I probably shove AK pre-flop more than anyone here. I play it pretty standard from LP, but almost always limp it in EP with the intention playign ABC if I hit in an unraised pot or pushing an LP raise from anyone other than a player with very low PFR.
It just sucks to play post-flop with AK in a raised pot OOP so I avoid doing it. If a player who has say 3% PFR raises and it comes back to me, I'm quite happy to drop AK for 1BB then and there. If a typical 25/15 TAG raises OTB, I shove.
Of course I buy in for 60BB and tend to play short sessions so I do spent more of my time than most of you guys less than full stacked. I feel the shove is really strong in the 50-80 BB range as you are gaining a lot of fold equity. Over that you are mostly just increasing the downside if he does have AA or KK. Obviously this a better used as short-handed strategy.
I am running at 2.1PTBB/hand with AKo in my current DB (8 months play at 6 max about 70k hands). I don't know how good that is compared to other players here, but I do know it's a lot better than my old AK stats.
What would be interesting would be to see other's AK stats and details of stakes and handedness played when they post their strategies. It's good to have some empirical data to look at when we're discsussing tricky stuff like how to play AK.
As for maths of a push - there is some in the AKs v LAG post a couple of threads below.