I have been carrying this question around for a lot of time. How exactly does a user's rating change in codeforces? I have read a couple of blogs that analyse the rating system, but I do have a couple of doubts.
The main one which I'd like to address (and possibly get answers to) through this blog is, this: Do rating changes in contest happen based on tags or based on rating?
For example, lets say a user is at 1599(specialist) and another user is at 1601(expert). If both of them have solved the same problems in the same time during a contest, does the rating increase significantly more for the 1599 user because he's a specialist and less significantly for the 1601 user because he's an expert? Or is the difference not significant for both of them because they have a very similar rating?
Thank you!
From my understanding of how the rating system works the tags are irrelevant. The rating is used to calculate the expected performance of the participant using some ELO type logic where the difference in rating gives the probability the system thinks one user will perform better than another. Then ratings are updated based on the difference between expected and actual performance (I have heard the rating change is roughly 1/4 of the difference between expected and actual but I don't know if this is correct). So for the 1599 vs 1601 case the expected performances should be very close and the difference should not be significant.
Yep, I believe it's a slight variant on the Elo system. The original Elo system is for 1v1 zero sum games like Chess.
The important part is that the number of problems solved isn't actually relevant, only your place in the contest, your old rating, and the ratings of the people you beat and lost to. So a good hueristic is that your rating will usually approach the rating of the people surrounding you on the scoreboard, assuming those people are having an average contest, i.e. not doing unusually well or unusually poorly.
Now that makes me wonder about the following situation. Assume you participate in a contest and you fix your placing but permute the placings of the all other participants will your rating change be different?
Right, that is very convincing! Thank you.
Oh right, that makes sense. I was not aware of this. Thank you!