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3. Chess performance and I.Q.

Hello there!
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.

I’ve followed these discussions for 30 years and the only correlation I see that such discussions lead to trouble. Actually every experienced player will prove right that Elo is not a function of what is commonly known as intelligence. Rather acquired practical skills.

What about high-intelligent people who are successful in other areas but not in chess?

There about a million definitions of „intelligence“ known - so define intelligence first. If you define chess playing strength as a form of intelligence - then it shall be.

en.m.wikipedia.org/wiki/Intelligence

PS: Rating equals „competition fitness“ in my opinion

@Sarg0n
I initially intended to post a much larger text, but realized, while writing it, that it was already Bible-worthy. As a consequence, I could not include every comment I'd like to, and chose to focus on the statistical (albeit very light) side of the approach.
My opinion regarding human intelligence is the following:

There exists _g_, the general factor. This is a (empirically verifiable, scientifically arrived at through factor analysis) fact. It positively correlates with any kind of mental activity involving identifying patterns and solving problems. In fact, it positively correlates with working memory, vocabulary, numerical aptitude, musical aptitude etc. We do not have a definition of intelligence, but we do have of _g_. I.Q. (in regards to licensed testing or well-constructed online testing) highly correlates with _g_ within testing scope.
Thus, we can say that the largest manifestation of human intelligence is _g_ (because it is).

Given that _g_ manifests itself in pretty much every mental exercise, one would think chess must be highly loaded with _g_! I mean, there are very few intellectual activities which are comparable to chess, concentration-wise.

Chess likely requires some form of "spatial intelligence" (note that the Theory of Multiples Intelligences is, as far as I'm concerned, not a theory at all, but a hypotheses... what Gardner recognized are multiple factors of intelligence, since all positively correlate with each other), together with other specific mental faculties which I wouldn't know to point out.
Of course, many people could be successful and bad at chess. Firstly, because they could be talented in other areas, as you mentioned, but not in chess, and that would not mean they are not intelligent; however, it would be more likely that, if they trained for a certain amount of time; they could become decent at it. Secondly, success only relevantly correlates with I.Q. of to a rarity of 1 in a thousand, so it could be that that successful person is not that intelligent to begin with!

If one wishes to talk about fluid and crystallized intelligence, then that's perfect! It is exactly how I should've phrased it initially!
I do know (as mentioned in the beginning of my post) that acquired practical skills are more important.

But, for this purpose, I think we could say that playing strength is a form of intelligence on the basis that, if we take two people who have played around the same number of rated games in their life, the higher rated one will, most of the time, be the more intelligent one.

It simply cannot work. For example, approximately one year prior to now I played at approximately 500-600 elo below the level that I currently play at, though my IQ was certainly not enhanced by 40+ points in that time. This equation/scale also indicates that anyone who can play chess at 1000 FIDE has an IQ of 155, which is simply not true.

It's a great concept and I am sure that people of above average intelligence are more likely to pursue chess as a hobby as compared to people with below average intelligence, but it just doesn't work as it is a trainable skill and more of a practical application of certain forms of intelligence.

The WAIS-IV (Weschlers most recently revised IQ test) includes many subindexes which include Processing Speed Index (PSI) and Verbal Comprehension Index (VCI), which are simply not correlational with chess 'IQ'.. For Example, you can have a below average processing speed and play great classical chess, but play poor bullet.

It also fails somewhat in an experimental sense as the use of a control will not work. If you find someone that has an IQ of 200+ who has never played chess before and ask them to play someone with chess experience of the same IQ, they will lose.

It's hard to study, pin down and hard to control. I would suggest using pairs of two controls, both of whom have never played chess before but have similar IQ differences and giving them both exactly the same introductory lesson to chess and then having them play many games after. The problem is that if they play chess for say a month and have an IQ of 200, their predicted FIDE rating by your scale will be 1900, which will by any possible method will take time to develop.

I would suggest 'cross-cultural differences of IQ in comparison to ELO' or something of the like, a more interesting and easy to implement study.

Best of luck though!

If you define intelligent = „suitable for daily use“ or „skillful“ then everyone knows: it‘s rather reciprocal... ;)

there are studies in intelligence (hereby the one measured by IQ-test). On children higher IQ correlated how quickly they acquired some skill but in the long run how enthusiastic they were about chess was best predictor of their skill.

