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Let's go into more detail about the skills:
KNOWLEDGE - as already mentioned, it limits the maximum mana reserve: MAX = 10 * Knowledge (visiting the Source once a week, as usual, allows you to immediately gain a double reserve).
SPELL POWER - for offensive spells, it affects the damage: HP = base * Spell Power.
For spells that inflict status effects, it is equal to the duration of the effect (time = number of rounds).
There are a number of spells that do not depend on Spell Power at all: Teleport, Dispel Magic, Dragon Slayer, and all spells from the Travel branch.
ATTACK SKILL & DEFENSE SKILL - these two go hand in hand.
First, each of these values for the hero is added to the corresponding parameters of the creatures in his army (it's like a bonus). By the way, you can build captains in the castle not only to use magic when defending in the absence of the hero, but also to slightly increase the parameters of the militia.
Now about the quantitative characteristics:
it is clear that the higher the attack of a creature, the more damage it will inflict (and the higher the defense, the less damage it will take). In general, when attacking, only the difference between ATTACK and DEFENSE matters.
Many years ago, I conducted experiments: 1000 peasants attacked 1 dragon with all possible values. And here's what I found (the first number is the difference [ATTACK - DEFENSE], the second is the damage multiplier):
-18 and below (0.2)
-17 (0.25)
-16 (0.25)
-15 (0.25)
-14 (0.3)
-13 (0.35)
-12 (0.4)
-11 (0.45)
-10 (0.5)
-9 (0.55)
-8 (0.6)
-7 (0.65)
-6 (0.7)
-5 (0.75)
-4 (0.8)
-3 (0.85)
-2 (0.9)
-1 (0.95)
0 (1)
+1 (1.1)
+2 (1.2)
+3 (1.3)
+4 (1.4)
+5 (1.5)
+6 (1.6)
+7 (1.7)
+8 (1.8)
+9 (1.9)
+10 (2)
+11 (2.1)
+12 (2.2)
+13 (2.3)
+14 (2.4)
+15 (2.5)
+16 (2.6)
+17 (2.7)
+18 (2.8)
+19 (2.9)
+20 and above (3)
It turns out that, on average, 1 ATTACK adds 10% to the damage dealt, and 1 DEFENSE reduces it by 5%.
By the way, the Dragon Slayer spell simply gives +5 ATTACK against dragons (green, red, black, I haven't checked it on bone dragons)!