"What are the odds?" The Chances the SJ Giants Come Back to Beat Visalia

Going into the bottom of the 5th inning last night, the San Jose Giants trailed the Visalia Rawhide 4-0, and also were down 2-0 in the best-of-5 series. I was asked "What's the win probability for the game at that point?"

The best way to determine this would be to simulate the rest of the game/series play-by-play, taking into account each player on each team and their respective performance throughout the season. However, I don't quite have my play-by-play simulator ready for baseball (although I'm very close!), so I adapted the simulator I wrote awhile back that simply simulates how many runs are scored in each half-inning. As before, this data was gathered from Baseball-Reference, which shows how frequently 0 runs, 1 run, 2 runs, etc are scored in a half-inning (in MLB in 2015; I'm using this as a proxy for MiLB).

The Giants had to overcome a 4 run deficit in 5 innings. I ran 10,000 simulations, and they only come back to tie the game (or take the lead) by the end of the 9th 2.55% of the time. To ultimately answer the first question, they only win the game 1.78% of the time.

Then there was a followup: "Down 4-0 heading to the bottom of the 5th in a best-of-5 series in which they were down 2 games to none. What was the series win probability at that point?"

We know their odds of winning Game 3 were down to 1.78%, so now we have to determine the odds they subsequently win Game 4 AND 5. Game 4 is at home, while a possible Game 5 would be on the road. Using both teams' second-half records (both finished at .600) in Log5 and factoring in home-field (0.24 runs in MLB) gives San Jose 52.27% to win Game 4 and 47.73% to win Game 5. So the odds of winning both Game 4 and 5 are 24.95%. Finding their series win probability headed into the bottom of the 5th last night is then 1.78% * 24.95% = 0.44%, or about 1 in 225. Even so, that's twice as likely as the Cowboys' comeback over the (New York) Giants on Sunday night.

Given that they did come back and win Game 3 means they're now at 24.95%, or about 1 in 4.