Sunday, October 10, 2010

Remainder of Season Simulation

I have expanded on my prior projects to determine the likelihood that a team will make the playoffs this season. As I said previously, the ability to be comprehensive in all possibilities of match outcomes eats into years of computing time, so simulation is an obvious answer.

I created a simulation that attempts to model all the matches in the remainder of the USCL season.

The goal was the same -- what is the chance that a team will make the playoffs. This time, however, I included by match points and the game points tiebreaker. (If a team was tied for a playoff spot with the same match and game points, I said they both would make the playoffs -- I didn't go beyond the first tiebreaker.)

To do this, I made several other assumptions.
  1. All teams have the same strength. Therefore, they have the same chances in each match against their opponents.
  2. The game point results of the match follow the historical distribution of USCL matches (which is here). That is, 2.5-1.5 is more common than 3-1, which is more common than 3.5-0.5, etc.
I ran 100,000 simulations for both the Eastern and Western division. Here are the results, where the percentages indicate a tie for fourth place or better.

Eastern Division (Chance to make playoffs)

New England 100.00%
Boston 98.43%
New York 97.49%
Baltimore 70.27%
Manhattan 24.79%
New Jersey 6.92%
Philadelphia 2.69%
Carolina 0.61%

Western Division (Chance to make playoffs)

Arizona 97.18%
Chicago 86.54%
San Francisco 78.07%
St. Louis 45.24%
Seattle 35.50%
Miami 27.39%
Los Angeles 23.44%
Dallas 12.92%

I also included the chance that a team will receive draw odds in the first round of the playoffs (tied for second place or better).

Eastern Division (Chance have draw odds first round of playoffs)

New England 98.37%
Boston 55.19%
New York 41.63%
Baltimore 4.90%
Manhattan 0.23%
New Jersey 0.00%
Philadelphia 0.00%
Carolina 0.00%

Western Division (Chance have draw odds first round of playoffs)

Arizona 80.94%
Chicago 50.92%
San Francisco 40.50%
St. Louis 13.13%
Seattle 7.55%
Miami 6.01%
Los Angeles 3.60%
Dallas 1.25%

Any scenarios you want me to run? Things like: If NJ wins the remainder of their matches 4-0, what's their chance to get in the playoffs... things like that....

Let me know in the comments...

No comments: