Understanding RNG (Random Number Generator) and how it is applied
RNG is probably the least understood principle in battle mechanics. As its name states, it a completely random multiplier applied to each time your troops attack. The multiplier range is .85-1.15 of the total attack power, and can ring at any number within that range for each type and time of troop attack.
The easiest way to wrap you head around this concept is to look at it like a "chance to hit' type of thing....like a real battle. If in real life a group of archer were to volley a group of...let's say, trees....most trees would get hit once, some would take two arrows or more, some would miss completely and hit the ground. Some would hard glance off of one tree and hit another...you get the idea. Or let's say 100 guys with swords charge a group of guys with shields....some would kill, some would block, some would swing big and hit two ppl...some would only wound.
That is the purpose of RNG in a DOA battle...it adds an element of randomness to the battle so exact prediction is impossible.
How do we look at this in terms of our attacks? Well...let's say your LJ attack is boosting 1 million total attack power. Because we want to get the job done....we are going to assume out LJ are cross eyed goofy little LJ and that they won't hit squat..so we assume our LJ will miss and multiply their attack power by the ugly end of RNG (.85)....thus giving us an attack power of 850k instead of the 1 million they should have. And on the flip side...if we are attacked with 1mill power LJ...we assume the attacker had marksmen LJ that won't miss...so we give then the other end of the RNG spectrum (1.15) so we assume they will hit with 1.15 million attack power.
Hopefully this gives a little clarity to that mysterious thing called RNG and helps you understand better why attacks don't always go exactly as calculated.