Duke I'm pretty sure yoou are wrong
Your way of counting it is kinda complicated, also it doesn't match an info from combat system
"25 armies attack a territory that has 20 armies.
The attacking 25 armies could have killed between 0 and 25, but on average they will kill 15 (60% of 25). Let's say they kill 15 armies."
So it seems logical to me, that thi is how it works:
1st number of killed armies is calulated as follows:
(number of armies) x (Offensive/Defensive Percentage)
2nd number of killed armies is obtained by rolling randomly for each attacking army if it killed the enemy or not.
So If you attack with 3 armies and 60% chance you have:
40% * 40% * 40% = 6.4% not to kill anyone
60% * 60% * 60% = 21.6% kill all 3 enemies
3 * 60% * 60% * 40% = 43.2% to kill 2 enemies
3 * 60% * 40% * 40% = 28,8% to kill 1 enemy
Then those results are averaged with weight depending on luck percentage
with luck percentage on 30% we will have in my example
(100-30)% * 3 armies * 60% offensive rate + 30% * 2 (lets assume most probable result of random rolls) = 1.86
Leaving 86% to kill 2 armies and 14 percent to kill 1 army
Try creating games with dfferent luck percentage and use analaze tool - you will see how decreasing luck percentage changes transition win/loose from a curve into sharp barrier
With luck distribution 100% you have pure "each army has separate 60% chance to kill enemy"