The foul ball, part three: What does it tell us about an at-bat?

In part one of this series on foul balls, I took a look at what they say about batters.  In part two, I looked at what foul balls say about pitchers.  Now, let’s take a look at what the foul ball tells us about an individual at-bat.  After all, baseball is a series of at-bats.  They are the game within the game, in which a batter and a pitcher square off in individual combat.  But, what does a foul ball tell us about the chances that a batter or pitcher will complete his mission during an at-bat (recording/not making an out)?  When you see a foul ball, should you be encouraged or discouraged?  Is a foul ball just another swinging strike?
I took my data base of all plate appearances from 2000-2007 (thanks Retrosheet!) and looked for the answer to that question.  I looked at how the ball-and-strike count progressed in each plate appearance, specifically whether the strike had been recorded by way of a foul ball or a swinging strike or (since I was in the neighborhood anyway) a called strike.  Of course, anything that produces a strike is bad news for the batter, but perhaps not all strikes are created equal.  A foul ball can only produce a strike if the count before the pitch had 0 or 1 strikes, so I looked only at those pitches (I’ll get to 2 strike fouls in a minute).  That left eight possible counts in which a foul ball could have produced a strike (0-0, 1-0, 2-0, 3-0, 0-1, 1-1, 2-1, 3-1).  I looked at all cases in which any strike had been produced whether by foul ball, swinging strike, or called strike and the resulting OBP of those plate appearances.  Before starting, I took a look at the expected OBP that would result from the batter/pitcher matchup in play (using the odds ratio method, since OBP is a probability number) for the purposes of making sure that my groups were roughly equal.  I used seasonal OBP’s as my baseline.
Let me show what I did by using an example.  I took a look at all plate appearances in which the first pitch (a 0-0 count)  ended up as a strike on the batter (so, now a 0-1 count.)  I tallied up how that strike managed to get there, so that it created three “baskets” of plate appearances (called, swinging, foul).  I should also note that I only used plate appearances in which a batter with 250+ PA in that season faced a pitcher with 250+ BF in that season.  First, to make sure that the baskets were roughly equal (batters/pitchers who swing at/induce more swinging strikes might have higher/lower OBP’s/OBP’s allowed than batters/pitchers who… ah you know what I’m getting at.)  The overall expected OBP for the three groups were called strikes: .332, foul balls: .329, and swinging strikes: .326.  This pattern actually played itself out pretty consistently.  The overall expected OBP for those who took a called first pitch strike was usually a little higher than those who fouled off the first pitch which was higher still than those who swung and missed.  However, the differences were never massively huge and at their greatest, there was a spread of about 7 or 8 points among the three groups.
(Methodological note: A plate appearance might be represented in two different “baskets” here.  For example, a batter who takes a called first strike pitch, then two balls, then fouls off strike two would be in the 0-0 called bin and the 2-1 foul bin.  Such is life.)
What then came of those plate appearances with the first strike?  The actual OBP for the three groups were:

• Called strike: .287
• Foul ball: .295
• Swinging strike: .263

The most important pitch for a pitcher is strike one, but how he does it is worth 32 points of OBP!  A ball would certainly be a better outcome for a batter (plate apperances with a 1-0 count have an OBP of .385), but if he’s going to have a strike against him, he’s much better off if he swings and fouls the ball off than if he swings and misses.  I went through and did the same analysis for all of the other eight counts in question.  The results:
count                     if called   if foul   if swinging
0-0                         .287        .295     .263
1-0                         .321        .329      .308
2-0                         .404        .407      .397
3-0                         .585        .596      .597
0-1                        .219         .233      .199
1-1                        .248         .256      .227
2-1                        .315         .322      .287
3-1                        .458        .486      .442
If the batter swings, the simple act of making contact and hitting it foul signals a much better outcome for him, often on the order of 20-40 points worth of OBP, even though the result of that swing (a strike on the scoreboard) is the same.  The only notable exception is a swinging strike on a 3-0 is a little better than a foul ball.  At 3-0, the batter is in a good position no matter what he does.  Then there’s the matter of called strikes.  A called strike is consistently better than a swinging strike, but worse than a foul ball, although usually closer to the foul ball.  A strike is not a strike is not a strike.  You ignored the poor foul ball all this time, but it’s been trying to send you a message.  It’s important to pay attention to not only what the count is, but how those strikes got there. 
What of two-strike foul balls?  The rules, of course, change and a foul ball at this point doesn’t affect the count.  A swinging strike or a called strike on a 2-2 pitch will result in a .000 OBP.  Does fouling off a two-strike pitch increase the chances that a batter will get on base?  What about spoiling multiple two-strike pitches?  In part one of the series, we saw that two-strike foul balls (at a seasonal level) were generally associated with different types of hitting outcomes (more singles, fewer HR), but weren’t really connected to OBP.  Does that finding still hold?
Again, I isolated all plate appearances in which there was at some point a count of 0-2 or 1-2 or 2-2 or 3-2.  I then counted up some foul balls that happened after that point.  I struggled with exactly how to compare apples-to-apples in this case.  Foul balls hit during the count in question, (i.e., foul balls only when the count was 1-2) solves the confound that different counts have different expected OBPs.  However, it doesn’t account for the fact that the mindset might be not so much focused on the count, but on spoiling as many pitches as possible and waiting out the balls and/or waiting for a good pitch to hit.  In that case, the better way to look at it would be foul balls from that point onward after that count had been reached.  (So, from the point of having a 1-2 count, if a batter fouled one off, took a ball, then fouled two more off on 2-2, that would be three fouls.)  I coded things the latter way (split it into zero fouls, one, two, and three-plus).  For fun, I did it the other way (not shown here), and the base conclusions didn’t really change.  Again, I first checked for the expected OBP based on the batter/pitcher match-up, and the differences were negligible.
Count    0 fouls   1 foul   2 fouls   3+ fouls
0-2        .209       .264    .231       .253
1-2        .235       .266     .279       .282
2-2        .307       .313     .314       .312
3-2        .468       .467     .451       .482
If the batter is fouling off two-strike pitches after being behind in the count, it means that he’s more likely to get on base (even though that effect is not linear with more fouls predicting higher OBP).  But after the count evens, there’s no particular advantage to fouling off a lot of pitches.  Seems like that even if the batter is behind in the count, if he’s still at least making contact, it’s a good sign.  However, the effects don’t seem to grow by huge margins when the batter spoils multiple pitches.  Talk of the pitcher having to “show” the batter extra pitches and this being a net gain for the batter doesn’t seem to hold water, at least as far as this particular batter being able to get on base in this particular at bat.  A lot of foul balls do, however, extend the pitcher’s pitch count, which might be helpful later in the game.  But, too often, commentators say that the batter is having “a good at-bat” if he fouls off a lot of 2-2 and 3-2 pitches.  In fact, he’s not likely to be having a better or worse at bat in terms of his result than if he hadn’t fouled those pitches off.
So, what have we learned in our examination of the foul ball?  First off, they matter.  A foul ball may count as a strike, but that’s not totally fair.  If it were just another strike, there wouldn’t be such major discrepancies between foul balls and called and/or swinging strikes.  It’s odd because a case can be made that the foul ball is something that’s positive for both the pitcher (it counts as a strike, and strikes are good) and for the batter (it’s not as damaging as other strikes).  A batter is better off if he collects balls, or perhaps home runs, and a pitcher is better off if the batter can’t touch his stuff at all.  But, it speaks to the importance of getting beyond simply counting balls and strikes.  In order to really understand a batter, a pitcher, or a plate appearance, it’s important to know how those strikes got there.  And you thought it was just a souvenir.