Hi guys!

First of all, sorry for my poor english and short translation:)

Now everyone could access rating formulas, and there is some not obvious mathematic formulas. So, I decided to check probability formula(probability that the i-th participant has better result than the j-th participant):

There was a lot of rating codeforces rounds, so it's easy to calculate this value by existing results. I choose cf rounds №200 — №350 (separately for each division). To solve this problem I wrote java program (sources). After getting results I copy/paste it to Excel and get plots:

for first division

for second division

Looks good, but lets try found something better:)

Unfortunately this formula doesn't look scientific, so I a little bit change it:

Now, lets build plots again

for first division

for second division

Now it's closer:)

Auto comment: topic has been translated by Wsl_F (original revision, translated revision, compare)Auto comment: topic has been updated by Wsl_F (previous revision, new revision, compare).I believe the formula should satisfy

P_{i, j}+P_{j, i}= 1.I think it should be p(i,j) + p(j,i) + (probability of both participants having identical result) = 1 :)

OK, that explains why the blue graph at 0 is less than 0.5.

Yep, the writer seems to have taken care of the mathematical details :P

you are right:)