Mike Fast at Baseball Prospectus — who seems to consistently produce the most interesting baseball research I read these days — takes his best stab at evaluating the merits of the hit-and-run play. It is, by his own admission, based on imperfect data, but it’s a great read regardless.
For whatever it’s worth, I’ve heard ex-players and coaches praise the hit-and-run as a manager’s means of forcing a struggling hitter’s hand in the right situation. By that thinking, if a skipper feels his player is not seeing the ball or approaching his at-bats well, calling for a hit-and-run when he’s likely to see a strike makes him adjust his approach while simultaneously taking the onus off his shoulders if the at-bat goes awry. I don’t know if there’s anything in there that’s quantifiable or if a manager is actually more likely to call for the hit-and-run with a struggling hitter, but I’ve heard it mentioned frequently enough that I thought it worth noting.