Pythagorean expectation and the NHL

Langley's own Brett Lawrie has earned the nickname "Gordie Dougie" among Blue Jays fans as a prototypical Canadian gamer. (Photo by Greg Fiume/Getty Images)

The climate in Major League Baseball is just so screwy this season.

Arguably, four of the 10 best teams in baseball are confined to a single division, the treacherous American League East. While the Tampa Bay Rays earned a couple of playoff spots in the last three seasons, it's virtually impossible to build a model of sustained success in that division. The New York Yankees and Boston Red Sox continually buy up the top talent, and, even in a season such as this, where several Toronto Blue Jays are having career seasons, they can't compete.

It's chaotic and as a result, I've taken to wondering how the Blue Jays would do in any other division, such as, say, the American League Central. If you look at the Major League Baseball standings page and click over to the splits, you see not only a very useful record of teams in one-run games, but also the team's expected record.

(I'll relate this to hockey after the jump)

There, you can see the Detroit Tigers have fluked out a few one-run games, and the lead the Central Division with a 69-68 expected record as of Friday at noon. The Blue Jays are at 70-67. I'm not a huge Jays homer, but I do take interest in what they do because each of their games are televised and they've become interesting to watch over the last month, I think that that's a more accurate reflection of the team. I think they are good enough to be in the playoffs.

That aside, the important takeaway from that opening bit is the expected wins and losses record, which shows up on the much-more efficient site but not's. Downloading shootout and overtime wins and losses record is problematic as well, but I decided to go through the standings page over each of the last two years and figure out each team's expected record. It is called the Pythagorean Expectation and was developed by Bill James. The basic formula is as such:

GF^2 / ( [ GF^2 ] + [ GA^2 ] )

It's not terrifically complicated, but it gets the job done. What I've done is slush out a team's regulation and overtime games and attributed the expected winning percentage to each of those. The system isn't perfect, but I came up with a pretty strong correlation over the last two seasons between a team's expected points and actual points, r-squared = .857, and the teams for the most part that were counted as "unlucky" have terrific players that pop up in my research, so it stays pretty consistent with my other models.

Since there isn't a place to find Pythagorean standings in the NHL, I may as well post it right here. As a bit of a tangent, I'm going to complain right now about hockey's point system because wins aren't as valuable in this sport as they are in any other. This makes it harder in hockey than any other sport to calculate a player's total output. Also, I might add that the NHL awards a goal for a shootout win. I kept that goal in the chart since I do apply the same expected winning percentage to overtime and shootouts as I do in regulation time.

Here's the standings chart from last season:

Yr Team GF GA xRW xOTW xW xL xOTL xPts Pts Diff
2011 Vancouver 262 185 45 9 55 23 5 114 117 3
2011 Boston 246 195 40 10 50 25 7 107 103 -4
2011 Pittsburgh 238 199 35 14 48 24 9 106 106 0
2011 NY Rangers 233 198 35 12 48 26 9 104 93 -11
2011 Washington 224 197 33 13 46 26 10 103 107 4
2011 San Jose 248 213 36 11 47 27 8 102 105 3
2011 Philadelphia 259 223 37 10 47 27 8 102 106 4
2011 Chicago 258 225 37 10 47 28 7 100 97 -3
2011 Nashville 219 194 35 11 46 28 8 100 99 -1
2011 Los Angeles 219 198 36 9 45 29 8 98 98 0
2011 Calgary 250 237 31 13 43 27 11 98 94 -4
2011 Detroit 261 241 34 10 44 29 9 97 104 7
2011 Buffalo 245 229 34 10 44 29 9 96 96 0
2011 Tampa Bay 247 240 31 11 42 29 11 95 103 8
2011 St. Louis 240 234 32 10 42 30 10 94 87 -7
2011 Phoenix 231 226 32 10 42 31 9 93 99 6
2011 Montreal 216 209 34 8 42 32 8 92 96 4
2011 Carolina 236 239 30 10 40 31 11 92 91 -1
2011 Dallas 227 233 30 10 40 32 10 90 95 5
2011 Anaheim 239 235 36 6 42 34 6 89 99 10
2011 Toronto 218 251 24 11 35 32 15 85 85 0
2011 NY Islanders 229 264 26 9 35 34 13 83 73 -10
2011 Atlanta 223 269 24 10 33 34 14 81 80 -1
2011 Columbus 215 258 24 9 34 35 14 81 81 0
2011 Florida 195 229 26 8 34 37 11 80 72 -8
2011 Minnesota 206 233 31 5 36 39 7 79 86 7
2011 Colorado 227 288 25 7 31 39 11 74 68 -6
2011 New Jersey 174 209 29 4 34 43 6 73 81 8
2011 Ottawa 192 250 26 5 30 43 8 69 74 5
2011 Edmonton 193 269 22 5 28 44 11 66 62 -4

