Most practical solution:
- rank games in the order they start (sze explains this above)
- rate the first 20 games exactly like how the seasonal ladder works
- use True Skill instead of the current ELO
Seasonal ladder's wiki:
"The rankings are determined using the same ELO scale that the existing ladders use, with one small modification. Players who play fewer than 20 games (due to leaving the ladder early or joining late) get a penalty of 40 rating points per game." Thus, games 15 to 19 would be a provisional rating on the 1v1 ladder.
True Skill (how it works and how it influenced the ladder right before I became #1):
http://blog.warlight.net/index.php/2012/01/trueskill/
With these changes, (1) people with less than 20 games couldn't game the system, (2) players with more games would be rated better, (3) the incentives of the rating system would encourage us to play more games, and (4) more good players would participate in the ladder.