## On Productive Outs

A couple of weeks ago, I read this blog post from Joe Posnanski, in which he discusses comments made by Red Sox GM Theo Epstein about outfielder J.D. Drew. The whole thing's interesting, but what caught my eye was the following quote from Epstein:

He [Drew] does the single most important thing you can do in baseball as an offensive player. And that’s not make outs.

Well, this really hit me, because it's about the most concise possible argument you could make about hitting - just to simply state, "We get only three outs an inning, and when we reach three, we have to start over. Wasting outs for any reason does not help us." And yes, I realize that slugging percentage plays a big part in scoring runs, too, and a single is sometimes more valuable than a walk, and all of that. But ultimately good hitters that help their teams simply don't make outs.

This, however, got me thinking about "productive outs," and sacrifice bunting and all the rest of the things that managers and announcers talk about. How many times have you heard the Twins broadcast crew laud Nick Punto for grounding out to the correct side of the infield, thus moving the runner from second to third?

With all this in mind, I went over to Baseball Prospectus to grab the Run Expectancy Matrix for 2009. If you're not familiar with this graph, simply put, it tells you how many runs a team can be expected to score, given a certain situation and all else being equal.  Here's the 2009 version:

 Situation / Outs 0 1 2 Bases Empty 0.5173 0.2789 0.1064 Runner on First 0.8834 0.533 0.2234 Second 1.1415 0.6884 0.3219 Third 1.3146 0.9655 0.3701 First and Second 1.4837 0.9217 0.4556 First and Third 1.7686 1.2018 0.522 Second and Third 2.0137 1.4138 0.5623 Bases Loaded 2.279 1.558 0.7499

If you're new to reading this table, examine with me the second row ("Runner on first"). This row says that, in 2009, a team could be expected to score .8834 runs, on average, if it had a runner on first with nobody out. With one out and a runner on first, it was expected to score .5330 runs, and so on.

What I thought I'd find, from this table, was the ability to state a hard-and-fast rule about outs.  I assumed that we could all live by the following statement: "Making an out ALWAYS decreases the number of runs a team can be expected to score in an inning."

What I found was close to that statement... but not quite.

Of course, the value of an out always depends on the situation, the batter at the plate, the runners on base, and so forth. (For example: it's a better idea to have Alexi Casilla try to bunt a run home than it is to have Joe Mauer try to bunt a run home, because Casilla is far less likely to get a hit or otherwise drive the run home.)  However, with all else being equal, I was surprised to find that there are productive outs.

By this, I mean outs that actually increase the expected number of runs that a team would score. Here's the list of plausible productive outs I've found; perhaps you can find more.

• With the bases loaded and fewer than two out, an out that advances all three runners is a productive out.  (Just as an example, here's the math: With nobody out and the bases full, a team is expected to score 2.2790 runs. If the batter advances all three runners - say, with a sacrifice bunt - a run comes home, and the team has second and third with one out, an expectancy of 1.4138. In other words, the run expectancy has gone from 2.2790 to 2.4138.  With one out, the expectancy goes from 1.5580 to 1.5623.)
• With a runner on third base and one out, getting the run home via a sacrifice or simple ground-out is productive (the expectancy goes from .9655 to 1). Interestingly, this isn't true if no one is out (decreases from 1.3146 to 1.2789).
• With runners on first and third and one out, moving both runners along is productive (1.2018 to 1.3219). This can plausibly be done via sacrifice, or possibly a deep fly ball to Johnny Damon or any other outfielder with a terrible arm.

And that's it. In all other situations, all else being equal, making an out - whether the announcers think it's productive, or not - doesn't help the team score more runs.

Of course, productive outs are better than non-productive outs. It's better for Nick Punto to move a runner over than strike out.  But these are Pyrrhic victories; in most situations, the team is worse off.

I thought, when I looked at the numbers, we'd end up with a strict rule.  Instead, we're stuck with more of the ambiguity that baseball will always be famous for: "For the most part, making an out decreases the number of runs a team can be expected to score, all else being equal."

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