Say what you want about Dibble but he said that Dunn was trying to see more pitches and retrain his eye when he took several walks over the course of several games when he was not hitting. If really want to assume independence, find that probability based on his walk rate of Zim getting that many walks in that few games, it's just multilplication.
Pretty low (though it's not multiplication). Keep in mind that we're not just looking for this result, we're looking for this result and anything higher--this is a common mistake that people make, not realizing that we're looking for exceptional performance rather than this exact one--so it's slightly more complicated than you might think. 31 walks in 128 plate appearances? Assuming a binomial distribution,
P(31 walks in 128 plate appearances) = (128!/(31!(128-31)!) * .114^31 * (1-.114)^(128-31) = .00225484843%
"Aha!" you say, "I knew it was low!" Not so fast--keep in mind that you have to add up
every walk total from 31 to 128. I used Mathematica to do just that:
Sum(i = 31 to 128) P(i walks in 128 plate appearances) = .00364256%
So yes, from a purely binomial perspective--if you assume that in every plate appearance, he either walks or doesn't walk, and the two events are independent--and his true talent during June was a 11.4% BB rate, it is highly unlikely that he would have had a month like that. So chances are good that he had a different plate approach in June. Keep in mind, though, that I don't think this is an ideal statistical method of looking at this, for the same reason that you need a ton of plate appearances to regress batting average--baseball is a very "streaky" sport full of unrepeatable (or only temporarily repeatable) skills. The same system says Zimmerman had a .25% chance of reproducing his September through chance alone, if his true skill were 11.4%, after all. And yet, from year to year, walk rates are correlated really strongly. What that most likely indicates is that in baseball, most skills are not really binomially (or normally) distributed. As TangoTiger points out, major league baseball players are all at the extreme right end of any talent curve anyway, which probably helps explain this. It is also why he recommends
heavy regression for pretty much everything and why announcers who say things like "Dunn is 10 for 20 against
insert pitcher here!" and "he hits well in [insert ballpark that the player has seen maybe 20 times in his career]" are being unreasonable.