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The last Aim for the Head,
about how offensive production varies with the number of pitches in the plate appearance,
generated a lot of questions. Let’s dig into the mailbag:

Ted Frank wrote:

Excellent article. One thing missing, though.

Of course BA is going to go down from the second pitch through the sixth; the more pitches, the more likely the batter is going
to have two strikes on him in the count (0% at 2; approx. 30-35% at 3; and so on up to 100% chance on the sixth and after, with
probably the biggest jump between pitch #2 and pitch #3), and the more likely it is that he is going to strike out.

What happens to batting average when you omit the strikeouts from pitches 3 through 20? (I.e., what’s the batting average for
balls put in play?) One would still expect it to go down from pitches #2 through #6 for the same reason (more two-strike counts
forcing the batter to protect the plate), but not as steeply.

It was interesting that first-pitch hitters are essentially identical to second-pitch hitters; the advantage of the 1-0 count
almost exactly counteracts the disadvantage of the 0-1 count apparently.

Many people brought up the point that strikeouts can only kick in at three pitches, and walks at four pitches. I did mention
this in the beginning of the article, but the fact that so many people felt compelled to write in about it indicates that I
didn’t call it out sufficiently when discussing the results.

Per many requests, I’ve recalculated the rates of production removing strikeouts, walks and hit batsmen from the totals, which
are presented below:

Pitch        PA     AVG     OBP      SLG      OPS
 1       283842    .323    .309     .497      806
 2       332025    .319    .310     .491      801
 3       288149    .317    .311     .488      799
 4       234588    .317    .312     .481      793
 5       174877    .318    .314     .491      804
 6       102105    .320    .317     .494      811
 7        41782    .327    .324     .517      841
 8        15910    .331    .327     .530      857
 9         5806    .333    .329     .551      880
10         2038    .317    .314     .525      839
11          760    .357    .352     .605      957
12          269    .404    .401     .683     1084

Removing strikeouts and walks accounts for nearly the entire change in production for at-bat lengths three and four pitches,
although it’s interesting to note that four pitches is also the length with the minimum OPS both with and without strikeouts and
walks. Still, the variation across pitches 1-6 is very small, indicating that the length of the plate appearance generally has
little to do with how effective the batter is when putting the ball in play in most cases.

However, we also see, as in the overall data, a gradual increase in OPS as the length of the PA increases. And since this takes
strikeouts and walks out of the mix, this suggests that batters who have seen a lot of pitches may be able to hold out for a
good pitch to hit, or that they are becoming accustomed to the pitcher’s repertoire. It’s also possible that such plate
appearances are skewed towards better overall hitters, and are proportionally overrepresented in the sample.

C.W. writes:

Excellent work on the number-of-pitches analysis.

How about the number of number of pitches vs. inning of the game? It seems to me the longer at bats occur towards the end of a

I grouped all plate appearances by inning, and considered it a long plate appearance if the batter saw at least seven pitches. I
computed the average length of a plate appearance, and the percentage of all PAs that were long.

INNING      PA     LONG PA   %LONG   AVG_PIT   AVG     OBP     SLG     OPS
1       247473      16264    6.57%     3.85   .273    .346    .420     766
2       238237      13897    5.83%     3.71   .255    .317    .394     711
3       242647      13539    5.58%     3.65   .266    .328    .410     738
4       243417      13260    5.45%     3.59   .269    .331    .425     755
5       243169      12962    5.33%     3.57   .268    .328    .416     744
6       245253      13518    5.51%     3.60   .270    .334    .423     758
7       244368      13614    5.57%     3.63   .263    .330    .406     736
8       243416      14307    5.88%     3.68   .257    .326    .394     720
9       184213      11166    6.06%     3.72   .248    .316    .375     691

We’ll look at long plate appearances in a moment, but take a look at the OPS column. While there’s not a consistent trend, there
are patterns that we can relate back to the way the game is played.

For example, the highest OPS posted is in the first inning, which is the only inning in which a team is guaranteed to have their
top of the order batting. Similarly, the ninth inning is quite a bit lower, most likely due to the use of closers. The
second-highest OPS is in the sixth inning, and the fourth through sixth innings in general are higher than the surrounding
innings. This is probably due to two effects: pitchers tiring and getting hit harder in the middle innings, and mop-up or
long-relief pitchers, who tend to be the less capable pitchers on a team, getting work.

