How do you know that the feat is making you hit less often unless you do the maths?
Well... you are sitting there, aren't you... or maybe you are pacing nervously as you roll the dice,... and the DM says, "you miss." That's a give-away you see. Or, what we gum-shoes in the business like to call "a clue."
But...the real clue is, and this is clever,... when the DM starts saying, "You Miss again." That "again" is a real dead-on ringer. A clincher that tells you all is not as it should be. When you hear that, "Again," you know that you're attacks are perhaps less effective than one might expect.
Though, even then sometimes there is doubt. But you know for sure something is up when you roll a 19 on the dice and the DM says, "And yet again, you miss, as you focus more on trying to do damage and less on getting through his defenses." Generally, if you have reached that point, the savvy player, keen and sharp-witted, knows that maybe he should stop using Power Attack. Unless of course he is confident that he can actually roll a 20 next round and then sometimes maybe, despite all his instincts
(and his mates around the table shouting "No you fool!"), he might give it another go.
Or, rather, given that the feat has to be declared before the dice are rolled, of course it is making you hit less often than you otherwise would. The trade off is increased damage. How do you know if the trade off is worthwhile without doing the maths?
If the answer is "rely on intuition" then I don't think that's a very good answer, because in my experience most people's intuitions involving probabilities and expected outcomes aren't that robust.
Maybe I just play with a higher grade of intuitively capable mathematicians than you do?
What sort of calculus, I wonder, does an outfielder do as he is running to catch the high fly ball, to figure out where the arc of the ball is going to take it?
But, as for whether using the feat is worthwhile, or not, sometimes you only know by giving it a try... That suspense in resolution is, some people think, part of the fun of the game. Apparently there are others who prefer using calculators to anticipate whether or not a given move is going to produce the results desired. I have yet to play with many of these souls, but I will take your word for it that they are out there.
If the point of the feat is to boost damage, just give a damage boosting feat.
Ah, but that's not the point of the feat now, is it.
The point of the feat is to offer a trade off in in return for a
spike in damage.
The Weapon Focus feat is the feat, as I think I mentioned before, which is the base damage boosting feat (and it works just fine for that). If you want to offer even more damage then the base-line of Weapon Focus, there must be something sacrificed elsewhere. Its a pretty basic concept in mechanical balance and it works just fine with Power Attack.
As to why I say it plays on the maths of the system, and is therefore metagamey, it simply trades on the fact that D&D separates the to hit roll from the damage roll. Which is not modelling anything in the fiction but is just an artefact of the mechanics.
Huh? I have vague memories of going down this road before with someone - might have been you, but the argument makes no real sense to me. I model the fiction via the mechanics just fine. Thank you and all, but that road seems to lead far afield and lets not go there shall we.