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# On Marlon Byrd bunting

I got into a discussion at Jamey's site about the wisdom of Marlon Byrd bunting this past weekend against Jered Weaver, with Hank Blalock on first base and none out in a 0-0 tie in the top of the second.

And it occurred to me...I could run the scenarios with various likelihood of events occurring (based on what I think are reasonable assumptions of the likelihood they would occur), and make a determination as to whether, from a run expectancy standpoint, it made sense.

The 2007 run expectancy table says how many runs would expected to be scored given a certain set of runners on base and a certain set of outs.  A runner on second, and one out, has an expectancy of .72482 runs.  So, if it makes more sense to have Marlon Byrd swing away rather than execute a successful sacrifice, the weighted aggregate run expectancies of all the possible outcomes has to exceed .72482.

So...first off, let's take into account the situation.  It is a slumping Marlon Byrd facing Jered Weaver, who, throughout the course of his career, has allowed a .228/.276/.348 line to righties, versus a .275/.329/.441 line to lefties.  Marlon Byrd is a career .271/.332/.391 hitter, which is a little worse than the line for the average A.L. hitter in 2007 (.270/.338/.423).  He doesn't have a huge platoon split, but he has been in a marked slump.

So, given that Byrd is a little below-average hitting-wise anyway, and given that he's in a slump, what is a reasonable expectation for what his average line against Weaver in this situation would be?  Say, .220/.270/.320?  I think so.

Now...Weaver allows righties 1 XBH in every 15 PAs.  Byrd gets an XBH roughly every 15 PAs.  So, for the sake of discussion, let's assume that the expected breakdown of XBHs for Byrd in this situation is the same as for Weaver overall, with a small discount for Byrd not having as much HR power as the average hitter -- 5% chance of a double or triple, 1.5% chance of a HR.  There's also a 1.5% chance of a GIDP, given Weaver and Byrd's historical averages.

Okay.  So there is a 71.5% chance that Byrd will make a non-GIDP out.  I am going to assume that, if he makes an out, he's not going to advance the runner.  A runner at first with one out has a run expectancy of .54239.

The 1.5% chance of a GIDP leaves you with 2 outs and none on, a run expectancy of .10899.

There is a 5% chance of a walk, which would generate a first and second, none out situation, worth 1.51044.  I am assuming a single would only advance the runner to second, given the situation, the runners, and the outfielders, so there's an additional 15% chance of having that 1.51044 (assuming that, with a 22% chance of getting a hit, 15% is a single and 7% is an XBH).

The 1.5% chance of a home run gives you a run expectancy of 2.53542 (2 runs scoring, plus the run expectancy of none on and none out), and the 5.5% chance of an XBH gives you a run expectancy of around 1.75, assuming 5% doubles and .5% triples.

So, totalling it out, using these run expectancies, that gives you an expected .825919 runs scored if you let Byrd swing away, versus a .72482 expected runs scored if Byrd successfully sacrifices.

Now, I think the reality ends up being a lot closer, when you factor in the possibility of Byrd successfully reaching on the bunt (either as a bunt single or an error) or a walk, versus the possibility of him not getting the bunt down.

But this ended up being an interesting exercise, because I would have expected the edge in favor of bunting to be a little closer than it was.  I think I may have overestimated the chances of Byrd getting an XBH, which is where most of the swing takes place, but maybe not.