Pytahgorean wins bode well for Senators

Those of you familiar with baseball statistics may be aware of Pythagorean wins. If you hate math, skip to the next paragraph. The idea is as follows: if a team scores as many goals as they let in, chances are they should have exactly a .500 record. If they score more goals than they let in, their winning percentage should move higher according to some mathematical relationship. Bill James determined that the relationship for baseball is runs scored squared divided by runs scored squared less runs allowed squared. Marc Foster and Chris Apple of determined that the same relationship holds true for hockey except that the exponential factor is 2.03. The hockey model usually understates winning percentage by about 4 points due to the awarding of a point for an overtime loss.

Here is the idea without any math. If a team had a lousy winning percentage but scored more goals than they let in, then chances are, all things being equal, they will have more wins the following year. And conversely, if a team lucked out and despite letting in more goals than they scored, had a winning record, it will catch up with them and they will likely win fewer games the next year.

This matters if you are Boston who scored 21 more goals than allowed and won the division. Ottawa scored 75 more than they allowed yet finished third in the division. Ottawa was much better than their win loss record indicated and the Bruins got statistically lucky.

In essence, the Bruins won a lot of close games and the Senators won a lot of blowouts but lost the tight games. Over time, usually that evens out.

The top three teams who got short changed in wins were the Senators, Devils and Wild. The teams who most outperformed their Pythagorean wins were the Bruins, Hurricanes, Penguins, Predators and Blues.

We can argue about intangibles such as clutch wins or superior coaching, but the stats say that Ottawa should trounce the Bruins in the standings this year.

Here is a list of actual and Pythagorean points for the most recent NHL season. The results are not adjusted for overtime loss points awarded.

Atlantic actual Pythagorean diff

Philadelphia Flyers 101 99.1 1.9

New-Jersey Devils 100 103.3 -3.3

New-York Islanders 91 92.0 -1.0

New-York Rangers 69 66.1 2.9

Pittsburgh Penguins 58 45.8 12.2


Detroit Red Wings 109 106.2 2.8

St. Louis Blues 91 79.0 12.0

Nashville Predators 91 81.6 9.4

Blue Jackets 62 58.1 3.9

Chicago Blackhawks 59 56.2 2.8


Boston Bruins 104 90.8 13.2

Toronto Maple Leafs 103 96.1 6.9

Ottawa Senators 102 108.2 -6.2

Montreal Canadiens 93 88.6 4.4

Buffalo Sabres 85 81.6 3.4


Vancouver Canucks 101 97.8 3.2

Colorado Avalanche 100 96.5 3.5

Calgary Flames 94 92.6 1.4

Edmonton Oilers 89 87.0 2.0

Minnesota Wild 83 84.2 -1.2


San Jose Sharks 104 96.8 7.2

Dallas Stars 97 90.5 6.5

Los-Angeles Kings 81 77.3 3.7

Mighty Ducks 76 69.9 6.1

Phoenix Coyotes 68 60.5 7.5


Tampa-Bay Lightning 106 101.9 4.1

Atlanta Thrashers 78 71.5 6.5

Carolina Hurricanes 76 66.0 10.0

Florida Panthers 75 68.7 6.3

Washington Capitals 59 57.2 1.8

29 Responses to Pytahgorean wins bode well for Senators

  1. tml28 says:

    MATH SUCKS!!!!!!!!!!!!!!!!!


    I HATE MATH!!!!!!!!

  2. Hockey_Fan_99 says:

    I dont think that can prove much anymore seeing as how the NHL is totally different

  3. distance7 says:

    “We can argue about intangibles such as clutch wins or superior coaching, but the stats say that Ottawa should trounce the Bruins in the standings this year. “

    The stats say that Ottawa should’ve trounced the Bruins in the 03-04 standings, not this season..since there aren’t any stats to prove anything at all for this season.

  4. GreatWhiteNorth says:

    How about the biggest tangible of them all.

    There was no season last year, teams have had an amazing amount of player changes since last year.

    Even if your idea holds up in baseball and some previous years in hockey, you can’t apply it to this year.

    Come back next year with your predictions Descartes!

  5. Flyer_Dman says:

    Very interesting. I liked the post. Better than the usual mind numbing BS. Too bad this post came at probably the worst time ever.

    1 – There was no season last year, which at least throws things off a little.

    2 – No team looks anything close to the same as they did at the close of the 03-04 season.

    3 – The “new NHL” should make some bad teams perform much better than two years ago. Along the same lines, it should also make some good teams perform worse.

    I love the outside the box thinking. However, it holds not water right now. Try again a couple years from now; it should be interesting.

  6. habsoverserver says:

    Are you certain there was more turnover this offseason than last offseason or does is just feel that way to you? I would argue that most teams didn’t change any more than usual.

  7. habsoverserver says:

    Fair point but, I’m arguing for reversion to the mean. Ottawa won fewer games than they should have last year and Boston won more than they should have. I think it evens out over time.

  8. DomiforPrimeMinister says:

    Yeah Math sucks, I think this guy should get out a little more!

  9. Air33 says:

    Too much has changed to refer to anyteams previous performances.

