Last week’s
column about pitch counts, game lengths and run scoring
quite a lot of response, most of it taking me to task for not answering the
question properly. Though MLB has backed down after the directive to
“hunt for strikes” caused an uproar, it still remains an
interesting topic for analysis. Here’s a sample of the comments:

Ted Frank wrote:

The data you showed was fascinating. But you reversed the causal arrow. Low
pitch counts don’t cause low-scoring games. It’s the other way around.

What needs to be looked at is Strike %. Pitch counts are just an
effect of the size of the strike zone. What is the run-scoring (and pitch
counts and game times) for various versions of strike percentages?

Theron Skyles wrote:

You study of pitch-count effects on the game was interesting, but I think it
might have been more useful if you had looked at different levels of Strike%
rather than average number of pitches. I realize that it’s the average
number of pitches that Alderson, et al want to drive down, but that’s not
what the umpires have been told to change. They’ve been told to call more
strikes in hopes that that will bring down the number of pitches. So it
seems to me you should be looking at games broken down by Strike% rather
than the number of pitches.

F. J. M. writes:

Your study of the correlations between Strike%, pitch count, runs scored,
and game time is interesting but misses the point. The fact that you found
more or less linear relationships between the variables is hardly
surprising. But you seem to be trying to reverse cause-and-effect.

M. W. wrote:

With good pitchers, a large zone does not increase strike percentages; it
just changes where they throw [the ball]. The whole basis of your theory is
not supported by the numbers. It assumes that pitchers are trying to throw
strikes and just missing (hence a bigger zone and the same pitches would be
more strikes). But once the umps go bigger, the pitcher moves farther
outside. The pitcher will still try to live on the corners, meaning the same
number of strikes. Now, offense will go down, because those new strikes are
harder to hit. But the changed strike zone would create a change in pitcher
strategy which would probably negate it.

There were probably a couple more that I’m missing, but you get the idea.
All in all, this probably means that the column wasn’t written as clearly as
it could have been, or I was just plain wrong, or both. I like to think that
I wasn’t totally off base with my analysis last week, but it’s also true
that I ended up answering a different question that what Nate (the submitter
of last week’s question) actually asked, and so I accept the blame for that.

The question I tried to answer was something along the lines of “what
does the world look like if Sandy Alderson’s goal of average pitch counts
around 270 is attained,” which I approached by looking at current games
that were at that level. However, the question that was asked (and what most
of the comments above reflect) was what kind of Strike% would be necessary
to attain that goal, thus focusing on the means to the end, rather than the
end itself.

We can look at games by strike percentage, rather than total pitch count,
and construct in a more “bottoms-up” fashion, how frequently the
umpires would have had to call a strike to get the desired pitch count

53.0-56.9 191 32 317 560 55.92% 5.85 .275 .388 .431 .819
57.0-57.9 188 36 306 629 57.48% 5.58 .262 .369 .424 .793
58.0-58.9 184 72 299 1254 58.57% 5.27 .266 .361 .428 .789
59.0-59.9 185 100 300 1750 59.54% 5.28 .263 .355 .417 .771
60.0-60.9 181 129 297 2263 60.50% 5.63 .265 .346 .444 .790
61.0-61.9 175 139 285 2418 61.50% 5.13 .263 .339 .431 .770
62.0-62.9 175 171 282 2995 62.48% 4.85 .260 .330 .415 .744
63.0-63.9 171 158 278 2769 63.53% 4.78 .256 .317 .423 .740
64.0-64.9 169 108 274 1894 64.46% 4.65 .256 .313 .414 .728
65.0-65.9 170 102 272 1790 65.45% 4.85 .267 .318 .431 .749
66.0-66.9 163 82 266 1433 66.46% 4.68 .264 .307 .431 .739
67.0-67.9 166 50 263 878 67.44% 4.23 .254 .300 .400 .700
68.0-68.9 158 24 248 422 68.44% 3.11 .235 .272 .350 .622
69.0-76.9 149 36 238 624 70.54% 3.53 .242 .270 .397 .667

Looking at the data this way, the strike percentage that averages out to
Alderson’s target of 270 is about 65.5%, which is a couple of points higher
than suggested in last week’s analysis. This goes to show that the strike
percentage that yields a certain average is not the same as the strike
percentage found in games around the average.

