Nargott
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Maybe instead of 10-20%, it should be a number that depends on the hero's level and attack value?
Ugh, but maps vary in size. Sometimes, to quickly reach an opponent, you need to break through many zones. Of course, I'm not talking about the very late game, but in the moderately late game (or even the mid-game, in general), this combination of abilities looks like a huge imbalance. In my humble opinion, it would be worth making the ability's weight more optimal for different stages, rather than forcing it to be only for the early game. However, I understand that you have a different concept for the mod.
Um, is your game duration 2 weeks? Let's do a calculation for two months (a normal average duration).
In addition, your calculations assume that this perk is taken from the very beginning, and not later. This means, among other things, that breaking through in the first week is a disadvantage (when there is no benefit from it, just like there is not much benefit from the leadership base). This will inevitably affect the late game in the same way as a snowball effect.
You also did not take into account the replenishment of troops from other cities (is a 2-month map played only with 1 city? I played in Heroes 3 (with similarly accelerated logistics) 2-3 week games with 8 cities, 2-3 of which were native). So, the relative bonus from Gathering for the lower tiers will be far from 300% even in 2 months, but much less.
That is, your calculations are made for: a huge map, for some reason with a small number of cities, and also for a slow pace of play. This is a combination of too many conditions at the same time. And yes, I understand that usually maps for single-player in Heroes 5 are designed this way. But I can't play them myself, and therefore I can't balance the mod for a game mode that is alien to me.
I don't understand why you would continue the game after fully building up the city (including even unnecessary buildings for the chosen strategy) and achieving key upgrades (without excesses), and also why you would keep dozens of dragons in the army and complain about weak Chaos. If you play for such a long time, then for you, "Deadly Cold" is a situational anti-ballista, anti-fen, and nothing more. While in reality, it is one of the most delicious and imbalanced perks, you just need to slightly increase the pace of the game. When there are only 2-3 dragons in the army, it's -30-50% of the top stack, "accidentally" hit by the ring with just one perk.
You are not suggesting strengthening "Deadly Cold" just because it is not intended for games of 2+ months? Or doing something about the education that already gives +15 stats at level 30 (+30, if translated to the original)?
The Necromancer gets more bonuses from this perk (due to the combination with necromancy). But this is logical, because he doesn't get anything at all in breaking through for the leadership base, unless he mixes troops. In addition, anticipating, necromancy will give 5/10/15/20%, and not 20/30/40/50%, which will not have a significant impact on the total number of raised creatures (due to the limitations on the economy), but it will affect the composition, it will be much more difficult to recruit only troops of lower tiers and, accordingly, increase the Gathering of troops.