My understanding of the numbering is really a matter of circumstance. Sauron was able to steal 16 rings from the elves and his thought was the enslave the dwarves. He gave as many rings to the dwarves as they would take, but the One Ring had no power over them, just made them more greedy and desiring if riches.

So, with all that he had left, the Nine, he gave them to men. And that was when the rings actually worked and the Kings became Wraiths.

I don’t know, maybe Hal9000 has a better understanding of this than I