Depending on your definition of "account for," a batter could conceivably "account for" all three outs in an inning in just two plate appearances (double play), or even in just one (triple play). But I'm guessing that's not what you mean. I believe Retrosheet's collection of boxscores is still incomplete. Most seasons before 1957 seem to be missing at least a few of them, so the collection is not exhaustive. This blog recalls a player making all three outs in a high school game, but seems to believe it has never happened at the major league level. Since the likelihood of somebody getting up three times in an inning, by itself, is quite remote, I think it's quite plausible that it's never happened.
Does Retrosheet have innings summaries for all games? Most of the modern games have a play-by-play listing, so if you find an inning with 13 or more runs, you could examine the play-by-play results to see who created the outs. For example, by looking at the bottom of the 2nd inning for this game, I can see that three different players created the outs. Or that in this game, 10 runs were scored before an out was recorded in the bottom of the 1st inning.
Since the likelihood of somebody getting up three times in an inning, by itself, is quite remote, I think it's quite plausible that it's never happened. Given that would take a minimum of 19 plate appearances, you only have a 3/19 chance of making one out. So the odds of making all three outs in such an inning are 3/(19^3), I think. And then multiply that by the odds of seeing such an inning to begin with.
Given that would take a minimum of 19 plate appearances, you only have a 3/19 chance of making one out. So the odds of making all three outs in such an inning are 3/(19^3), I think. And then multiply that by the odds of seeing such an inning to begin with. And that assumes that the leadoff hitter makes all three outs. If the leadoff hitter gets on in a big inning (which is probably more likely), then that splits the denominator into some kind of fraction I can't even measure. Chase Utley just finished his climb into another list that mathematicians love -- Exhibit Z in evidence of how truly unbreakable that record is. (I haven't gotten around to that Numbers book yet, Grum, but it's on my list.)
Wow, BullpenPro, that boxscore was a trip back. Look at the pitchers the Angels scored 11 runs on, Catfish, Lightning, and Sparky. And Tanana getting shelled in the 9th. Quite a first game to see. I also agree that while Chase Utley's streak was truly amazing, he was a LONG way from breaking the record, one reason I made this somewhat brazen prediction, heh heh.
