Playing a double into a triple (or a home run?!)




Unlike others here, I like Nyjer Morgan's attempt to make the spectacular play, because I believe it was worth the risk.  I've tried to make this point a couple of times, but haven't got much traction. So naturally I'm going to try to make it again.

Let's say there are two outs and nobody on base. A ball is hit hard towards the gap. If Nyjer attempts a spectacular play to dive for the ball, or leap for the ball before crashing into the wall, there are two potential outcomes. Either he makes a spectacular play and the inning is over, or the runner ends up on third (or, in very rare circumstances, at home). If he doesn't attempt the play, i.e. he lays up and lets the ball drop or bounce off the wall, the result is a double.

The question is whether Nyjer should attempt the play, and the answer is dependent upon the likelihood that Nyjer makes the play if he attempts it. Let's say that likelihood is p. For purposes of the following analysis, I'm going to assume that failure will result in the runner making it to third, as an inside-the-parker is extremely unlikely. Now, a run expectancy matrix I have indicates that the number of runs expected with 2 outs is

  •  .344, if a runner is on second, and
  •  .387, if a runner is on third.


Of course, the actual expectancy is dependent on the game situation (it's different if Albert Pujols is next up instead of, say, Melky Cabrera, but we'll ignore that point). Thus, the number of runs expected if he attempts the play is

0*p + .387*(1-p),

and the number of runs expected if he doesn't attempt the play is .344. Setting these quantities to be equal gives

p = .11.

In other words, if Nyjer has at least an 11% chance at making the play, he should attempt the play.

Of course, I don't really expect Nyjer to calculate his chances of making the play to determine whether he's at least 11% likely to successfully do so. I do, however, think that Nyjer is practiced enough to know when a play is simply out of his reach and not worth an attempt. If anything, we've seen him be a lot less aggressive on balls this year than he was last, allowing flares to drop without much overt effort to prevent it.

Also, note that all this is dependent on there being two outs. With 0 or 1 outs, the equal-outcome value for p is a lot higher, i.e. he has to be much more sure of himself in these situations.

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