Let's say a Red Dragon is attacking bunch of light infantry in a level 1 city. So it is Strength 50 vs 10. Question is how many light infantry does a Red Dragon kill on average. And the answer is not 5 but it is 9. Be cause one factor is the chance of rolling a favorable dice, but the other factor is your opponent should miss.
There are several ways to calculate relative strength of units and chance to hit. Two of them are pointed out by KGB at the thread about Dread Knight, both of them valid and common sense, but if we continue the calculations to the full extend we will see that a third one is also valid. Let's call the Attackers strength A and Defender D.
a) Your relative chance to make a hit is proportional to your strength ratio. So you can divide Attacker strength by defender strength A/B. But in order to make a hit, not only you should roll a favorable dice but also your opponent should miss it. So chance to hit is inversely proportional to the miss ration. Which is (100-A)/(100-B)
Formula -> Relative Chance to produce a hit R=(A/B) / ((100-A)/(100-B))
Which is the formula using the first approach. But you can rewrite the final formula in two different ways.
b) R= (A*(100-B)) / (B*(100-A)
The logic of the second way is as follows. The attackers chance to hit is when he rolls a favorable dice ( A ) and the defender misses it (100-B). Defenders chance to hit is that he is rolling a favorable dice ( B ) and attacker misses it (100-A). The ratio of two values gives the relative chance to make a hit.
C) R= (A/(100-A)) / (B)/(100-B)
The term A/(100-A) is the attackers Hit to Miss ratio and I call this the true strength of a unit. By rewriting the equation, I can compare increase in my units strength with no regard to the opponents strength.
Strength 75 -> Hit to miss ratio = 75/25 = 3
Strength 60 -> Hit to miss ratio = 60/40 = 1.5
Strength 50 -> Hit to miss ratio = 50/50 = 1
Strength 33 -> Hit to miss ratio= 33/67 = 0,5
Strength 20 -> Hit to miss ratio = 20/80 = 0.25
Strength 15 -> Hit to miss ratio = 15/85 = 0.17
Strength 10 -> Hit to miss ratio = 10/90 = 0.11
Strength 5 -> Hit to miss ratio= 5/95= 0.05
Same thing is true for undead lore and ruin searching. Adding a scout increase your chance of survival a lot. So with level 1 ruin and 12 faced dice here is the true strength
Undead lore 12 -> Hit to miss ratio = 12 / 0 = infinity. You never lose.
Undead lore 11 -> Hit to miss ratio = 11/1 = 11. With 11 undead lore your true strength is also 11.
Undead lore 10 -> Hit to miss ratio = 10/2 = 5. Here comes the dramatic drop
Undead lore 9 -> Hit to miss ratio = 9/3 = 3
Undead lore 8 -> Hit to miss ratio = 8/4 = 2
Regardless of who you are facing at the ruin, going from undead lore 10 to 11 makes you more than twice strong. If you are searching a ruin with 8 undead lore, your chance to win is 20% of the hero with 11 undead lore.