But enough digression. C.W.’s question was about whether longer PAs occur towards the end of the game. In fact, the highest
average length, and the highest percentage of long plate appearance come in the first inning, which is a manifestation again of
the top of the lineup batting. Perhaps some of the effect comes from batters taking more pitches early on to see what the
pitcher has working that day. But the ninth inning has the second-highest number in both categories, so it doesn’t appear that
we have a straight linear effect here. Let’s graph %LONG and AVG_PIT by inning to see if that reveals anything:

What we see is not so much that long plate appearances come towards the end of the game, but rather that the middle of the game
has decidedly shorter plate appearances than either the beginning or the end. So while C.W.’s intuition is partially true,
you’re even more likely to see long plate appearances when the game first begins.

B.L. writes:

You’re kidding, right? That was a really, really interesting article-and thanks, by the way, for writing it-but you’re really
going to leave out the one point of trivia that every BP reader is undoubtedly dying to know? As silly and inconsequential as it
is, as unimportant for its implications for your study, you nevertheless determined that in 12 years there were exactly two
at-bats with 19 or 20 pitches. Aren’t you going to tell us which two batters and which two pitchers were involved?

"Who had the 20-pitch plate appearance?" This was the single most common question I got, and some of the requests were
more desperate than B.L.’s plea. Sure, I could have mentioned it in the original article, but it’s much more fun to keep you
hanging, and wanting more. Well, I won’t keep you hanging anymore… the 20-pitch at-bat occurred on June 26, 1998. Bartolo
was pitching to Ricky Gutierrez with the Indians leading the Astros 4-2 in the eighth inning with none out in

Strike 0-1
Strike 0-2
Foul 0-2
Ball 1-2
Foul 1-2
Ball 2-2
Foul 2-2
Foul 2-2
Foul 2-2
Foul 2-2
Foul 2-2
Foul 2-2
Ball 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Strike Strikeout

An 0-2 count, and just 18 pitches later, strike three. It took 13 pitches to make it to a full count. This single plate
appearance represents 18% of all the pitches Colon threw that day.

The 19-pitch at bat occurred on July 23, 1988 with Steve Bedrosian pitching to Kevin Bass,
Astros and Phillies tied at six with two outs in the eighth inning.

Foul 0-1
Ball 1-1
Foul 1-2
Ball 2-2
Foul 2-2
Foul 2-2
Ball 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
Foul 3-2
In Play Flies out to left-center

Eleven straight foul balls. That’s more consecutive pitches fouled off than 99.8881% of batters see in their entire plate
appearance. Bedrosian faced 10 batters and threw just 52 pitches in this relief appearance.

Lastly, here are some other trivial notes I have about long plate appearances (1988-2000):

  • Most pitches in a plate appearance not ending in an out: 17, done three times

    Chris Hoiles walks against Jim Abbott on May 5, 1991
    Pat Listach walks against Ron Darling on September 26, 1992
    Darren Bragg singles off of Brad Radke, June 16, 1995

  • Most pitches in a plate appearance ending in an extra-base hit: 16, done twice

    Jermaine Dye homers off of John Wetteland, May 22, 1998
    Karim Garcia doubles off of Mike Munoz, June 2, 1998

  • Most pitches in a plate appearance ending in a hit-by-pitch: 13

    Edgar Martinez hit by Chuck McElroy, July 12, 1996 (tenth inning)

  • Longest first-inning plate appearance: 18 pitches

    Bip Roberts grounds out to second against Felipe Lira, May 18, 1997

  • Longest ninth-inning plate appearance: 18 pitches

    Brian Downing lines out to second base against Ken Patterson, September 1, 1990

  • Longest extra-inning plate appearance: 15 pitches, done twice

    Kevin Jordan line out to center against Dennis Cook, July 19, 1998
    Jack Howell walks against Bobby Thigpen, April 6, 1988

Keith Woolner is an author of Baseball Prospectus. You can contact him by
clicking here.

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