You're not calculating it correctly.
The Out of Unit (OOU) ability shifts the hero by 0.25 on the scale, and the hero will start the battle within the range of [0.25; 0.5].
This means the unit's initiative range is [10; 20], below which the unit has no chance of going before the hero, and above which the unit will definitely go before the hero with OOU.
A unit within this range has a chance to go either before or after the hero.
Orc units, without any artifacts, fall within this range, meaning they already have a chance to go before the hero with OOU.

My math is fine; it's part of my profession. Due to the significant initial spread, I assumed, FOR THE SAKE OF ESTIMATION, that all units have an AVERAGE starting position of 0.125 on the ATB (Action Turn Bar). By the way, this is mentioned there. And if the assessment, under these EQUAL conditions, shows that the hero goes first, then he will go first in more than half of the cases (under the natural assumption that the spread is symmetrical relative to the average), i.e., in more than half of the cases, the Orc will definitely lose, because, at the very least, he didn't bring his entire army. As can be seen from the same post, even with a 10% increase in the Orc's initiative due to artifacts, he loses with a probability of more than 1/2. Moreover, for the described tactic, it is necessary that not just one stack goes before, and the Cyclops needs to be hit more than once. If the form of the probability distribution for the initial spread were known, then it would be possible to estimate the probabilities much more accurately.

Furthermore, the tactic was described, as can be seen from the example, for the late game.
This means that many initiative artifacts will likely be collected.
This needs to be taken into account. These artifacts are not fully compensated for by anything, and the hero's initiative is not increased either.

I agree, it is not fully compensated, so I also conducted an assessment for +10% initiative. Of course, if there are many small initiative artifacts and 2 rings, or if we know that we will start with level 1 of Rage, then we can confidently engage in battle; even the Staff won't scare us. In less pleasant cases, it's at our own risk.

Furthermore, 120 Warlords, 10 per week, even from a single castle, is 12 weeks.
Not 5 months, but only 3.

Of course, 3, it was a typo, but it's still a long time. Although, in my opinion, I didn't evaluate anything beyond 10 weeks.