As for are chess players more intelligent than folks in average it seems so www.acsh.org/news/2017/05/31/do-chess-players-have-higher-iqs-11366
half SD is meaningfull difference. As expected people who have good problem solving skill tend to gravitate hobbies and careers where problem solving provides some help.

But I am very skeptical if your average online chess player is smarter.... People playing behave very differently from the ones I meet IRL so I think the expectation of similar IQ distribution would be silly-

Also I think saw somewhere about GM intelligence and on average they are more intelligent but there was at least one then was of IQ 100. SO being intelligent helps it is not mandatory.

If IQ would not correlate with chess skill that would be amazing. I mean it has correlations with just about anything. Like negative correlation with dying on accident. And positve correlation in some forms on alcohol overuse. It is a strong predictor. Wheter high IQ is intelligence is meta discussion. IQ is good predictor and this undefined intelligence, dunno what it could be used for

@FakeCrabMeat
I'm not sure if I wrote the formula incorrectly, but for 1000 Rating, the lichess one gives an I.Q. of 75, while the FIDE one gives an I.Q. of 79.
Furthermore, I'd like to comment on... pretty much on everything you said, since I found all remarks interesting.

I just said this in my response to Sarg0n, but lots of comments were left out of my post in fear that it'd be too long.
One of those was important, because it clarified the translation from Rating to I.Q.: this is a rarity/percentile translation (or z-score equating), i.e., if an I.Q. of 135 rests above 99% of people, what Rating rests above 99% of online players (lichess)/potential chess players (FIDE)?
The answer, for FIDE Ratings, would be "around 2000", while for lichess Rating it would be "around 2300".
Thus, the interpretation should not stationary, but volatile. One could think of it as "given my I.Q., if I dedicate enough time to chess, my Rating should not go much further than ...".
In fact, what happens it that most people can never go above 1700 (for real tournaments, don't know about online).

This is why my idea (one of them) was to compare people who've played approximately the same amount of tournament games (or rated games, for online comparison). This is pretty much identical to your idea... in fact, could it be done, we'd have a formula for Rating climbing with respect to time played, and one that varied given one's innate abilities.

One more thing: an I.Q. of 200, in my scale, would equate to a Rating of 3150 (FIDE) and a whopping 3700 (better than Komodo and Stockfish) on lichess.
Of course, again, the lichess scale is gonna go overboard because it incorrect assumes a global average and variance for a sample which obviously consists of not-so-average people.

With regards to the WAIS-IV, I think that within its scope (accurate for 95% of the population/those clustered around the mean) it is great, but past that not so much. This also happens with the RAPM and pretty much every standard I.Q. test.
ELO, however, is built on a proper ratio scale (with an absolute zero), has no major issue regarding reliability, and thus is accurate everywhere.
The only difficulty is that some people play chess for a couple of years (like I did), while others play it for a couple of decades or even their whole lives.
If the comparison is made with this fact in mind, it becomes much more powerful.

Thank you for your kind response and forgive for the terrible writing, getting real sleepy here.

@petri999 In my formula for online players, although I mentioned that they should be smarter than average, I did not include it; it is considering, as it stands now, that lichess players are a random sample of 100 thousand people from USA.

Funnily enough, in the other formula (FIDE), if you try 1550 (the average of lichess players), it outputs an I.Q. of 110, which is almost half a standard deviation above the mean (difference of 2.5 points).

FIDE equation is hardly a result of extensive studies. And correlation is threre but I doubt that estimated os max strength could be more accurate than say +-400 points elo and way more than one SD in IQ. IQ is a factor but things like short term working memory and sheer training are hugely influental as well.

As why most people cap IRL in 1700 it has lot to do how much effor is needed to improve. as it increases a lot as one becomes stronger. From 1400 to 1700 is is way easier thatn say from 2100 to 2200.

@Acoffe interesting! tired here too, just slogged through exam season. I'll be looking forward to any updates. I believe that I rad Kasparov has an IQ of approximately 190, your theory works reasonably well in regards to his particular case. All of the Wechsler scales are quite dubious in regards to foreign cultures also and I don't believe that there has been any IQ test which works perfectly for everyone. It would be interesting to see how young GM and IM's (<15 years old) develop in terms of IQ and measure if there is any predictability here in terms of mental development over time . Do you plan study any of this professionally / academically? I was quite surprised to find not a single chess book in my university several months ago :/

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