I understand where you are going when you state that there ought to be some sort of "formula" to this, but as you should know, three policemen monitoring one hundred sixty six citizens is not a good comparison since, unlike those policemen, moderators can jump from thread to thread within a matter of seconds. As for how many there should be at a time, that is really up to you. How much vandalism, spammers, or malicious people visit your site? If it isn't very many, then you may make do with two moderators appointed from the active community. If, however, your forum becomes large, that is, in the thousands to ten thousands, then you will need anywhere between four to twenty moderators or more.
It really depends on the circumstances, there is no formula but your own intuition. You can create your own system and it would be perfectly fine.