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July 27, 2001

Aim For The Head


by Keith Woolner

Last week's column about pitch counts, game lengths and run scoring got 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 levels:

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 minutes

  • 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 superior.

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.

Keith Woolner is an author of Baseball Prospectus. 
Click here to see Keith's other articles. You can contact Keith by clicking here

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2001-08-30 - Aim For The Head: The Men In Black
2001-08-16 - Aim For The Head: More Reaching on Errors
2001-08-02 - Aim For The Head: Reaching on Errors
2001-07-27 - Aim For The Head: Feedback
2001-07-19 - Aim For The Head: Pitches and Game Length
2001-07-12 - Aim For The Head: Walk Rate Spikes
2001-06-26 - Aim For The Head: Fan Satisfaction

2001-08-30 - Aim For The Head: The Men In Black
2001-08-16 - Aim For The Head: More Reaching on Errors
2001-08-02 - Aim For The Head: Reaching on Errors
2001-07-27 - Aim For The Head: Feedback
2001-07-19 - Aim For The Head: Pitches and Game Length
2001-07-12 - Aim For The Head: Walk Rate Spikes
2001-06-26 - Aim For The Head: Fan Satisfaction