Alternative rating.

Since the rating is calculated using a statistical formula, it only makes sense if a player has played a certain number of games. Therefore, I suggest excluding players who have played, say, fewer than 5 games. Then Valentine's position would be twice as high.)
Secondly, the rating counts games played during the year, not the season, so people with approximately the same statistics for the spring may be at different ends of the table.

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 rating ... which, by the way, is not reset!