An interesting proposal. Sure is easy to gather the data.
While you’ve already addressed it in your comments, I would mention that luck, in the abstract, and in general, does not matter–most battles are not outcome-in-doubt. You send what you need to win; usually this 3-4 units + 1 air to blast 2-3 defenders, its a 90% odds battle. Whether the Chinese infantry gets a retal or not, or whether 4 units attack West Russia and 2 survive or 3, really don’t move the ball enough to matter.
You could have great, consistent rolls across most of the game, during blowouts, and attrition, but miserable luck during the situations it matters, which account for less than 20% of the total rolls.
Alternately, you could have awful general luck, but simply hit the averages during key battles, which may be all you need to win (for example, when your opponent blows the retal).
When you get 9 hits among 12 “2s”, or get few or no hits at all for an entire round during a big fleet battle, those are luck-excursions occurring when they matter.
Dropping 3 / 5 AAA hits is devastating, but during dark skies, Germany just replaces the bombers and continues the blasting, such is their structural advantage. The same hits would a lot worse during a fighting combat for Moscow where you lost punch at the start of the fight…
Big battles for Moscow, India, Fleet tend to move towards the averages, such that you don’t know the outcome and have to go to the odds, and there is always a chance for a flub. However, you tend to roll a lot of dice during these battles, which regresses to the mean.
Luck matters, but you have to make it matter as little as possible, to retain the value of skill, vs luck, since skill would be your advantage (we hope!)
The real challenge then is to consistently win, regardless of what the dice do. Good efforts.