Make a note of this event – it is very rare that I am going to defend a player on a rival team.  All stats are prior to Wednesday’s game.

Mark Reynolds of the Diamondbacks is having a great season in an otherwise forgettable year for the Snakes (although he has been struggling quite a bit this month).  He has hit 43 homers, driven in 100 runs, and has a .919 OPS.  He has also struck out 206 times.  Reynolds is the only player in Major League history to strike out 200 times in a season – and this is the second year he has done it.

Reynolds gets some criticism from people who think that the strikeouts are hurting the team, because strikeouts are inherently worse than “productive” outs.  But are they?

Let’s delve into this a bit.  Let’s keep all of Reynolds’ stats the same, except that we’ll turn 100 of his strikeouts into other types of outs.  I’m not including bunts in the mix, because it isn’t likely that the manager would ask Reynolds to bunt.

First, let’s take care of a few basic questions:

  • Why aren’t we turning some of the strikeouts into hits?  Because that would affect his batting average.  I’m not trying to ask the question of whether or not Reynolds would contribute more with a .300+ average and 100 strikeouts vs. his current .266 average and 206 strikeouts – clearly he would.  Hits are always better than outs – any sort of outs.  Instead, I am looking at the relative value of a Reynolds with .266 and 106 strikeouts vs. .266 and 206 strikeouts – determining the negative impact of the strikeout itself.
  • Why aren’t we taking into account the fact that Reynolds could reach on an error?  Because  this is not statistically significant.  Against a .980 fielding team, this would mean Reynolds reaches on an error an extra two times.  This is easily offset by the extra occurences of double plays and runners being thrown out trying to advance

First, we must realize that not every non-strikeout out is a productive out.

  • In 320 of Reynolds’ 621 plate appearances (51.5%) the bases have been empty.  In this situation, it is impossible to advance the runner, since there is no runner.
  • In 220 of  Reynolds’ plate appearances (35.4%), there were two outs in the inning.  Regardless of whether you strike out or hit a lazy fly ball to center field, the inning is going to come to an end.

We can’t simply subtract these percentages from 100%, of course.  They double count the situation of 2 outs and the bases empty.  I don’t have the number of plate appearance for this situation (although I am able to derive a boundary of the estimate based on other data).  We’ll estimate the intersection of these two points by multiplying.  This results in an estimate of 18.2% of plate appearances with 2 outs and these bases empty.  I stress that this is an estimate, although it should be fairly close (and, if anything, is slightly higher* than the true result, meaning that productive outs are actually less prevalent that my calculations indicate).

Now we add 51.5 and 35.4 and deduct the intersection of  18.2.  This results in 68.7% of plate appearances where it is impossible for a productive out to exist.  This leaves 31.3% of plate appearances where it is actually possible for an out to advance a baserunner.  In our example of 100 strikeouts that we magically turned into other outs, this would mean 32 opportunities for productive outs.

Of course, this doesn’t mean that Reynolds would actually have 32 more productive outs.  Even though the situation makes is possible, he would still need to execute.  An infield fly isn’t going to advance the runner.  Nor will a shallow fly ball.  Only a deep fly ball will advance a baserunner from first to second – because of the short throw to second base.  Runners will also have difficulty advancing from second to third on a fly to left field.  Many ground balls will result in the batter reaching first and the lead runner being retired.  Let’s estimate that Reynolds would be able to make a productive out 40% of the time.  (If you don’t think this is fair, watch a few games and pay attention to how many times a batter is able to advance the runner).  That’s 13 times advancing the runner.

Of course, not all of those runners are going to score.  If the guy batting next makes the third out of the inning, it really doesn’t matter if Reynolds struck out or if he advanced the runner with a fly ball – the runner is still going to be stranded (unless the runner was on third base, of course).  If the next guy hits a homer (or a rally ensues), it’s also academic, as the runner would have scored regardless of whether or not Reynolds advanced him.  Out of those 13 times advancing the runner, perhaps half the time (we’ll round up again to 7) the productive out makes a difference in whether or not a run scores.

So, do the extra strikeouts have a negative impact on the Diamondbacks?  Sure – perhaps 7 runs over the course of the season.  But are they really that much worse than other types of outs?  No, not really.  Not enough to make a productive hitter make a fundamental change to his approach.

Math alert – here’s more background at how we arrived at the intersection of the two outs scenario and the bases empty scenario. 

While I don’t have the statistics for the number of plate appearances with two outs and bases empty, we can chip away at this a bit by coming from the opposite direction of plate appearances with runners on base.  We know that Reynold had 95 plate appearances with two outs and runners in scoring position (second and/or third base).  We also know that Reynolds had some number of plate appearances with runners on first (but not second or third) and two outs.  We’ll assign this X.  With our estimate of the two outs, bases empty of 18.2%, we get this equation (35.4% is the percentage of plate appearances with two outs – we subtract the situations where there are base runners in order to determine the percentage of the time when there are not baserunners):

18.2% = 35.4% – (X + 15.3%)

18.2% = 35.4% – 15.3% – X

X = 35.4% – 15.3% – 18.2%

X = 1.9%

Thus, our estimate allows just 1.9% of plate appearance (12 PAs) to be two outs with single runner on first base.  This is almost certainly too low.  If we adjust this upward, it also pushes the 18.2% downward … meaning that the intersection of the two outs occurence and the bases empty occurence is smaller that we have calculated, and that those two numbers (51.5% and 35.4%) are double counting fewer plate apperances than originally thought – meaning that we can carve away more than bats than the 68.7%, resulting in even fewer plate appearances where productive outs are possible.  If this isn’t clear, play around with the math a bit and see what happens when you adjust X upward.

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Kosmo is the founder of The Soap Boxers and writes on a variety of topics. Many of his short stories have been collected into Kindle books.

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