[ Legend: xRW Expected regulation wins xOTW Expected overtime and shootout wins xW Expected total wins xL Expected regulation losses xOTL Expected overtime losses xPts Expected points Pts Actual points Diff Actual point total minus expected point total * ]

*If the differences look off by a point, it's because I used whole numbers in the chart, while the expected point totals rounds up decimal points*

Oddly enough, Vancouver and Boston, the two best teams in the regular season, wound up meeting in the finals. Boston were neck-and-neck with the deceptively-worse Montreal Canadiens team for a majority of the season and didn't start pulling in the Northeast Division away until the end of the season.

The New York Rangers, who were the only team to win every game where they led after two periods of play and therefore probably expected to win a lot more close games, actually had the opposite effect happen. They had a pretty strong goal differential, so after seeing this I feel differently about their playoff chances this season knowing that they didn't have as much ground to make up as originally thought against the other teams in the East.

Calgary and St. Louis, two teams with some good hockey players, probably should have made the playoffs. Anaheim benefit from luck in two ways this season, with some good offensive shooting percentages from their star players and winning a lot of close games as well, so I expect them to regress, particularly since their division got stronger. The other Western team that shouldn't have made it are the Phoenix Coyotes.

In the East, all the expected teams made it, but they were all out of order. New Jersey are further out than it appears, although they're getting a big boost this season with the return of Zach Parise. Toronto and Florida, the two teams who have yet to make the playoffs in the post-lockout NHL, still have a lot of work to do.

Comparing the chart to the 2010 standings, I can tell you that Phoenix (+4) got a deceptive boost last season playing, and winning, a LOT of overtime games and came back to earth in 2011, but that was the only real outlier that changed. A lot of the expected teams made it, and Washington ( +6 ) and Pittsburgh ( +3), both having been upset by Montreal ( -3 ), were not as good as their regular seasons showed, so the regression was felt in the playoffs for those two teams.

Some other tidbits I found, totaling up the teams' records over the course of two seasons.

-Edmonton, if you can believe it, were a worse team in 2011 than in 2010, going from a -70 goal differential to a -76 differential. They won just 25% of their overtime games this season.

-The Canucks have won 90 regulation games over the past two seasons. The next highest team, Washington, have 80. Washington, however, have won a higher regulation winning percentage of 67.8% to 65.7%.

-There are no records for one-goal games, but percentage of overtime games won didn't correlate well year-to-year, r-squared = .158. I think that overtime may be more random, but until I'm sure, I'm not going to modify the way I calculate overtime games.

-From dicking around with team goal totals, it appears that a win is approximately equal to six goals. That doesn't mean that a player that scores 41 goals is worth just under seven wins, since goals against matter as well.


*EDIT* Good guy Chemmy over Pension Plan Puppets has done similar research. You can find some info up at The Leafs Nation and the Puppets although I might add to Chemmy that neither of those posts has a standings chart from the 2011 season, which is what I was aiming for here.

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