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). The basic thing is you will get an expected rank based on the probability of beating other users. Now the confusion is how the rank is calculated, here is the quote from Um_nik: "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."
I've heard that the ratings are used to calculate your expected place, so probably for each participant, they calculate your probability of losing with him and summing these probabilities to get your expected place. It makes sense that the deltas are similar.
You can think about it like about two situations: $$$(you, red)$$$ and $$$(you, purple \times 10)$$$. The probability of being the first in both situations can be similar, yes?
The example of (you,red) and (you,purple×10) does makes sense. But I can't figure out the fact of the expected place. In that div2 round about 600 purple registered for the contest, obviously all of them didn't participate, still, if we consider all of them did then my rank is expected to be in the top 600? And in that div1 round, I should be in the last 75 as my rating, but I placed higher than my expected place! So if we think about the expected place, then shouldn't I get a negative delta on the div2 and a positive delta in the div1?
Your expected place is not the number of participants with higher rating + 1. The probability of you placing higher than someone calculated as $$$\frac{1}{1 + c^{r_{2} - r_{1}}}$$$ where $$$r_{1}$$$ is your rating, $$$r_{2}$$$ 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.
In div.2 there are more participants, hence we have this result.
Oooh... I see that fact! Now everything makes sense! Thank a lot for the explanation!
Auto comment: topic has been updated by Farhan132 (previous revision, new revision, compare).
It's also worth considering there were a lot more participants in the div2 round. You can think of it as placing above ~300 reds/orange/purples (mostly purples) vs placing above ~12000 purple/blue/cyan.
Your seed(which is same as expected rank ?) in round 664 was 862 and your actual rank was 789.
In round 663 your seed was 1068 and your actual rank was 784.
Your performance comparative to your seed was better in round 663(div2).It is actually more strange that even after doing considerably better in the div2 round your rating change was lesser in that round.
May I know how did you calculate the expected rank? It would be great if you share the formula or some generator for that!
Here's a link to one such website which tells your your rating seed etc. Link
I am not sure if I am correct or not but there used to be some small bug with this that it calculates your seed based on your current rating instead of what rating you had before the contest but still it's useful.
I see! It's really nice! Thanks!
I used CF Predictor for it.