In the bottom of the 8th inning of tonight’s game 3 of the NLDS, Anthony Rizzo blooped a single to shallow left and Leonys Martin scored what proved to be the winning run. The noteworthy thing is that Martin scored from second base on a ball that was so shallow it was playable by the shortstop.
The reason he was able to score from second is that there were two outs and he was free to run without worrying about potentially tagging if the ball was caught. So this raises an interesting question: was this a situation in which the Cubs were better off with two outs (as opposed to one or zero)?
Hint: neither answer is cut and dry correct but I do claim there is a right answer.
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October 9, 2017 at 10:14 pm
Scott
Situations in which it is better to have two outs are only possible if base runner incorrectly judges probability of catch and/or the relative value of various situations (or the runner is risk averse and has misaligned incentives).
And even if base runner is perfectly rational, he may (correctly) stay put with one out, only to see shortstop miss catch. If next batter grounds into double play, then only in retrospect would two outs seemed to have been better.
Bottom line: Fewer outs is always better, but only with perfectly rational runner, and only a priori.
[Though with all that said, my gut wagers that runners (and base coaches) are probably overly conservative and are reluctant to role the dice. So at least during that brief moment while ball is in air, two outs may be better. Having a football place-kicker break leg might be good, but only in very select situations, and only when the coach is bad.]
October 10, 2017 at 8:27 am
Anonymous
To the runner, V(we lost when I was tagged)<V(we lost when the ball was caught). To the team, those are equal.
October 10, 2017 at 5:27 pm
Dan R
One out before the at bat, specifically contact on the hit, takes place must be at least as good. The cubs could order an intentional out of some sort by the batter if two were better in that situation.
Likewise if at the moment if contact (bloop hit) running as if two was better, they could have done that on one out. The fact that their strategy would have been different shows that one out is at least as good as two at the moment of contact /it’s a bloop hit/etc.
In no case is two outs better. The fact that no team ever commits intentional outs or runs the bases as if more outs suggests that one out is strictly better (or managers aren’t making the best play) Sometimes extra factors should tilt a close call if it’s close, so it probably isn’t a negligible difference either.
October 10, 2017 at 8:38 pm
Gerardo
Ex ante one out is almost certainly. superior. The only downside to zero or one outs on a bloop single is that the runner might get thrown out at the plate. Otherwise you have first and third with the four and five hitters coming up with less than two outs. I would say the expected number of runs is almost certainly higher, though there is reason to be risk averse here and take a run in hand rather than multiple potential runs.
Two outs has also makes it more likely that Rizzo gets intentionally walked. Or at least I think it does. Who knows with Dusty.
October 18, 2017 at 11:34 am
Dan
Assuming optimal play, one out must be better ex ante. Let V be value of the problem to the Cubs, given the situation and everyone’s strategy.
V(one out, Cubs play optimal strategy, Nats play optimal strategy) >=
V(one out, Cubs play some other strategy, Nats play optimal strategy)
Since “optimal strategy with 2 outs” is one possible strategy with one out,
V(one out, optimal strategy, optimal strategy) >=
V(one out, Rizzo pretends there’s two outs, Nats don’t know and don’t best-respond) >=
V(one out, Rizzo pretends there’s two outs, Nats best-respond)
But this must be at least as good as
V(two outs, Cubs play optimal strategy, Nats best-respond)
which is where we’d be with two outs.
Basically, the Cubs are free to tell Rizzo to just run as if there’s two outs, and get the added bonus that the Nats might not best-respond; since they don’t do that, they must be better off playing “traditional baseball strategy” with one out.
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