MMH5.5 - Heroes of Might and Magic 5.5

In theory all the math is correct but in practice things are a little different.

I agree, this is just a rough estimate with some assumptions, but it shows that the chances for 5-6% skills are quite high (around 80%).
And rare (2%) skills aren't supposed to be caught normally, only when you're lucky. They are rare, after all.

However, perhaps the mod authors believe that rare skills should also remain relatively accessible, which is why it's 4% there?
While 2/5/10/18 might seem harsh, the 2/6/11/16 option could at least work for testing. If it's already been tested, then it's ok.

So the hero gets roughly ~5% damage for that perk.

Correct (at +3). But normal Luck gives ~7% damage per perk.
If the bonus goes up to 200%, then it'll be around ~10% damage per perk (at +3) and ~7% (at +2).

Though, your Luck skill itself is significantly stronger than the standard "+2 ability". I would estimate it closer to "+3 Attack" (equivalent).
Since from +8-9 to Attack (at 3.33%), I will on average get a bonus close to +3 Luck (around +20% of total, not base damage).

If you want to equalize +1 Luck and +2 Attack (at 3.33%), I would recommend +50% lucky damage (instead of +67%). Increasing to +70% with a maxed Critical Strike.

the aim is to benefit the hero with around +2. This is how much all perks should give on an average.

The problem is that players won't level up this skill if it doesn't look attractive. Bonuses around +1-2 are less than a +2 bonus. I suggest testing the herds and making sure the average bonus looks definitely no worse than +2, considering the strength of the units receiving the bonuses. Because if it's +1 for important units and +3 for trivial ones, it won't be ok.

What you say only refers to half of the skill. Combat main purpose is to make the hero hit.

In other words, the skill is made very weak, but the abilities within it are strong enough to compensate?
In that case, the +1/+1 attack/defense ability is even less relevant, as it requires 2 levels immediately (one for the weak skill to unlock the ability, and a second for the ability itself).
+2/+2 is better in this regard, but then it should be given immediately, without waiting for level 20.

0.1 ATB for the mass spells is because of the hardcodded issue. There is no way you can put 0 value. It crashes the game and 0.1 is the lowest possible.

Interesting, because in my executable modification (not 5.5, but based on the old RPE with 24 classes), I use 0.0 ATB for mass spells and the game hasn't crashed yet. In what situations is the game supposed to crash?

It will simply be too powerful if they were in the same branch. Tent and Catapult will never be picked. Basically here I can answer the same way I did for "Retribution" the synergy is too good.

(regarding fire arrows)

Actually, the option I proposed to move fire arrows to siege engines should solve this problem:

As a potential solution to the problem, perhaps including fire arrows in combat engines instead of engineering; then the growth would look like this:
- ballista +100% = 200% (plus manual control and durability)
--- fire arrows x2 = 400% (+200%)
----- rapid-fire ballista x1.5 = 600% (+200%)

...Alternatively, from the catapult - engineering (instead of sulfur rain), but then the bonus should be much higher, like +5 to initiative.

Each new ability in this line gives only up to +200% damage (we conventionally took the effect of fire arrows as doubling the damage, this is a rough estimate).
Consequently, I can comfortably choose not to take the rapid-fire ballista or even fire arrows in favor of some other abilities of similar strength.