Is All Fair in Love and WAR?: The Importance of Hard-Hit Foul Balls

Even in this case, strikeouts occurred less often after barreled fouls, as 29.0% of at-bats with a singular, barreled foul (there were 607) ended with the batter taking the long walk back to the dugout, while 32.3% of at-bats with a sole, non-barreled foul (there were 47,987) did.

Why might strikeouts follow barreled fouls less often? Well for one, as the first scatterplot above demonstrates, hitters who barrel fouls at high rates also typically barrel their balls in play at high rates; in other words, they’re usually more fearsome hitters, and they are more likely to be pitched around. But it’s possible they are also being pitched around because they just hit the snot out of a pitch, even if the batted ball in question landed out of play. To add yet another layer, what if there isn’t any pitching around at all, and the pitchers who give up more foul barrels are just more wild in general/don’t throw in the zone as much?