Captains are chosen by voting, and based on the number of votes, they are assigned numbers, for example, Gomunguls is number 1, and LuckyF is possibly number 20 among the captains.

I would question this point. The voting for captains is a subjective choice, not an objective one. And the one with the most votes is not necessarily the highest-ranked. A simple example – me. I participated in two team tournaments, in one I was captain number 1, and in the other, captain number 3, although my ranking was clearly far from the top 3. The same goes for Gomunguls and LuckyF; based on the voting, they could be the opposite, 20 and 1, respectively. Therefore, the distribution of captains can be considered partially random. This makes your calculations incorrect, or rather, the opposite, and the balance results in an even number of choices (not players). IMHO.