For anyone who is interested in playing around with these charts, the various assumptions that under pin them etc. I've thrown together a colab notebook as a starting point. Observation: if you rank via true "skill" and assume for a particular instance the predicted performance and observed performance are independent but both have the true skill as their mean you dont observe the effect. CC of 0.00332755. If you ran…
What your simulation includes and the original article didn't (and I didn't touch at all in my article) is the statistical reliability of the tests they administered. Where you got a CC of -0.38 you used equal reliability (/ unreliability) of the skill tests and self-assessments. You can see that as you increase the test reliability, the CC shrinks and the effect disappears.
I have no idea what's the actual reliability of the DK tests, they do seem to consider that but maybe not thoroughly enough. In my view it's very fair to criticize DK from that angle. But that would require looking at the actual tests and their data.
My point being, that any purely random analysis is based on assumptions that can easily be tweaked to show the same effect, the opposite effect, or no effect at all.