, 2010 3:52 PM EST up reply actions

I think a sv % of .910 is average. After four years of Raycroft and Toskala, I’m sure most, if not all, Leaf fans would be delighted with that.

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by mf37 on Mar 4, 2010 3:22 PM EST up reply actions

I’d take .906.

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by 1967ers on Mar 4, 2010 3:26 PM EST up reply actions

I’d take .900

by leafsfan4life94 on Mar 4, 2010 3:44 PM EST up reply actions

I’ll take a 5th of jack

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by JaredFromLondon on Mar 4, 2010 3:53 PM EST up reply actions

Fantastic post

It took me far longer than I’m sure a normal person would understand these calculations, but really educational post chemmy. As said above, the balance of deeper statistical analysis with factual based op-ed articles, no wonder this site brings so many visitors.

More so than goalscoring, finding a good permanent solution in net is a problem the Leafs haven’t solved in five years. That’s major.

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by bkblades on Mar 4, 2010 3:44 PM EST reply actions

I don’t think we need a good solution, we just need a “pretty ok” solution.

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by Chemmy on Mar 4, 2010 4:08 PM EST up reply actions

Question

How did you determine the 1.12 correction factor? I’m trying to figure it out and it seems like just an average from all the differences from pyth% – pts%. Am I in the ballpark?

As for “pretty ok”, league average for me is good. I can’t expect excellent goaltending.

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by bkblades on Mar 4, 2010 4:45 PM EST up reply actions