[Foucault]

I don't see the value of such a formula. It really depends on what you are trying to accomplish with your re-raise, on your read of Villain, on your history with Villain, on stack sizes, etc. A quick sampling of things I might be trying to accomplish with any given re-raise:

1) Re-steal. I'm looking to take it down pre-flop first and foremost, but depending on stack sizes, I am also thinking about whether I can get away if Villain/anyone else comes back over the top and whether effective stack sizes will allow Villain to fold some flops if he flat calls.

2) Pot commit myself without revealing my hand. Sometimes I will re-raise a smaller amount than all-in, even though I am clearly committed to getting my whole stack in at some point, with a hand like AK just because I think it gives me slightly better fold equity against small pairs that don't expect an overbet push from AA/KK. The immediate odds I am offering Villain aren't all that relevant here because in actuality he will be committed to calling for the rest of my stack eventually, and if he chooses to fold then, he is making a FTP mistake, which is fine by me.

3) To induce a mistake later. A smallish re-raise with a big pair may induce a call from a broadway hand like KQ or AQ that, while technically correct, will result in a bloated pot and prevent them from getting away from top pair.

4) To establish myself as the aggressor. A pre-flop re-raise may allow me to win the pot with a c-bet on a flop that missed both of us, where a call would allow Villain to win the same pot. Often these will be coin flip situations or even spots where I am dominated, so re-raising more will not result in Villain making a bad call, and may even be -EV for me.

It seems like you are considering only situations where you are re-raising for value, and even then a formula may not be that useful, as ideally you'd size such re-raises to match the sort you are making for the above purposes. Finally, remember that you pick up EV when Villain makes bad folds just as well as when he makes bad calls, and many players play way too tight against re-raises.