Formula for Ranking Players

Has anyone here had to rank players playing against each other before?

• Player1 plays 10 games, wins 8 out of the ten games -> so 80% win / loss ratio.
• Player2 plays 100 games against the same easy opponent, wins 99 of the 100 games -> so 99% win / loss ratio
• Player3 plays 1 game, wins that 1 game -> so 100% win / loss ratio
• Player4 plays 50 games, wins 40 games -> so also a 80% win / loss ratio.

Player1 might play against Player2 today and tomorrow Player1 might not play at all, but Player2 might play against Player3 - so not all players will be playing at the same time, some might play many more games than other.

Which player should be ranked highest and what formula did you use to make that decision?

Also, how would your scoring system encourage weaker players to play against stronger players and stronger players to want to play against the weaker players.

I have some ideas, but would like some input from Hashnoders

Update - rating systems so far:

• ELO
• Glicko2
• How Not To Sort By Average Rating
• WN8
• NoobMeter Performance Rating algorithm
• Bayes Estimator

And in case you need to calculate these things without a computer, by hand, there's a simplified version of ELO called the Harkness Rating System, you start with a rating of 1200 and then based on the difference in rating between player1 and player2, you transfer points according to this table: