THE BOOK--Playing The Percentages In Baseball

Tuesday, August 04, 2009

Continually fouling-off 3-2 pitches

Sky takes a look:

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.

In the face of fantastic work, I have no idea why Sky would be quoting batting average, especially considering that it’s a 3-ball count, meanings TONS of walks.  Let me restate Sky’s work:
0 foul balls: 465 OBP, 373 SLG, something like .403 wOBA
1: 461, 384 = .405 wOBA
2: 496, 432 = .442 wOBA (on 2500 PA)
3: ?
4+: 414, 312 = .352 wOBA (on 599 PA)

How many SD is the PA that end after 2 foul balls from the 0 foul balls one?  That’s 3.7 SD, making the non-zero difference highly significant.  That does NOT mean that the true difference is 39 points.  It only means that we’ve strongly sure it’s not zero.  How about with 4+ foul balls?  That one is 2.4 SD, going the other way.

At this point, I’d like to know the talent level of the batters and pitches involved, and I certainly need to see something other than “batting average”, whatever that metric means.

Also, it is not the “at count” that we want, but the “through count”.  The question is not “given that the at bat ends after 2 foul balls, what happened?”.  The question is “given that the at bat has already gone through one foul ball, what happens after that?”.

Finally, I’d like to know the rate of foul balls after each time the batter fouls off a pitch.  For example, if the number of foul balls the first time the batter enters a 3-2 count is 25%, then what is the foul rate after already fouling one off?  And after fouling two off?  Etc…