About rating pools?

So lets say for example a club was composed of 10000 1800 rated players they average .50 scores against everyone in the pool. Is a ratings distribution possible and will small rating differences mean a lot more?

If you can find 10000 1800 rated players we could test it out. 😛

The following assumes that the 1800 rating is a true reflection of ability rather than an arbitrary start value.

If the ratings are calculated at the end of a period of time, say after a tournament, and all score 50% then no rating changes will occur. Everyone ends up on 1800.

If the ratings are calculated on the fly after each game then a certain amount of variation will be introduced if anyone beats anyone else. I doubt the amount of variation will be huge as once a player has a rating other than 1800 his rating will tend to return to 1800 as he racks up draws against others still rated 1800. Of course, that will also serve to move his opponents away from 1800 but not by as much as a loss.

So the average rating should remain 1800 and standard deviation should be small. I would expect the distribution of scores to be Gaussian. I may just run up a simulation to see what actually happens.

Results of simulation:

To maximise variation I set things up so that no draws occur. I used 100 players playing in 100 double round robin tournaments, 990000 simulated games altogether.

The mean is always 1800, not surprising since any reduction in one players rating results in a symmetrical rise in the opponent's rating. The standard deviation is between 50 and 60, the maximum rating is between 1900 and 1950, and the minimum rating between 1650 and 1700.

I may run this with more rounds later on just to see what happens over longer time scales.

Edit: Missing zero in number of games.