Originally posted by Phillidor
I propose that the "OpponentRating" variable and the "YourRating" variables be determined by the respective ratings AT THE START OF THE GAME. (See formula calculation at the bottom of this post)
This is certainly an interesting idea.
I am not so keen. For detail, read on.
I am not sure of the benefit of using the out-of-date rating as the basis for allocating rating points.
Assume you start playing in a tournament, with other guys of the same sort of rating, and play no other games.
If I start a tournament, I get say 20 games starting at once. These games finish in whatever order, but the rating points allocation after the last game in the round treats both players as having the rating they had at the start.
Assume that the round winner and the round loser play their last game of the tournament against each other. This means that the guy who is improving gets lots of rating points, and the guy who was at his peak at the start of the tournament loses lots of points. But in the meantime, all their other tournament games have finished.
In comparison to the current system, where the ratings difference between them (due to the other tournament games) is now large, neither gets/loses many points.
I think that making the change is likely to give an "overshoot" of rating - the guy who is doing well gets more points added. The guy who is losing loses more.
This is pretty much based on my "gut feel". I haven't analysed too much. It somehow feels wrong that stating each game when the last has finished should give a lower final rating than starting them all at once, which is what I expect your change to do.
I agree with you that some improvement to the rating system might be possible, but I think that effectively deciding how rating will change (for a given result), and then delaying the change for the duration of the game does more harm than good. I see rating as a "best guess at ability/future result, based on past results". Each win or loss tweaks it a bit, up or down. If you store the change which will be made, for a lot of games starting at the same time, when those games finish you overcompensate for a "current" rating which was too high or low, when they started.
On the later posts with average and weighted average.
These feel like a tweak to the first system, to work around the disadvantages.
Simple average: Easy to calculate. But less of an advantage. For your 1500 - 1700 example, it is still worth B waiting because it is better to lose against (1800+1500)/2= 1650 than against (1650+1500)/2= 1575, as less points are lost by B in the first case.
Weighted average: Lots of calculation, but data should be available, and computers are fast. However, is there enough gain for all of this calculation? If someone's rating rises, the weighting still biases it towards the rating at the start for calculation purposes. Would it solve the 500 games against players rated 900? If I calculate correctly, no, as rating levels off at 2032, rather than 1630 with the current system.
I'll agree that the weighted average looks interesting.
How do you deal with a new player, rated low, but quite strong, playing in an open tournament? The guy at the top of the ratings list starts playing him, and as the game progresses, the new guy gets closer to his "final/ability" rating. The top guy eventually loses to the new player, who is now rated the same. Under the current system, the top guy loses a few points. Under the system you suggest, he loses a lot more.
I think you introduce a disincentive to start to play people whose rating change a lot.