My goal here is to propose a discussion concerning the correlation between chess ability and intelligence.
We known very well, from both observation and experience, how much effort is needed for one to greatly improve at chess; indeed, very rarely does one become a GM without training since childhood.
However, we do not known how latent ability is manifested. We do known, for instance, that Magnus Carlsen is more talented than most people who were ever born, but that's about it.
It is possible, now, to estimate one's relative I.Q. using the data available here, on lichess!
Around 100 thousand people play Blitz every week. As we can see in "Rating stats", the median is located just below 1550 (51th percentile), the 16th percentile is located at 1225 and the 84th percentile is located between 1850 and 1875. Furthermore, since the mode (3157 players) is located at 1525, we known the mean must be a bit above 1550.
This is symmetrical enough. Our model will then be a normal distribution with mean of 1550 and standard deviation of 325.
Our vision suffices to inform us that our model has good predictability for ordinary Ratings. Now, we may test some of its predictability within extraordinary Ratings in lichess.
Our model predicts that a 2500 Rating is at the top 0.17% of lichess' competition. If we count how many actually are, we arrive at 105 players. Dividing it by 101335 gives us 0.1%.
For 2600, our model predicts 0.062% and the actual value is 0.027%.
For 2700, it predicts 0.001%, while the actual value is 0.004%.
It it very good at predicting even large values, which means we can equate its z-scores to I.Q.s in the Wechsler scale. The translation is done linearly, according to the following formula:
I.Q. = 100 + 15*(Rating - 1550)/325
A Rating of 900 is equivalent to an I.Q. of 70.
A Rating of 2200 is equivalent to an I.Q. of 130.
Magnus, with his 2948 real-life FIDE Blitz Rating, would be around 165.
But, nope. This is a key point: I assumed that the average (and variance) I.Q. of lichess players is the same as the expected global I.Q.. This is not the case; regarding chess, the higher the I.Q. the higher the incidence, i.e., more people, in percentage, with I.Q.s of 120 and 125 are interested in chess than people with I.Q.s of 115. Likewise, more people with I.Q.s of 115 are interested in chess than people with lower-average I.Q.s.
The estimation of central tendency and variance was done in 2014 by Melão. It had been done before, two decades ago, in a very interesting article (http://miyaguchi.4sigma.org/eloiq.html), but Rating inflation was not taken into consideration.
Melão, however, calculated a mean of 1367 and a standard deviation of 268 for classical time controls.
Thus, the translation would be on the lines of:
I.Q. = 100 + 15*(RatingFIDE - 1367)/268
Now, Magnus, with his spectacular 2837, should have an I.Q. of 182. Much more believable.
There are still a few statistical issues (and lots of conceptual ones, which is why I'm initiating this discussion), like the fact that intelligence does not distribute normally outside -2 SD to +2 SD, or that the actual global average is not 100, because the tests are normed in the USA and Europe, but we are likely on the right track.