Fun with Numbers: Strikeouts vs. Ball-in-Play Outs

I was having a discussion on another Reds' board, and came across one of my favorite types of Reds' fans; the "put-the-ball-in-play-and-let's-manufacture-some-runs" guy.  He, of course, hated Chris Dickerson.  I like Chris Dickerson.  He told me that strikeouts were terrible, and productive outs were awesome.  I said that strikeouts are bad, productive outs are slightly less bad, and GIDP's are really bad, and that most of the gains that result from productive outs are erased by grounding into double plays.  He said, "Nuh uh."  I said, "Yes huh."

It actually turned into a really good discussion, with one poster making a great point after I launched into my usual tirade about strikeout rate correlating with Walks, Power, and ever so slightly, run production.  The point was that we need to separate strikeouts from players who strike out.  There's an inherent selection bias in the correlation rates I cited, as players who strike out have to have those secondary skills in order to make the Big Leagues in the first place.

So, this is my attempt to isolate the effects of strikeouts, and compare them to Ball-in-Play outs.  I haven't seen anything like this done by anybody else, so I hope I'm showing you guys something new here.  It's long, and it's got a lot of math, all of which I did myself.  You've been warned.

First, we need to determine a run value for every type of out in every baserunner situation and every out situation. The most important tool in making this determination is the 2008 Run Expectancy Matrix, as compiled by Baseball Prospectus.  Most of you are familiar with this, but for those who haven't seen it, a quick explanation. On the left side is the baserunner situation. 1, 2 or 3 indicates a runner on that base, 0 indicates the base is empty. So, 103 means runners on first and 3rd. On top is the Out situation. The numbers in the middle indicate the average number of runs scored by all teams in all innings (except walk-off 9th innings) throughout MLB in 2008.

So, with this information, we'll determine Run Values for Productive Outs by subtracting the "after" run expectancy from the "before" run expectancy, adding runs as applicable when there's a productive out with a runner on 3rd. For example, for a Sacrifice Fly with runners on 1st and 3rd and 0 out, the Run Value would be 1.77 - (1 + 0.53) = -0.24, where 1.77 is the run expectancy for runners on 1st and 3rd with 0 out, 0.53 is the RE for a runner on first with 1 out, and 1 is added because a runner scored. I'll make the assumption that every Productive Out happens with the same frequency regardless of the Out situation, and thus can take a simple average of the 0 out and 1 out Run Value for a Productive Out in each Baserunner Situation. Here's what I came up with:

100= -0.205
020= -0.26
003= -0.08
120= -0.22
103= -0.02
023= -0.13
123= -0.12

I made the assumption that in 1st and 3rd situations, the man on 1st advances half the time; in 2nd and 3rd situations, the man on 2nd advances half the time; and in bases loaded situations, 1/3 of the time, nobody advances; 1/3 of the time, only the man on 2nd advances; and 1/3 of the time, both men advance. It's probably not perfect, but it's probably close.

This jives pretty well with intuition. The best time for a productive out is with a man on 3rd, since at least you get a run home. However, when the bases are stacked behind him, you get some diminishing returns, as you hurt your chance for a big inning.

Now, we do the same for Strikeouts. This is considerably easier, as we don't have to consider "before" and "after" Baserunner Situations. Here's the results I got:

100= -0.34
020= -0.41
003= -0.58
120= -0.54
103= -0.65
023= -0.71
123= -0.76

So, yeah, productive outs are better than strikeouts. That shouldn't shock anybody. However, there's a 3rd type of out that can also result from putting the ball in play; the dreaded GIDP. The only real assumption I made regarding other baserunners was that any runner in front of the DP advanced 1 base when there were 0 out. I gave the same credit for a DP with a runner on 3rd that I did above. The run values for GIDP:

100= -0.63
120= -1.05
103= -0.91
123= -1.28

So, now that we have Run Values for every type of Out in every Baserunner Situation, we can calculate the weighted average, multiplying Run Value by the Percentage of Plate Appearances in that situation. When we're done, we'll divide that by the aggregate of %PA to determine a Total Run Value. Being very familiar with them, I utilized Adam Dunn's splits for the %PA's for each Baserunner Situation (come on, you knew I wouldn't go an entire post without bringing him up). Here's the Total Run Value for each type of out:

TRV (PO) = -0.19
TRV (K) = -0.46
TRV (DP) = -0.81

So, now, we need to determine the ratio of Productive Outs to GIDP's needed to break even with Strikeouts. Get ready for some Algebra:

-0.81 + -0.19*x = -0.46*(x+1)

We need 1.3 Productive Outs for every GIDP in order to break even. So, how do MLB teams do in that regard?

ESPN actually kept Productive Out stats for a while as Buster Olney tried to convince us that they were some sort of hidden indicator of success. ESPN hid that data once it became apparent that teams with large numbers of productive outs had bad offenses. I found Productive Out data for 2008 buried deep on ESPN's site, though. The average MLB team had 187 Productive Outs in 2008.

GIDP's were considerably easier to find. The average team had 129 of those.

187 / 129 = 1.45

So, the average MLB team does gain a little bit by making ball-in-play outs instead of strikeouts. Let's see how many runs they gain over the course of a season with their Ball-in-Play Outs.

187*(-0.19) + 129*(-0.81) = -140 Runs
(187+129) * (-0.46) = -145 Runs

So, over the course of an entire season, the average MLB team gains 5 runs as a result of their Ball-in-Play outs.  The question I leave to you, dear reader, is; Are the benefits of late-count hitting (walks, high opponents' pitch counts, seeing more pitches) enough to offset those 5 runs a team gains by trading strikeouts for Ball-in-Play outs?

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