## Updating Playoff Probabilities - CHONE

So the title is a little misleading as I never got around to publishing the preseason CHONE based playoff probabilities.  That being the case you get a two for one on new information today, both the preseason CHONE playoff probabilites and an updated version based on games already played.  I'm calculating the probabilities using a simulation I described at Fangraphs as

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.

All that was needed to do the updating was an updated schedule and each teams current wins.  For this iteration I kept the preseason true talent levels; however, in the future I would like to adjust those either using updated in-season projections or some weighted mean with the BtB power rankings.

I'll look at the AL first. The tables contain preseason playoff probability (PS P%), current probability to win the division (C DW%), current probability to win the wild card (C WC%), and current playoff probability (C P%).

AL East
Ps P% C DW% C WC% C P%
Yankees 83% 66% 22% 88%
Rays 33% 19% 35% 54%
Red Sox 64% 15% 32% 47%
Orioles 3% 0% 0% 0%
Blue Jays 1% 0% 0% 0%
AL Central
Ps P% C DW% C WC% C P%
Twins 47% 60% 2% 62%
Indians 27% 15% 1% 16%
White Sox 22% 12% 1% 13%
Tigers 7% 10% 1% 11%
Royals 5% 3% 0% 3%
AL West
Ps P% C DW% C WC% C P%
Rangers 45% 43% 1% 44%
Angels 33% 29% 2% 31%
A's 17% 19% 2% 21%
Mariners 13% 9% 1% 10%

Coming as no surprise to anyone the Rays move up in the East at the expense of the Red Sox. In the Central the Twins have strengthened their grip on the division, and the West remains clustered.

NL East
Ps P% C DW% C WC% C P%
Braves 62% 37% 12% 49%
Phillies 38% 31% 12% 43%
Mets 16% 17% 9% 26%
Marlins 13% 8% 5% 13%
Nationals 8% 7% 5% 12%
NL Central
Ps P% C DW% C WC% C P%
Cardinals 74% 81% 6% 87%
Cubs 21% 7% 10% 17%
Brewers 21% 5% 8% 13%
Reds 13% 5% 8% 13%
Pirates 4% 1% 1% 2%
Astros 4% 1% 0% 1%
NL West
Ps P% C DW% C WC% C P%
Rockies 40% 28% 6% 34%
Dodgers 39% 21% 5% 26%
Diamondbacks 27% 19% 5% 24%
Giants 8% 13% 3% 16%

The Phillies closed the gap with the Braves for the division lead (CHONE's starting lineup method was clearly very high on the Braved) in the East and the Mets also made a decent jump. In the Central the Cards have jumped out to a hot start and have a firm grasp on the division already. The West, like their AL counterparts, is extremely bunched up. All in all the only division to have teams change order was the AL East, which also, not coincidently, saw the biggest jump (Rays +21%) and decline (Red Sox -17%). The biggest swings in the NL were the Cards (+13%) and Dodgers (-13%). Check back in a couple weeks and see how things are different then.

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