The Memory Remains

We often hear about pitchers setting up batters, changing eye level, throwing pitches out of the zone, pitching backwards, etc. Instinct and reaction are of utmost importance in catching, throwing, and hitting, but pitching is deliberate. First pitch strike? Inside or outside? Fastball or offspeed pitch? And after that?

Pitch sequence is something that Heater Magazine’s John Burnson investigated in the Hardball Times 2007 Annual (makes a great Christmas gift!). Primarily, he looks at whether the batter’s propensity to swing at a pitch depends on the pitch sequence and not simply the count. John’s far more eloquent than I, so I’ll just quote him here:

We students of baseball often find it helpful to present our findings in tables; however, tables exult states. If baseball players have memory (and they seem to), then tables might hide a good deal of nuance.

He’s right. With splits easily available on ESPN or Yahoo! Sports, it’s a little bit easier to get some numerical insight on the importance of pitch sequences. For example, everybody remembers their Little League coaching stressing the importance of getting ahead in the count (unless you were me, in which case the coach stressed the importance of not picking your nose in right field). And, indeed, the old coot was right: in 2005, National League hitters hit .236/.275/.366 after a first pitch strike, compared to .262/.330/.414 overall. Throwing a first-pitch strike is a good thing.

But what happens when the count evens up? NL 2005 hitters went .250/.313/.390 after a 1-1 count. A-ha, you say, the first-pitch-strike advantage has been squandered. The problem is that this particular statistic focuses on where the count stands and not so much on the direction in which it is travelling. A 1-1 count can come about in many ways: foul, ball; ball, called strike; swinging strike, ball, etc. Is a 1-1 count simply a 1-1 count, or is there an underlying aesthetic to the path taken?

(A note on the data: For the rest of this article I’m going to focus on the 2005 National League as a model system. I’d like to give you a good reason why the entire Major Leagues isn’t being considered, or why only 2005. Unfortunately, the answer is simple and not very sexy: Excel can only fit 65,536 rows of data onto a single worksheet, and the NL alone had over 97,000 plate appearances. I needed two worksheets just to do the NL, and any more would have become cumbersome (or forced me to write a computer program). Clearly Bill Gates and friends weren’t thinking about baseball when they designed their software.)

An Even Count

Consider the above case of the 1-1 count. When the first pitch is a ball and the second pitch a strike (called, swinging, or foul), batters have a line of .243/.312/.378. Curiously, batters perform better when the all-important first pitch is a strike and the second pitch is a ball; they hit at a .257/.314/.402. That’s a 25-point difference in OPS; not world-breaking but statistically significant (p<0.001 for you stat wonks) nevertheless. The path taken to reach the 1-1 count is important: better to throw a first-pitch strike in general, but better to throw a second-pitch strike if the count is going to 1-1 regardless.

Memory, of course, fades as time passes, and it’s a natural hypothesis that this difference in performance based on path is tied to the first pitch following the 1-1 count. When the third pitch is put into play (including home runs but excluding foul balls), batters hit .318/.501 (AVG/SLG) (OBP and AVG are the same in this situation because the ball is being put into play and there is no opportunity to draw a walk For comparison, the aggregate AVG/SLG on balls in play is .329/.532.) But path is very important here: if the 1-1 count is the result of a first-pitch strike and second-pitch ball, batters hit .336/.528. If, however, the first pitch was a ball and the second pitch a strike, batters only managed .299/.472. That’s a pretty big difference, and tests for statistical significance indicate that this difference is real. To summarize:

Situation	                   AVG	OBP	SLG
After 1-1 pitch			
   First pitch strike	.257	.314	.402
   First pitch ball	.243	.312	.378
Ball in play on 1-1 pitch
   First pitch strike	.336		.528
   First pitch ball	.299		.472

In turns out that the large difference in performance on the third pitch accounts for most of the difference in performance for the plate appearance as a whole. That is, the memory of the first two pitches in a plate appearance affects performance most on the third pitch and less so on subsequent pitches. Duh.

So what’s going on? I’m not totally sure, but I’m not above guessing. In the case where the first pitch is a ball and the second a strike, there may be a psychological advantage for a pitcher to having just thrown a strike. Perhaps it proves to the batter that the pitcher can hit his spots. The batter becomes more aggressive on the next pitch and doesn’t make good contact. Conversely, in the case where the first pitch is a strike and the second pitch a ball, the second pitch may be the result of a pitcher missing his spot. The pitcher responds by throwing a cookie on the subsequent pitch in an attempt to regain his control. It may be true in general – I haven’t checked – that batters have more success on pitches following balls than pitches following strikes (if indeed that’s true, then we have the somewhat mundane conclusion that it’s always better to throw strikes). If there are readers who are familiar with the psychology of pitching or hitting, I’d love to hear your thoughts. I never played competetive baseball past cookies and Capri Sun, so I don’t exactly have first-hand experience to draw upon.

Details, details

There are some additional details. For example, there is a difference among called strikes, swinging strikes, and foul strikes:

Ball in play on 1-1 pitch	          AVG	     SLG
   First pitch swinging strike	.303 	.486
   First pitch called strike 	.338 	.532
   First pitch foul strike           .346 	.528
   Second pitch swinging strike	.261 	.367
   Second pitch called strike 	.290 	.452
   Second pitch foul strike          .328 	.472

Swinging strikes do not bode well for the batter, whereas foul balls are a harbinger of good offense. This is an interesting subtlety, but probably not all that informative. Good pitchers are generally adept at generating swing-throughs, so it is probably no coincidence that at-bats in which there is a swing-through result in better outcomes for the pitcher. On the other hand, when the batter fouls the ball off, he’s at least making contact and likely getting his timing down; it’s no surprise that sequences where the strike is from a foul ball correlate with a better offensive outcome. These are interesting details but probably reflect the overall skill of the pitcher (or the relative skill of the batter-pitcher combination) and not the pitch sequence itself.

Anybody who’s watched Greg Maddux throw the ball knows that pitch sequence, and not just count, has an affect on the outcome of plate appearance. But whe we talk in numbers, as John Burnson noted, we focus on states and not on stories. In the case of the 1-1 count, at least, the story matters. There is a memory effect from the first two pitches, one that’s strongest when the batter swings on the third pitch and one that depresses offense when the previous pitch is a strike. Life’s a journey, not a destination, goes the old adage. One might say the same about pitching.

References & Resources
Pitch-by-pitch data was gathered from the incomparable Retrosheet. I’m obligated to say the following: the information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at “www.retrosheet.org”. I am not obligated to say the following (it comes from the bottom of my heart): Retrosheet is the greatest thing to happen to mankind since H. Habilis defeated the dinosaurs.

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