Sunday, November 18, 2012

MLS Odds: DC United may be in better shape than it appears

Edit: DC Gave up a goal in the first half. Guess those 18% chances don't come home as often as you like :-). New odds:

Initial Post
There are three games left in the 2012 MLS season: two conference final games, then one game for the title.

The conference final match-ups follow a two legged format - one game is played at each team's home field and the winner is whoever scores the most goals across both games. In the case of a tie, OT, then penalty kicks, is played in the second game. This gives a small advantage to the team playing at home in the second game (the higher seeded team).

One game in each conference final has been played. LA leads Seattle 3-0 with the remaining game to be played in Seattle, and Houston lead DC 3-1 with the remaining game to be played in DC.

I ran a Monte Carlo simulation of the remaining three games and was surprised to learn that DC United are not in as weak of a position to win the MLS Cup as their current deficit implies. See below:

Despite being down two goals going into today's second leg, DC has nearly as good a chance to win the MLS Cup as Houston, for the following reasons:

1. Home field advantage in Major League Soccer is quite strong.
2. DC has been excellent at home: they've allowed just 1.0 goals/game while scoring 2.2 goals/game.
3. Houston has been weak on the road, allowing 1.7 goals/game and scoring 1.0 goals/game
4. Today's second leg game is played in DC.
5. If DC makes the championship, that game will be in DC. If Houston makes it, the championship would either be in LA or Seattle.

Actual Math (very short though) below.

I assume goals are Poisson distributed with an average calculated as follows, using Houston and DC as an example:
• Houston (Goals scored by Houston on the road + Goals allowed by DC at home) / 2 = 1.0
• DC (Goals scored by DC at home + Goals allowed by Houston on the road) / 2 =  1.94
The Poisson means that goals are scored at random times, but on average they happen 1.94 times/game for DC. This translates into 0 goals some of the time, 1 goal some of the time, 2 goals, 3 goals, etc. with decreasing frequency.

I simulate OT (if needed) using the same method with the same Poisson averages divided by 3. If the match goes to PKs, I assign 50% win probability to each time. The assumptions inherent with the methodology are:
• Goals scored this season (at home and on the road) are a good predictor of future goals.
• Goals are Poisson distributed.
• Each team has a 50/50 chance when the game goes to PKs.