Sunday, August 12, 2007

Pythagorean Records

It has always bugged me a little bit that the sport of hockey seems to be way behind other sports in the field of sabermetrics. Hockey is much more difficult to measure statistically than other sports, but there's still very little out there beside the basic stuff. College hockey is even tougher since many stats, including time on ice aren't kept during the year(though I think it's only a matter of time before TOI is kept, as it's fairly simple if you have the right software).

Anyway, Marc Foster of the Junior Hockey Blog has been ressurrecting some old columns he wrote for CNNSI called Just the Stats. Reading some of those old columns motivated me to try and calculate Pythagorean Record for last season.

Pythagorean Record uses a formula to measure a team's record against how many goals a team scored and gave up. The formula is Goals For^2/(Goals For^2 + Goals Against^2). I don't think it's a perfect system, but it's worth taking a look at. You can read more about it here.

Here are the results for the CCHA and WCHA. I only looked at conference play, because that makes the schedules a little more insular. The results are listed as such: Team, Winning %, Pythagorean Win %, and Difference Between Percentages. Theoretically, a team with a positive difference over-achieved, while a team with a negative difference under-achieved.

Notre Dame .804 .757 .047
Michigan .661 .662 -.001
Miami .643 .638 .005
Michigan State .589 .608 -.019
Nebraska-Omaha .536 .581 -.045
Western Michigan .518 .455 .063
Ohio State .500 .517 -.017
Lake Superior .446 .436 .010
Ferris State .393 .367 .026
Northern Michigan .375 .405 -.030
Alaska .339 .377 -.027
Bowling Green .196 .223 -.027

Minnesota .694 .648 .046
St. Cloud .625 .618 .007
North Dakota .554 .606 -.052
Denver .536 .500 .036
Colorado College .518 .533 -.015
Wisconsin .482 .553 -.071
Michigan Tech .482 .538 -.056
Minnesota State .440 .401 .039
Minnesota-Duluth .357 .367 -.010
Alaska-Anchorage .304 .274 .030

So what conclusions can be drawn from this? I'm not really sure. I'll let people take from this what they will. I think it's pretty obvious that Western Michigan was one of the biggest over-achievers last season, while Wisconsin was one of the bigger under-achievers. I also think it's interesting that both teams that ran away with their conference did so well in this metric. In all, however, I'm not seeing any consistent, major trends here. It's still interesting to see though.


Marc Foster said...

Hey Chris, thanks for the reference. I'm also going to be pulling out all my old NHL data, which runs from 1917-98 and is also sorted by franchise. I hope to have this online again shortly. I have yet to do anything with seasons where OT or SO games are worth three points. My thought there is to just adjust them back to two point systems, and note the teams benefiting (or not) from OT/SO wins/losses.

Runninwiththedogs said...

But... see... this is the problem with sabermetrics. It's all just made up. You can make up any sort of statistic by manipulating raw data any way you want.

So, I want to measure the value of a player. I'm going to take goals*2 (goals are good!) + assists*1.5 (assists are less good) - PIM1*.5 (penalties are bad! Sometimes. So PIM1 is Bad penalties - Good penalties) for every player. And whoever has the highest number is the best. It's going to be called the RWD Arbitrary Awesomeness rating, or the RAAR!

Marc Foster said...

And that is exactly the kind of crap I try to avoid. One cannot mix apples (goals) with oranges (assists) with bananas (PIMs). While all three are fruits, one is a citrus, two grow on trees, one comes from a plant, and they are all different colors (unless allowed to rot).

I actually wrote a little something about this in the original columns, at least in terms of fantasy leagues -

Marc Foster said...

Ack, let me try the link this way...

Runninwiththedogs said...

Excellent article. I totally agree.

Friggin' baseball. I hate VORP. It doesn't make any sense.

Anonymous said...

Thanks, because it's interesting to look at but...
just as hard to justify. Especially having M.Tech being the third worst 'acheiver'.
Just my two cents.

Chris said...

Re: Tech

Michigan Tech's Pythagorean Record is a little messed up because of their 9-0 win over Alaska-Anchorage. If they had only won that game 3-0, their Pythagorean Win% drops to .492, or just .01 below were they actually were.