Wednesday, October 31, 2012

Playoff Predictions - Pt 2



Elo Ratings
Chance to Win


Rtng Team (Chng)
Team QF SF Cup
1631   Los Angeles Galaxy  (+6)
Sporting Kansas City 0.584 0.351 0.203
1624   Sporting Kansas City  (---)
San Jose Earthquakes 0.486 0.268 0.182
1621   San Jose Earthquakes  (---)
Los Angeles Galaxy 0.514 0.292 0.145
1600   Seattle Sounders FC  (---)
Seattle Sounders FC 0.550 0.254 0.116
1565   Real Salt Lake  (---)
New York Red Bulls 0.512 0.225 0.110
1565   Houston Dynamo  (+26)
DC United 0.488 0.209 0.100
1557   New York Red Bulls  (---)
Real Salt Lake 0.450 0.186 0.076
1549   DC United  (---)
Houston Dynamo 0.416 0.215 0.068
1529   Chicago Fire  (-26)




1515   Columbus Crew  (---)




1488   Montreal Impact  (---)




1480   FC Dallas  (---)




1443   Colorado Rapids  (---)




1433   Philadelphia Union  (---)




1418   Vancouver Whitecaps FC  (-6)




1418   New England Revolution  (---)




1409   Portland Timbers  (---)




1335   Toronto FC  (---)




1320   Chivas USA  (---)










West Average: 1498.55




East Average: 1501.3





After the wildcard round, this is where we are at. Astonishingly, the eight remaining teams are the eight "strongest" teams in the league, according to my rater. That results in all the quarterfinal match-ups being pretty even. The most heavily favored match-up is Kansas City over Houston, and that is only by the relatively slim margin of 0.584 to 0.416.

Monday, October 29, 2012

Playoff Predictions


Elo Ratings
Chance to Win



Rtng Team (Chng)
Team WC QF SF Cup
1625   Los Angeles Galaxy  (---)
Sporting Kansas City 1.000 0.612 0.368 0.213
1624   Sporting Kansas City  (---)
San Jose Earthquakes 1.000 0.536 0.296 0.202
1621   San Jose Earthquakes  (---)
Seattle Sounders FC 1.000 0.550 0.263 0.114
1600   Seattle Sounders FC  (---)
New York Red Bulls 1.000 0.512 0.229 0.112
1565   Real Salt Lake  (---)
Los Angeles Galaxy 0.842 0.426 0.238 0.111
1557   New York Red Bulls  (---)
DC United 1.000 0.488 0.214 0.102
1555   Chicago Fire  (---)
Real Salt Lake 1.000 0.450 0.193 0.078
1549   DC United  (---)
Houston Dynamo 0.648 0.246 0.118 0.035
1539   Houston Dynamo  (---)
Chicago Fire 0.352 0.142 0.071 0.031
1515   Columbus Crew  (---)
Vancouver Whitecaps FC 0.158 0.038 0.011 0.002
1488   Montreal Impact  (---)





1480   FC Dallas  (---)





1443   Colorado Rapids  (---)





1433   Philadelphia Union  (---)





1424   Vancouver Whitecaps FC  (---)





1418   New England Revolution  (---)





1409   Portland Timbers  (---)





1335   Toronto FC  (---)





1320   Chivas USA  (---)












West Average: 1498.55





East Average: 1501.3







Using my Elo Ratings, I can determine the expected value of a given match-up. I can then use Bayes' Theorem to determine all possible playoff match-ups and come up with an expected outcome of the playoffs as a whole. Above is the probability - given by my Elo Rater - that each team has to advance to a specific round of the playoffs. For instance, the numbers above say that Sporting Kansas City has a 100% chance to make it through the Wild Card (because they don't play one), a 61.2% chance to make it through the quarterfinal, a 36.8% chance to make it through the semifinal, and a 21.3% chance to win MLS Cup 2012. On the opposite end of the spectrum, Vancouver has a 0.2% chance to win the playoffs.

These values will of course change game-to-game as new information is added to the rater, so I will update these after each round of the playoffs.

