Alternative rating.

In my opinion, players who have played less than one game in a season should be removed from the ranking altogether... so as not to confuse anyone.

No - that's not entirely fair, what if this "non-player" plays another 10 games in a month or two?
We just need to introduce a minimum barrier (3 or 5 games) to be included in the ranking... which, by the way, is not reset!