  10. hockeyhead says:

    in defence of the bruins let me make this math reference pertaining to my favorite math….poker stats.

    say your startin hand is pocket aces (best hand to start) and your opponent has 2-7 off suit (worst starting hand.

    now on the flop it comes A-K-J all of the same suit as the guy with 7.

    you bet with a set of A’s and your opponent calls with four to the flush.

    next card comes with no result. you bet and opponent makes a terrible call. he has a 15 percent chance of winning.

    then the same suit comes on the last card. the guy with the worst starting hand has made the miracle even tho he should of never played that hand.

    they call that a bad beat and in the long run the aces will hold but you cant put stats into luck.

    luck plays a role in everything.

  11. habsoverserver says:

    Your analogy suggests that the Bruins should have folded long ago.

    That may be the smartest thing you’ve written in a while.

  12. hockeyhead says:


    theyre are some teams that would be dead money,, have no chance of winning.

    there are those teams that have the skills but are running bad luck.

    there are those that totally suck but every dog has his day.

    my real point (although your joke is funny) is that you have to play out the games.

    if it was about winning on paper then those without a chance would never play.

  13. shapter07 says:

    perhaps that river card of the same suit pairs the board…….

  14. hockeyhead says:

    but that would ruin my bad beat and give the guy with aces a full house.

    glad to see another poker fan.

    tonight is actually one of my poker nights. i can truly relate to the bad beat stories.

    it sux when you know what youre doing and you never really get lucky. your cards just hold up. i always have people calling me when i have the goods and they luck out.

    i would say i am about 15 and 8 with pocket aces.

    bluffing is another thing in it self.

  15. Heinzee57 says:

    You never slow play aces…. you’ll end up folding them or lose.


  16. Leaf_fans_can_blow_me says:

    Thanks for the poker lingo there Mike Sexton.

  17. Heinzee57 says:

    English doesn’t appear to be doing you any favors either.


  18. hockeyhead says:

    believe you me heinzee…i learned that the hard way.

    i was 2 and 7 with pocket aces when i first began playing.

  19. hockeyhead says:

    your welcome vince van patton.

    its the only math i am good at.

  20. rojoke says:

    Either you copied the wrong formula or the whole things is incorrect. Here’s what you gave as the formula:

    runs scored squared divided by runs scored squared less runs allowed squared.

    or to make it easier to read

    RS²/RS² – RA²

    If you go back to elementary school math, you will know that multiplication and division functions are always calculated before addition and subtraction. Based on this rule, the formula becomes 1 – RA² which makes me wonder how they came up with the formula they did.

    I think what the formula should like like, and probably does, is RS²/(RS²-RA²).

    There’s is a logical problem with this formula, however. The number of wins a team amasses during a year is dependent on the number of goals it scores, but the inverse is not true. A team which plays a more defensive oriented game could win just as many games during a season as one which employs a more offensive style. For example, Ottawa, New Jersey, San Jose and Vancouver all won the same number of games on 2003-04, 43. Ottawa scored 262 goals during that season, but San Jose only scored 219.

    What it all comes down to is that a simple algebra formula is a less-than-accurate barometer of how a team will perform, or an individual. After years of trying to pick pool players that way, I can assure you of that. I just wish I could remember the regression formulas from my stats classes.

  21. Heinzee57 says:

    I’m Heinzee57 over at too.

  22. hockeyhead says:

    do you like playing on line? i played once and one table i got voted off for being too slow.

    i like playing live (i know its harder to get a game)…can fake people out or read people obviously.

    travis green played at the WSOP and knocked out phil helmuth.

  23. habsoverserver says:

    Thanks for your comments.

    The formula is based on a scoring differential, since the denominator of the equation, as you pointed out, is the difference between the squares of scored and allowed. Perhaps I was too vague in my description of the formula, but I did calculate it as you expressed.

    I agree that there is no single formula that captures all of the factors that go into winning. However, I think it is logical to think that a formula that looks at *****ulative goal differential over a season should correlate to actual results.

    Hockey has the crudest stats of any pro-sport. Goals and assists as stand alone stats are mostly useless in determining player value. In addition to payer skill, scoring is also a function of three player independent variables (1) ice time (2) linemates (3) coaching style. I think most GM’s are in the dark ages when it come to assessing talent.

  24. chanman says:

    Very interesting. But lijke someone above said, this may be relable if last season was not wasshed, and it depends on the teams style, ie off/def.

    good work on the #s.

    So it would appear the Pens are due for a down season……..


  25. monley89 says:

    tml28 i couldnt agree anymore ughhhh

  26. rojoke says:

    I don’t see the analogy between the two. It’s not a team game. In tournament poker, the players have the least amount of control over the play. In fact, depending upon the size of the table, most players fold more hands than they play. The skill involved in playing is knowing the players you play against, knowing the hand you have, and the probabilities of winning and losing. You have no idea exactly what cards are in play. It’s pure conjecture and probability. And once you go all in, you’re no longer in control of anything anymore.

    In hockey, as in most other team sports, each player has at least some control over the play. Pass or shoot, pass or carry, freeze the puck or play it, passive or active defense, block a shot or let it through, play the man or the puck, the puck carrier or the trailer. Even players without the puck control where defenders play themselves, which opens up opportunities for other players on both teams.

  27. hockeyhead says:

    mathmatical statistics….not games

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