Last week David posted projected standings generated from the FANS projections. I thought it would be interesting to dig a little deeper and investigate what it means for example to have the Yankees projected at 98 wins and the Red Sox at 94. My metric of choice will be playoff probabilities and my method will be simulation.
Before I get to the results of the simulation for the AL, let’s get into the nuts and bolts a little bit. In order to run the simulation needs the season’s schedule and each teams true talent win percentage. The simulation is a simple Monte Carlo that determines the winner of each game using random draws bounced up against log5 based winning percentages. For example, if we want to simulate the outcome of a game between Team A that has a 0.600 true talent win percentage and Team B that has a 0.450 win percentage, we first calculate the probability that A beats B using the log5 equation linked above. That calculation says that Team A should have a 0.647 winning percentage against Team B.
To simulate a game between these teams then, the simulation draws a random number between 0 and 1 and if the number is less than or equal to 0.647 then Team A wins, otherwise Team B wins. This process is repeated for all of the games for the entire season. Run the simulation for 10,000 such seasons and you have your results. Also built into the simulation is some up front uncertainty about the true talent win percentage. Before each of the 10,000 simulated seasons, the true talent win percentages for each team are varied slightly by using a random draw from a normal distribution centered at the input win percentage (which is based off of the projected standings) with a standard deviation of 0.030. For example, some seasons the Yankees will simulate as a 0.605 team, sometimes a 0.600 team and sometimes a 0.610 team. The standard deviation was derived through testing (read trial and error) and some of the comments in this thread at The Book Blog.
Now on to the results, starting with the East
East Div Win % WC Win % Playoff % Yankees 53% 27% 80% Red Sox 26% 31% 57% Rays 20% 28% 48% Orioles 1% 3% 4% Blue Jays 0% 0% 0%
Central Twins 38% 1% 39% White Sox 24% 1% 25% Tigers 19% 1% 20% Indians 13% 1% 14% Royals 6% 0% 6%
West Rangers 38% 2% 40% Mariners 27% 2% 29% Athletics 19% 2% 21% Angels 16% 1% 17%
and finally some other useful data points compared to historical data
Division Avg. Wins 2002-2009 Avg Wins East 101 99 Central 89 93 West 90 96 Wild Card 94 96
Overall nothing too shocking. According to the FANS all of the divisions should offer plenty of intrigue be it in the form of a dogfight for the division title with likely no Wild Card safety net (the West and the Central) or the powerhouses taking it to each other all season (the East).
Next up I’ll do the same with the NL.