A few technical details and an example: For the wildcard and MLS Cup, I treat the game as a single game with home field advantage. For the quarters and semis, I treat the match-up as a single game with no home field advantage. After the first game in the series, I will treat the second leg as a single game match-up with home field advantage with a certain result (determined by the score of the first leg) necessary to move on. Here is an example:

Los Angeles will play host to Vancouver. Using their current ratings (LA at 1625 and Vancouver at 1424) and giving LA home field advantage, we figure out (through the methods used in my Elo Rater) that LA has an expected outcome of 0.842. This value is shown above under the WC column, indicating that LA has a 84.2% of making it through the wild card. Conversely, Vancouver has an expected outcome of 1 - 0.842 or 0.158. which is also shown above. Then, San Jose will play either LA or Vancouver in the next round. To come up with San Jose's probability of winning their quarterfinal, we use Bayes' Theorem. First, San Jose has a 49.4% chance of beating Los Angeles in a home/away series, and a 75.7% chance of beating Vancouver in a home/away series. Then, San Jose has a 84.2% chance of facing LA and a 15.8% chance of facing Vancouver (determined by the expected outcome of the LA/Vancouver game) so San Jose's chance to make it through the quarterfinal is 0.842 * 0.494 + 0.158 * 0.757 = 0.536, or 53.6%. LA, on the other hand, has a 1 - 0.494 = 0.506 expected outcome against San Jose, so their expected outcome for getting through both the wildcard and the semifinal are 0.842 * 0.506 = 0.426. We then continue this process through all the match-ups and get values for every stage through the cup for each team.

Sunday, October 28, 2012

10/28/2012 - End of Regular Season


Elo Ratings

End of Season Points Predicted
Rtng Team (Chng)

Team Pts Pred
1625   Los Angeles Galaxy  (+11)

San Jose Earthquakes 66 66.000
1624   Sporting Kansas City  (+6)

Sporting Kansas City 63 63.000
1621   San Jose Earthquakes  (-5)

DC United 58 58.000
1600   Seattle Sounders FC  (-11)

Real Salt Lake 57 57.000
1565   Real Salt Lake  (-9)

Chicago Fire 57 57.000
1557   New York Red Bulls  (+28)

New York Red Bulls 57 57.000
1555   Chicago Fire  (-5)

Seattle Sounders FC 56 56.000
1549   DC United  (+5)

Los Angeles Galaxy 54 54.000
1539   Houston Dynamo  (-24)

Houston Dynamo 53 53.000
1515   Columbus Crew  (+5)

Columbus Crew 52 52.000
1488   Montreal Impact  (-23)

Vancouver Whitecaps FC 43 43.000
1480   FC Dallas  (-10)

Montreal Impact 42 42.000
1443   Colorado Rapids  (+24)

FC Dallas 39 39.000
1433   Philadelphia Union  (-34)

Colorado Rapids 37 37.000
1424   Vancouver Whitecaps FC  (+9)

Philadelphia Union 36 36.000
1418   New England Revolution  (+23)

New England Revolution 35 35.000
1409   Portland Timbers  (+5)

Portland Timbers 34 34.000
1335   Toronto FC  (-5)

Chivas USA 30 30.000
1320   Chivas USA  (+10)

Toronto FC 23 23.000






West Average: 1498.55




East Average: 1501.3






Interestingly, Los Angeles jumps on top of the ratings with the last game of the regular season - by one point. The East finishes barely atop the West, and Chivas finishes rock bottom despite Toronto grabbing the wooden spoon.

Friday, October 26, 2012

10/21/2012


Elo Ratings

End of Season Points Predicted
Rtng Team (Chng)

Team Pts Pred
1626   San Jose Earthquakes  (-5)

San Jose Earthquakes 65 66.899
1618   Sporting Kansas City  (+1)

Sporting Kansas City 60 62.294
1614   Los Angeles Galaxy  (+5)

Real Salt Lake 56 58.319
1611   Seattle Sounders FC  (+4)

DC United 57 57.904
1574   Real Salt Lake  (+6)

Chicago Fire 56 57.792
1563   Houston Dynamo  (+11)

Seattle Sounders FC 56 56.953
1560   Chicago Fire  (-19)

New York Red Bulls 54 55.214
1544   DC United  (+10)

Houston Dynamo 53 54.569
1529   New York Red Bulls  (-1)

Los Angeles Galaxy 51 52.737
1511   Montreal Impact  (-3)

