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:)