Seems like a good question, but my counter would be what is the Alternative (your opponents counter).
For example, if I have 51% battle to attack, what is the counter if I just stand pat and stack? If I can stand pat and the counter is only a 30% success rate for my opponent, why would you risk 51% when you can have 70% on Def?
This happens b/c it is cheaper and easier to defend. Your 1’s (inf), now become 2’s, your 3’s (ftrs) become 4’s, and any multinational forces get to defend as well.
If I’m the Allies, I’ll sit all day on the 50% battles and just wait out my opponent, until I have better odds or my opponent gets impatient. Unless you are seriously down in economics or TUV the Allies can wait all day long. Even an overall 1-2 IPC deficit per turn doesn’t hurt the Allies (not recommended :-) ), it is only when the Axis really approach 90 for a few turns do you have to be worried.
As the Axis, I’ll try to pick my spots better, and would only take a 50% (or less) if it was a desperate Capital shot or something.
I shoot for early position, the economics will come after that if I do my job right in rds 1-4.
By continually taking 51-52% battles over the long run you’re probably going to end up with maybe a 52% win %. I try to limit dice and their effects, it is not necessarily conservative play, but it isn’t “I’ve got 55% to take, lets go!”
You also have to consider the counter attack even if successful. A thin Germany means a thin Russia, this is very good for Japan. German units for Russian units is good (for the Axis), regardless of who does the attacking. Again if you take 51% and do win but all you killed were a bunch of Inf yet you lost 4 arm and left 3 more arm as sitting ducks on a counter attack to ftrs and inf I don’t know why you’d take that attack.
Maybe that is a bit simplistic as well, but all in all I’d only consider an attack with 50% odds if the alternative counter if I stacked was much worse.