You've probably heard your local announcer say it at one time or another after a hitter has fouled off pitch after pitch on a 3-2 count: As the at-bat is extended the pitcher has to show more of his arsenal, and the advantage shifts to the hitter. In this week's article, the last in a series which has analyzed baseball by the count, I check in to see if this is true, or if it's simply one of baseball's old wives tales.

While obviously the hitter helps himself by fouling off pitches to stay alive rather than striking out, it's unclear if a hitter really gains by extending the at-bat, or if he just puts himself back in the same position on the pitch before. I remember watching a Cubs-Dodgers game in 2004 when Alex Cora battled through an 18-pitch, 13-minute at-bat to eventually hit a home run off Matt Clement. Did Cora gain an advantage by fouling off so many pitches, or was he just as likely to hit that home run on the first 3-2 pitch of the at-bat? Or on the other hand, was his home run even more unlikely due to the mental and physical drain or fouling off so many pitches?

Who Has the Advantage?

While there aren't many data points on 18-pitch at bats, I used 2007 retrosheet data to take a look at this question (removing intentional walks and at-bats with bunt attempts, pitchouts, etc). Focusing just on the number of foul balls with a 3-2 count, I looked to see whether hitters who fouled off a lot of pitches really did fare better than those who resolved the at-bat soon after it reached 3-2. The table below shows how hitters fared after various numbers of 3-2 foul balls.

The result shows that there is some truth to the old wives tale, but does not back it up whole-heartedly. At-bats that resolved after the count first reached 3-2, made up the majority of the data. These batters hit .225 with a .465 OBP and a .373 SLG average. This was virtually identical to the numbers hitters put up when the count resolved on after one foul ball. The numbers there were .229/.461/.384.

However, we start to see the myth become reality after two foul balls. When the at-bat is resolved after two fouls, we see a dramatic increase in all three key measures, with the numbers measuring .260/.496/.432. With over 2500 PA's in the sample, this was a statistically significant difference from 3-2 at-bats that resolved earlier. The standard error of BAV and OBP is approximately 10 points. When the at-bat gets to this point, it appears that the batter does indeed gain an advantage as conventional baseball wisdom would suggest.

However, these numbers decrease again after 3 fouls, and after the 4 or more foul balls, they decrease sharply, with batters putting up a .201/.414/.312 line. In this case, only 599 plate appearances contributed to the data, so the standard error is fairly high at 20 points, making the difference from the average 3-2 count BAV not quite significant. The differences in OBP and SLG however, are significant, showing that not only does the batter not gain from a long at-bat, in fact, it is the pitcher who earns the advantage.

At this point you may be wondering if perhaps there was some sort of selection bias. Perhaps good hitters simply don't foul off pitch after pitch, so this is the reason that we see the difference results. As a matter of fact, this isn't the case. The chart below shows virtually identical overall batting averages for the hitters in each of the situations.

0 Foul Balls: .269
1 Foul Balls: .270
2 Foul Balls: .271
3 Foul Balls: .270
4+ Foul Balls: .271

If there were selection bias, we would expect there to be a different quality of hitter in each situation. Since we don't see this, we can be reasonably confident in the above results. Conventional baseball wisdom is right: Fouling off pitches does favor the hitter - but only to a point. Four or more fouls sees the pitcher re-take the advantage for the remainder of the count.

Why?

The results are basically that after two foul balls, the batter does indeed gain the advantage, but after four or more fouls, the pitcher has the edge. However, why this is the case is unclear. The pitcher "showing all of his pitches" argument could be a factor in why the hitter has the advantage after two foul balls. However, why would that advantage decrease after four fouls? Perhaps this is simply an indication that the batter is struggling against a pitcher and not getting good swings against him. Rather than being the cause of decreased plate performance, it may instead be a sign of decreased ability to get a hit. Since there are no randomized experimental trials in baseball, it's difficult to tell.

Thinking back to the Cora at-bat, I wonder if this result is not unexpected. Part of the reason his at-bat was so incredible was the fact that it went on so long, but part of it was the fact that, after all of it, he actually hit a homerun. If batters really gained the advantage during a long count, then we would not have been surprised to see a home run, or at least a hit, after so many foul balls. Instead, people were calling it an amazing and incredible plate appearance. Had Cora struck out, we likely would not have heard much about the amazing pitching performance by Clement to get a strikeout after so many of his good pitches were fouled off - in fact it feels as though the strikeout would be more expected.

This intuitive expectation is backed up by the data. The batter gains an advantage up to a point, but after four fouls or more, it's clear he is just staying alive and is more likely struggling against the pitcher rather than building an advantage. The probability of a making an out is increased and his walks and power and decreased dramatically.