Aim For The Head: OPS by Length of Plate Appearance

This week's question comes from Don Coffin, who asks:

I was watching a game on TV the other day and wondered whether a longer at-bat favors the hitter, in terms of its final outcome. More specifically, how do things like BA/OBP/SLG differ with the number of pitches in an at-bat?

Thanks for the great question, Don. Before we look at the actual results, let's stop a moment and think about what our intuition might lead us to believe.

For starters, a walk requires at least four pitches, so the difference between batting average and on-base percentage for one to three pitches should be minimal, with sacrifice flies and hit-by-pitches accounting for any gap. Walks become possible at four pitches, so OBP (though not necessarily batting average) should rise at that point, and probably remain high at five and six pitches as well (walks occuring on 3-1 and some 3-2 counts). Similarly, a strikeout requires at least three pitches, so any outs of the one- or two-pitch variety would have to come via balls in play.

It's not immediately obvious what to expect from slugging average. Based on the way most hitters approach their jobs, they would protect the plate with two strikes, so as the counts go deeper (any PA lasting beyond five pitches must end on a two-strike count), power should stay fairly constant after five pitches. You might expect aggressive first-ball and bad-ball hitters to be swinging hard and swinging early in the count, so the low pitch plate appearances might show a higher slugging average.

What about unusually long at bats? An extended plate appearance can only be prolonged by foul balls, as no more than five pitches in a plate appearance can be non-fouls. Does repeated fouling off of pitches indicate a batter who is unable to get around on an effective pitcher, or instead is it the pitcher who is struggling, and can't find the speed or location to put away the hitter? Do the odds favor the hitter more as the pitch count increased?

Finally, what pitch length most favors the pitcher, and which most favors the batter?

I looked at all plate appearances from 1988 through 2000 for which I had individual pitch data, a data set that covers 87% of all PAs during that span. I grouped the PAs by the number of pitches, and looked at AVG, OBP, SLG, and OPS as simple measures of offensive performance. I did not attempt to control for park or league factors, nor for differences between patient hitters—who see more pitches per PA, and thus represent a higher fraction of the sample at higher number of pitches—and impatient hitters, who are proportionally represented more in the lower pitch totals. I used a cutoff of 500 plate appearances of a given length over the years covered to be significant, although I show the entire table below.

Pitch #      PA    AVG  OBP  SLG   OPS
  1     286,695   .323 .316 .497   814
  2     334,951   .319 .316 .491   807
  3     340,944   .267 .269 .411   681
  4     371,885   .227 .333 .346   678
  5     304,844   .215 .346 .333   679
  6     193,051   .211 .374 .326   700
  7      79,250   .223 .405 .354   758
  8      29,939   .231 .418 .370   788
  9      10,797   .237 .427 .392   819
 10       3,743   .229 .419 .379   798
 11       1,393   .258 .442 .438   880
 12         515   .290 .485 .491   976
 13         176   .242 .426 .394   820
 14          61   .239 .368 .391   760
 15          28   .222 .464 .778  1242
 16          11   .333 .455 .778  1232
 17           4   .500 .750 .500  1250
 18           2   .000 .000 .000   000
 19           1   .000 .000 .000   000
 20           1   .000 .000 .000   000

Everyone who guessed that four pitches was the best PA length for pitchers (678 OPS), and 12 the best for batters (976 OPS) can go to the head of the class. The 3-5 pitch range was actually pretty equally favorable for pitchers, bringing in a sub-700 OPS. Offense was pretty high for the first couple of pitches, then dips sharply before slowly recovering over longer and longer plate appearances. The chart below makes this easier to see.

The first two pitches are more than 100 points of OPS better for the hitter than pitches three, four, five, and six. Slugging, in particular, dips sharply, almost 175 points worth between one-pitch PAs and six-pitch PAs. Batters start to gain ground again at the seven-pitch level, and have equalled their production when putting the first couple of pitches in play once the plate appearance goes for at least nine pitches.

Contrary to the traditional sabermetric support for patience, seeing such a swing towards the pitcher suggests that aggressively going after pitches early in the count may be a viable strategy for some hitters. We'd really need to do a much deeper analysis, though, to see how individual batters perform in varying length plate appearances before concluding anything along such lines.

As expected, batting average and on-base percentage match closely until four pitches, and we see a steady rise in OBP thereafter, indicating that long at bats start to turn the batter's way. Curiously, even slugging rises after a while, and more than can be explained by the rise in batting average alone. Perhaps a batter gains an advantage after having seen several pitches from the same pitcher in quick succession, allowing him to time his swing, or recognize the type of pitch earlier in its delivery. Or, as speculated earlier, maybe the inability to retire a hitter in six pitches indicates a tiring pitcher, or one struggling with his command.

This chart is only a reflection of what has happened, and can't be used to directly infer causality, so we don't know which alternative is true. We can, however, note the break point between the outcomes at two and three pitches, where we see the sharpest decline in aggregate OPS.