The thing is neither is actually a meaningful indicator of a 3+ run inning and that's why this thread is a little weird (JMO and interesting, but still weird). The HR wins, because a 2 run inning is more common than a 3 run inning, but neither is a good enough indication, especially in relation to the other - they're both good signs for your offense - that a big inning is coming. I think a 2-3 batter sequence is a better discussion: like HR, FB, 1B vs. BB, 2B, sac, but the single AB, the differing outcomes pale in comparison to the specifics of the instance. Who's the pitcher? Who'd they walk/give up a HR to, what's the inning/score, etc...
While there may be ways to "tango" it out (BTW isn't .555 run expectancy for every opening of an inning high?), I cannot believe it would be an overly meaningful number as to which event is a better indicator of future events. Either one could be a symptom of a struggle beginning or just one bad pitch or even just an semi-intentional work around. I'm a stat guy almost as much as the next guy (well in a baseball or polling number context), but I think this is the point where we piss off the purist old-schoolers. Ask yourself, at what point do you feel a big inning coming on? I've felt it after a lead-off HR and a lead-off walk, but they're both so contextually contingent. It's not that my superstitions are more accurate than whatever probability matrix, but we're in it's 65% right 14 times out of 19, which is another way of saying coin meet flip.
But please remember, my maths ended quite some time ago, so if anyone wants to outmath my feelings, I'd actually be quite pleased.
