IF you have the win/loss/tie record of the opponent(s) then you have a much better basis for predicting the outcome.
If not then you will need to "weigh" the numbers of games. That is, as you indicate, a person who has played more games has more experience and thus has a much more reliable indicator of results.
It may be that a person who has won 9 of 10 is a far better player that one who has won 90 of 100, but one assumes that experience is worth something.
The ranking method used for basket ball teams appears to be a likely format for what you are attempting.
How much data can you get for each player?
Number of wins/losses/ties.
The actual time length or number of moves per game.
The opponents statistics.
The total number of players who play.
Is there a home/away statistic.
Get ALL possible data for each player, then generate a correlation coefficent for each facet for each player. The more indicators you have, the more reliable they become in predicting probabilities.
How much data can you acquire?