By Mark Malter
A few weeks ago, I wrote about my Baseball Stats R shiny application, where I demonstrated how to calculate runs expectancies based on the 24 possible bases/outs states for any plate appearance. In this article, I’ll explain how I expanded on that to calculate the probability of winning the game, based on the current score/inning/bases/outs state. While this is done on other websites, I have added some unique play attempt features -- steal attempt, sacrifice bunt attempt, and tag from third attempt -- to show the probability of winning with and without the attempt, as well as the expected win probability given a user determined success rate for the play. That way, a manager can not only know the expected runs based on a particular decision, but the actual probability of winning the game if the play is attempted.
After the user enters the score, inning, bases state, and outs, the code runs through a large number of simulated games using the expected runs to be scored over the remainder of the current half inning, as well as each succeeding half inning for the remainder of the game.
When there are runners on base and the user clicks on any of the ‘play attempt’ tabs, a new table is generated showing the new probabilities. I allow for sacrifice bunts with less than two outs and a runner on first, second, or first and second. The stolen base tab can be used with any number of outs and the possibility of stealing second, third, or both. The tag from third tab will work as long as there is a runner on third and less than two outs prior to the catch.
I first got this idea after watching game seven of the 2014 World Series. Trailing 3-2 with two outs and nobody on base, Alex Gordon singled to center off of Madison Bumgarner and made it all the way to third base after a two base error. As Gordon was approaching third base, the coach gave him the stop sign, as shortstop Brandon Crawford was taking the relay throw in short left field. Had Gordon attempted to score on the play, he probably would have been out at the plate- game and series over. However, by holding up at third base, the Royals are also still ‘probably’ going to lose since runners only score from third base with two outs about 26% of the time.
The calculator shows that the probability of winning a game down by one run with a runner on third and two outs in the bottom of the ninth (or an extra inning) is roughly 17%. If we click on the ‘Tag from Third Attempt’ tab (Gordon attempting to score would have been equivalent to tagging from third after a catch for the second out), and play with the ‘Base running success rate’ slider, we see that the break even success rate is roughly 0.3. I don’t know the probability of Gordon beating the throw home, but if it was greater than 0.3 then making the attempt would have improved the Royals chances of winning the World Series. In fact, if the true success rate was as much as 0.5 then the Royals win probability would have jumped by 11% to 28%.