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