Pythagorean Expectation for Hockey?

by fat_daddyo on Jan 26, 2010 12:20 PM EST

I'm sure most of you have run into the Pythag Expectation as a baseball stat; for the uninitiated, it correlates runs scored and runs allowed with expected winning percentage. It's not entirely precise, but it is a handy metric to gauge if a particular team is winning (or losing) more than their actual performance might warrant.

I have searched in vain for a similar formula in hockey.

Do any of you know of something I've missed? If so, please leave in the comments.

In a similar vein, I am not quite sure what stats are and are not predictive in hockey. I vaguely remember hearing that shot differential is predictive, but Google searches have not yielded me anything meaty here. Is goal differential predictive, similar to baseball? Can't find anything that corroborates or dismisses that.

Again, if you know of any prior work in this vein, please leave us a link in the comments.

If there's nothing out there, I might try to carve out a little time to mess around with some numbers to see if there's a simple formula that will correlate. If I get that motivated, I'll of course share the results here.

Thanks,

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I’d recommend trying this link and seeing what you think.

Formula: Estimated Wins = (GF * GF) / ((GF * GF) + (GA * GA)) * 82

by David Getz on Jan 26, 2010 12:49 PM EST reply actions

I forgot my MarioD – it’s not win pct we’re looking for, it’s points pct. As noted below, the charity point screws things up. Again.

Well, I’ll play around with it.

Any thoughts on the predicitive value of shot differential, Mr Getz?

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

by fat_daddyo on Jan 26, 2010 1:21 PM EST up reply actions

Bill James' Work

Hey there, I’ve been a fan of Bill James and he used to call it the Pythagorean Expectation until he realized that the work he did with it was a repeat of the work of an Italian mathematician name Fibonacci, and he changed the name to Fibonacci win-scores. The formula is pretty simple:

(RF)2
-——————————- = winning percentage
(RF)2 + (RA)2

RF = Runs for
RA = Runs against

The 2’s in the formula above are supposed to be exponents, meaning the formula is The square of runs for divided by the sum of the squares of runs for and runs against. Since a goal in hockey has similar value to a run in baseball (meaning to win, the object is to have more of that item than the opponent) it is reasonable to substitute GF and GA for RF and RA.

For example the Caps (as of 1/25/10) have scored 195 goals, and allowed 143. Plugging those numbers into the formula yields an expected wining percentage of .650. That would project over 51 games to 66 points. The Caps actually have 72, so they are playing about 6 points ahead of their expected won-loss percentage. Not coincidentally, 6 is the number of games the Caps have lost in overtime.

The problem with mapping this to hockey is that a game is not always worth 2 points or 3 points. It can be worth no more than 2 to a team, but it can be worth 0 or 1 to the losing team. In baseball, there’s no such thing as a point for an OT/SO loss. Either the game is won or lost.

If we apply the resultant percentage and multiply it by games played, the Caps should have 33 wins… which is right on the money.

Let's go Caps!

by MikeL-Pivonka on Jan 26, 2010 12:53 PM EST reply actions

The GF on the NHL site is padded by the addition of a gaoal to the team totals for shootout wins, I think. That’s another variable to consider…

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

by fat_daddyo on Jan 26, 2010 1:25 PM EST up reply actions

true but negligible difference

Looks like we’re 4-2 in shootouts. So change those numbers to 191 GF and 141 allowed. Still get win percent of .647, 33 wins. So good point, but it doesn’t really affect our numbers to date.

Does anyone think there’d be a way to derive an expected number of charity points based on this formula?

by Flash-fried on Jan 26, 2010 2:27 PM EST up reply actions

At this point, I’m thinking the thing to do is take the charity point out of it, and go back to W-L-T standings, with a tie being worth one point. Then try to tinker with the formula to get to a points. percentage.

Assuming that the Gimmick is basically a 50/50 proposition, you could count the extra pointg gained in “ties” to luck.

Maybe.

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

by fat_daddyo on Jan 26, 2010 3:06 PM EST up reply actions

There’s a similar formula used by basketball analysts, but they discovered different exponents for their sport. 14 and 16.5 are the most common exponents used, ESPN’s John Hollinger was the one who introduced 16.5

So really, there’s a lot of math that goes in to finding the exponents. It’s just kinda dumb luck that it comes out to something simple like 2 for baseball

by Tromni on Jan 26, 2010 5:56 PM EST up reply actions

Even further examination of James’ original equation has come up with some better (read: more accurate) exponents.

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

by D'ohboy on Jan 26, 2010 6:16 PM EST up reply actions

I haven’t looked in to it too seriously, but from the brief sets of numbers I’ve run, using the same formula, but substituting goals for and goals against for runs for and runs against gives a number that corresponds roughly to absolute winning percentage (e.g. total wins/total games played), which would make sense from the derivation posted in the article to which you linked.

GUTEN TAAAAAAAAAAAAG!

by Wheeler on Jan 26, 2010 1:04 PM EST reply actions