Sending Salty: WPA, Risk, and Reward

Like most fans watching the game Tuesday night, I was shocked to see Jarrod Saltalamacchia break for home. Salty got a good jump off second on Ellsbury’s grounder up the middle, but this was a catcher running. I mean, come on! Salty scored against all odds, no doubt allowing the Heart of Gold to reach some legendary lost planet. Even though all ended well, the vast majority of Red Sox Nation has raised a collective eyebrow at third base coach Tim Bogar, as if to say, "are you out of your mind?"

Thankfully, a perfect tool exists for the evaluation of this strategy. No, its not BIAR (Bogar Insanity Above Replacement), though I thoroughly endorse the development and use of such a statistic. No I am referring to WPA, or Win Probability Added. 

At the time that Jacoby Ellsbury entered the batters box, there was one out, runners on first and second, and a 71% chance that Boston would win (or a Win Expectancy of .711). Salty scored, winning the game and adding 29%  to the probability of a win for the Sox (or giving the play a WPA of .299). Because Ellsbury hit safely, two other reasonable scenarios could have occurred. Bogars could have significantly lowered his BIAR by holding Salty at third. The result of that would be the bases loaded, one out and Dustin Pedroia at the plate. Second, Salty could have been thrown out, the result of which would be runners at second and third, two outs, and Pedroia up.

The difference in Win Expectancy between runners on first and second and one out (.711) and the bases loaded and one out (.835) is a very substantial .124 WPA, just a bit under half of the best case scenario of Salty actually scoring. Salty getting thrown out would have reduced WE to .639, a WPA of -.072. Bogar stands to up the chances of winning by 17.5 % by sending Salty instead of holding him. He stands to decrease those odds by 19.6 % if he is wrong and Salty gets throw out. The difference between best case scenario and worst case scenario is an unbelievably high .371 WPA. If the probability of Saltalamacchia beating out that throw is better that .639, the gamble makes at least some sense, if the probability he scores is better .835, sending him in is a no brainer. Does anyone think there was a 64- 84% chance he would beat that throw? Does Tim Bogar really think his catcher beats short throws from center to the plate the vast majority of time? God, I hope not.

The outrage at his decision might be a little bit overkill, but it is hard to see how the risk of sending Salty can be justified in that situation under anything that passes as a rationale. While I am sure that Tim Bogar calculates all this in his head, right in the moment (with Salty running, he has the time); even if he has no earthy clue what the win expectancy of these events might be or what this win expectancy crap is, for that matter, he should see that the bases loaded and one out for Dustin Pedroia is a better bet than a foot race involving Salty and a short throw. Whatever they were, how ever he arrived at them, assessment of the odds at play here baffles the mind.

Note to self: Invite Tim Bogar to weekly poker night.