At the office, we'd like to start a table tennis league with perpetual standings. That is, as each match is completed, the scores should be logged and individual player ratings should be adjusted accordingly. We've got 10-12 players. Some play every day, some play once or twice a week. Each match is a best 2 of 3, and frequency of play shouldn't be a significant advantage or disadvantage.
How should we set the league scoring up to accomplish this?
I would recommend an Elo Rating System. This system is primarily used in rating of chess players and ranking of players in games like badminton, tennis and table tennis.
Each player has a rating score and his/her score increases when they win and decreases when they lose. The margin of change in rating depends on the rating of the opponent. A win against a strong player will give you a better rating than a win against a weak opponent.
The systems has drawbacks like difficulty in understanding how it works and complex mathematical calculations but it will solve your purpose.
I strongly suggest a ladder ranking system. This is a common system used in workplace and other community areas that provides for asynchronous tournament play.
Basically order your players 1-x and then any player can challenge a player higher on the ladder than themselves (within some boundary).
The tournament proceeds via a system of challenges. Any player can challenge a player above him or her on the ladder. If the lower-placed player wins the match, then the two players swap places on the ladder. If the lower-placed player loses, then he or she may not challenge the same person again without challenging someone else first. Usually, there is a limit as to how many rungs above themselves players may challenge.[3][4] When first setting up a ladder tournament, usual practice is to place the more skilled players at the bottom of the ladder, so that they have to play to work their way up.[3]
There are some flaws with this system, but it allows for asynchronous play, and does not unduly penalize people for not playing as often. Basically set a start date and an end date and use the final results of the rankings as either your final, or as the brackets for a single day tournament play event. Alternatively you could use something like ELO from chess, but ladder is much simpler as it does not require math.
frequency of play shouldn't be a significant advantage or disadvantage
...providing that it's not very high above or very low under average frequency.
'Parking the bus' approach (a player gets a high level in ranking, then he stops playing) is one of the most known practical issues of Elo ranking, that someone suggested in another answer.
Many post-Elo ranking systems, as Glicko (for chess), or TrueSkill (for X-box games), or rankade (our multipurpose ranking system) have some 'activity dynamics feature' to avoid this.
Glicko and ree have free online calculator/webapp/app, that fits your needs, maybe.
