That is true for basically all issues which require a call to the random number generator in this game (damage rolls, critical and evasion rolls, AI decision-making, creature-spawning item and scroll results...). Load the same game twice, do the exact same thing, and you get the exact same result. Load the same game twice, do the exact same thing except for something that seems like it *ought* to be irrelevant, and you might get different results.
I don't know how they actually programmed it, but it looks to me like the save-game file probably saves your random seed in it as well. In that case, you ought to be able to also change the damage and results by e.g. swapping an army to reserve, using a griffin egg then dismissing the griffin, and swapping that army back from reserve just before the battle.
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