As mentioned in the blog:

A higher CF rating, with a gap of at least 100, correlates with an 87% chance of achieving a better placement at IOI.

I think I have some thoughts here. Arpa mentioned:

"A higher CF rating, with a gap of at least 100, correlates with an 87% chance of achieving a better placement at IOI."

Now, this statement can be true, but at the same time, it needs a bit more investigation maybe.

Imagine a list of people with rating like [1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700]

(I know this is not perfect, of course as the distribution should have much less occurrence of high ratings, it shouldn't be equal etc)

So, the thing is: in the cases with "a gap of at least 100", there can be lots of cases with 400-500 gap or more which might inflate this statistic a bit. I think the more correct question would be something like: "what %age do we see if gaps are between 100-150 points" or "150-200" and "200-250" respectively.

Because otherwise, I feel compared to gaps between 100-150 (say), there are lots more cases of gaps bigger than that!

After all, gaps of size 100 are O(n) in the list I showed, but gaps > 200 or > 100 can be O(n^2)!

Arpa maybe it would be enlightening if you could do this analysis for different gap ranges or something, or something which accounts for the issue you mentioned. I know long back you had shared this data with me, but due to some technical issues, i wasn't able to access the site which you had shared the data on. (And didn't want to disturb you back then)

As for you, TimDee, there is one issue with the argument you showed as well. You used the IOI rank vs CF rating, right? And claimed because there are inversions, the predictions won't make sense. Now, the thing is you could probably use CF rank vs CF rating as a graph as well, and there also maybe you find quite a bit of inversions (I suspect less than IOI of course but not very less).

In that case though, I'm sure we can't say that "CF rating is not a predictor of CF skill", because CF rating is CF skill by definition! So, what I mean is: maybe what you point out could have a lot of noise too.... as in "real expected IOI rank is x" (as predicted) but inversions also come from noise.

Both the factors I mentioned above, are in opposite directions, maybe the truth lies somewhere between these two, and perhaps somewhere between Arpa and TimDee and Dominater069

ah yes