What actually happens after an IBB?
Dave Cameron provided some good research here
Looks like hitters don't typically hit that well after an IBB
There are certainly times when the IBB does backfire, and I wouldn’t use this data to suggest that the IBB is always the correct decision. There is a real cost to giving the opponents an extra baserunner, and there needs to be a substantial increase in likelihood of getting an out in order to offset the larger potential for an extra run to score from giving the opponent a free baserunner. However, I do think the data suggests that IBBs do serve a strategic function, and can reduce the odds of giving up a run in a situation where preventing one run is of the utmost importance.
To those that do not know mathematics it is difficult to get across a feeling as to the beauty, the deepest beauty of baseball. If you want to learn about baseball, to appreciate baseball, it is necessary to understand the language she speaks.