Columbus Crew 49 51.352
1510   Columbus Crew  (-10)

Montreal Impact 42 44.178
1490   FC Dallas  (-10)

Vancouver Whitecaps FC 42 42.474
1467   Philadelphia Union  (-11)

FC Dallas 38 40.381
1419   Colorado Rapids  (+23)

Philadelphia Union 36 37.948
1415   Vancouver Whitecaps FC  (-21)

Colorado Rapids 34 35.106
1404   Portland Timbers  (+21)

Portland Timbers 33 33.811
1395   New England Revolution  (+19)

New England Revolution 32 32.583
1340   Toronto FC  (+3)

Chivas USA 29 29.427
1310   Chivas USA  (-23)

Toronto FC 23 23.449






West Average: 1495.88




East Average: 1503.7




Monday, October 8, 2012

10/8/2012


Elo Ratings

End of Season Points Predicted
Rtng Team (Chng)

Team Pts Pred
1631   San Jose Earthquakes  (+19)

San Jose Earthquakes 64 67.842
1617   Sporting Kansas City  (---)

Sporting Kansas City 59 62.590
1609   Los Angeles Galaxy  (-22)

Chicago Fire 56 59.754
1607   Seattle Sounders FC  (+8)

Real Salt Lake 55 58.080
1579   Chicago Fire  (-6)

Seattle Sounders FC 52 57.024
1568   Real Salt Lake  (+22)

DC United 54 56.606
1552   Houston Dynamo  (-6)

New York Red Bulls 53 55.521
1534   DC United  (+12)

Houston Dynamo 50 53.665
1530   New York Red Bulls  (-28)

Los Angeles Galaxy 50 52.633
1520   Columbus Crew  (---)

Columbus Crew 49 52.324
1514   Montreal Impact  (+6)

Montreal Impact 41 44.986
1500   FC Dallas  (-3)

Vancouver Whitecaps FC 42 44.510
1478   Philadelphia Union  (+42)

FC Dallas 38 40.978
1436   Vancouver Whitecaps FC  (+16)

Philadelphia Union 36 38.757
1396   Colorado Rapids  (-19)

Colorado Rapids 31 33.283
1383   Portland Timbers  (-8)

Portland Timbers 30 31.524
1376   New England Revolution  (-8)

Chivas USA 29 30.922
1337   Toronto FC  (-12)

New England Revolution 29 30.428
1333   Chivas USA  (-13)

Toronto FC 22 23.418






West Average: 1495.88




East Average: 1503.7




Monday, October 1, 2012

9/30/2012


Elo Ratings

End of Season Points Predicted
Rtng Team (Chng)

Team Pts Pred
1631   Los Angeles Galaxy  (-5)

San Jose Earthquakes 61 66.361
1617   Sporting Kansas City  (+15)

Sporting Kansas City 58 62.964
1612   San Jose Earthquakes  (-9)

Chicago Fire 53 60.195
1599   Seattle Sounders FC  (-4)

New York Red Bulls 53 57.559
1585   Chicago Fire  (-15)

Seattle Sounders FC 49 56.403
1558   New York Red Bulls  (+8)

Real Salt Lake 52 55.698
1558   Houston Dynamo  (+8)

DC United 51 55.196
1546   Real Salt Lake  (+26)

Los Angeles Galaxy 50 54.994
1522   DC United  (-2)

Houston Dynamo 49 54.725
1520   Columbus Crew  (+8)

Columbus Crew 48 52.637
1508   Montreal Impact  (---)

Montreal Impact 40 44.656
1503   FC Dallas  (+9)

Vancouver Whitecaps FC 39 43.465
1436   Philadelphia Union  (-8)

FC Dallas 37 41.611
1420   Vancouver Whitecaps FC  (+4)

Philadelphia Union 30 34.682
1415   Colorado Rapids  (+5)

Colorado Rapids 31 34.269
1391   Portland Timbers  (+2)

Portland Timbers 30 32.078
1384   New England Revolution  (-8)

Chivas USA 28 31.697
1349   Toronto FC  (-8)

New England Revolution 29 31.260
1346   Chivas USA  (-26)

Toronto FC 22 24.511






West Average: 1495.88




East Average: 1503.7