Separate from the strike percentage issue, how do the time and run-scoring
comparisons fare? I ran a linear regression on the data above, and estimated
the values at a pitch count average of 270:

  • Using games around 270 pitches (last week’s approach): 4.10 RA, 167

  • Using strike% that yields average of 270 (this week’s approach): 4.47
    RA, 168 minutes

The two time-of-game estimates are quite similar, reinforcing the idea that
increasing the percentage of strikes would knock about 10 minutes or so off
of game length. The decrease in run scoring is not as dramatic as last
week’s analysis suggests, and in retrospect I am probably more comfortable
with the more conservative estimate.

M.W.’s comments about pitchers responding to changes in the strike zone by
altering their approach to batters is a valid one, and I touched on it in
last week’s column:

[W]e’re also not considering how batters and pitchers might react to the new
strike zone. Would batters become more aggressive earlier in the count, and
drive pitch counts further down as a side effect, but without actually
lowering offense anymore than expected? Would pitchers and catchers change
how they work a batter, relying more on nibbling at the fringes of a
generous strike zone, and less on challenging them in a tiny zone in the
batter’s wheelhouse?

One underlying assumption in this analysis is that the side effects
resulting from such a change are minimal, and we can therefore effectively
model how the world looks after a change by looking at the subset of
outcomes we currently have that are closest to the variable we want to
change. That may work in some cases, but in systems where you have
intelligent agents at work (no Scott Boras jokes, please), the interactions
are more complex.

You have to consider not just the game-theoretic aspects of how pitchers
would alter their approach to a hitter (and how a batter alters the way he
tries to protect the plate), but also the uncertainties in how well a
pitcher can execute that strategy. If a pitcher with control problems had
difficulties hitting a spot at the edge of the old zone, he’ll probably
still have troubles as he aims for the edge of the new zone. He’ll still
gain some benefit, since if he misses his spot inside the strike zone, it’s
less likely to be as hittable as before (the new spot being where he wanted
his pitches to go before the change). But the relationship between the size
of the zone and the percentage of strikes called isn’t obvious, and
therefore we have to be a little careful in assuming that we can project the
effect of such a change with high degrees of confidence.

One other comment I got in e-mail was along the lines of “changing from
62% to 63% strikes only affects a handful of pitches per game–there’s no
way it could have that large an effect on run scoring.” It’s true that
a 1% change in strike rate means a shift of only about 1.5 pitches per team
per game. However, as usual the problem isn’t quite that simple. Shifting
the strike percentages also has an impact on the distribution of counts the
opposing batters face during the game. A few 0-1 counts changed to 1-0
counts can substantially alter the way both the pitcher and the batter
approach that plate appearance. Also, as the percentage of pitches change,
the total number of PA in a game doesn’t remain constant. Fewer strikes
means more batters coming to the plate. Roughly speaking, a 1% increase in
Strike% corresponds to 0.8 more expected batters faced during a game. Extra
batters generally mean more run scoring. The nonlinear nature of offense in
baseball makes such assessments tricky.

On the other hand, there is a selection bias in the data we have–better
pitchers may have both better strike percentages, and better than average
results with a given strike percentage. A good pitcher may throw his strikes
in better locations, where a bad pitcher may throw strikes down the heart of
the plate. So even pitchers with comparable strike percentages can vary in
quality. For example, Esteban Loiaza has a better strike percentage
than Kevin Brown so far this season, but Brown’s results have been

All of this is a very long-winded way of saying that if you don’t accept the
assumptions that underlie this (or any other) analysis, then the conclusions
can be considered suspect. But without some assumptions, many problems of
interest can become intractable. If you are willing to believe that we can
learn something about run scoring at a 270-pitch-count level, either by
looking at current 270-pitch games, or building up a strike-percentage model
that yields an expectation of 270 pitch counts, then the past couple of
columns have been worth reading. If not, you probably tuned out several
paragraphs ago.

Thanks again to Nate for the original question, and to everyone who wrote in
with their thoughts and comments. Remember that you can send in your
question or suggestion to us by
clicking here.

P.S. Those of you who saw last week’s column soon after it hit the Web site
probably noticed a problem with the table of numbers presented. The average
number of pitches per game for games in the 250-259 pitch count range was
262.96. To make a long story short, there were some double entries for one
day’s worth of games in the database, which threw off the averages. The
corrected figures were posted soon after it was discovered, and that’s what
should be up there now. Thanks to several eagle-eyed readers who pointed out
my mistake.

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