Yesterday on my commute home I'm listening to the Brewers and Phillies game on the radio. The Brewers are down 3-1 after Ryan Braun hit a run scoring double down the right field line. With Prince Fielder up down 2, Michael Kay and Steve Philips begin to talk strategy and whether or not they would walk Howard. Michael Kay said that he would and that he would rather face JJ Hardy as the winning run than Fielder as the tying run. This struck me as remarkeably stupid, so here is the blogpost. Let us for the purpose of the post completely forget about how Fielder struck out and simply look at that moment.First let us look at something called win probability. Which is what it is sounds like, the probability of winning at any given moment in the game. After Braun's Double the Brewers probability of winning stood at 9.2%, or not very good. Now I couldn't find a website where I could see what the probability would be after a Fielder walk but I came close with this win expectancy simulator. With 1 out a runner on second down 2 the simulator states that the visiting team has a 6.5% chance of victory. Now, with 1 out runners on first and second down by 2 the visiting team has a 13.7% chance of winning. That's a massive increase. In the actual game, later in the inning the Brewers chance of winning went from 3.9% to 7.5% following JJ Hardy's walk.
Ok now all that was straight numbers not taking into consideration Prince Fielder's better than average skill set. So let's take a look at all the possible outcomes of Fielder's at bat. Let's run over the assumptions to be used. For the point of putting this argument into Kay's favor a little bit we will utilize Fielder's splits in September where he had a season best average (.316) and OPS (.998). We will run under the assumption that on any hit Braun would score to move the game to 3-2. And we will utilize the Fangraphs win % after a Prince Fielder out of 3.9% for the Brewers rather than the simulators more harsh 1.8% chance. And finally this all assuming that Prince Fielder is the same hitter against All-World Brad Lidge as he is against the average pitcher he faced in September. All of these assumptions should skew in favor of Kay.
So let's take a look at the results. Walking Fielder as Kay suggests reduced the Phillies chance of winning to 86.3%. Now pitching to Fielder could result in a run scoring single, a run scoring double, a walk, a hit by pitch, or an out. The percentages for each are in the table given Fielder's September spilts and the probability of a Phillies is given for each of the results. To calculate the expected Phillies win percentage after Fielder's at bat given the spectrum of possible outcomes all you do is a summation of the probability of result * the win percentage after the outcome. Thus the winning percentage for the Phillies by deciding to pitch to Fielder is 89.8% or better than 86.3% if they decided to walk him.
I put all the assumptions in Kay's favor and still the numbers don't lie. Walking Fielder intentionally would have been one moronic decision.
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