A Strange Observation About Rating Changes

Revision en2, by Farhan132, 2020-08-31 22:54:50

In both of the rounds 664 and 663, I have placed in the same rank 783. The fact is one of them was Div1 and another one was Div2. Strangely enough, I got almost the same delta change from almost the same initial rating! So this made me think of placing behind 782 reds/orange/purple is the same as placing behind 782 cyan/blue/purple.

UPD: Um_nik gave a really nice explanation for this case (Also thanks to Radewoosh, though I couldn't understand the fact fully from him) . Here is his quote: "Your expected place is not the number of participants with higher rating + 1. The probability of you placing higher than someone calculated as $$$\frac{1}{1-c^{r2-r1}}$$$ where $$$r1$$$ is your rating, $$$r2$$$ is their rating and $$$c$$$ is some constant. Now we sum this (1 — this, actually) over all participants and get the expected number of people who will place higher than you."

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en4 English Farhan132 2020-09-01 08:55:49 2 Tiny change: '\frac{1}{1-c^{r2-r1}}' -> '\frac{1}{1+c^{r2-r1}}'
en3 English Farhan132 2020-08-31 22:59:34 162
en2 English Farhan132 2020-08-31 22:54:50 574 Tiny change: 'ulated as \frac{1}{1-c} where _r1' -> 'ulated as $\frac{1}{1-c}$ where _r1'
en1 English Farhan132 2020-08-31 21:24:07 515 Initial revision (published)