Back in 1988, there was an impressive chess festival in the small industrial town of Saint John, Canada. Two large and very strong Open tournaments were combined with the complete set of seven Candidates’ matches in the World Championship cycle of the time (Karpov was to join the seven winners). The English contingent were all on good terms and in good cheer (Nigel Short was making mincemeat of Sax in his match, likewise Jon Speelman of Seirawan) and usually formed, combined with certain selected ‘foreigners’ (like Spassky), a massive eating party which the local restaurants struggled to accommodate. I have a fair recall of the conversation on one such evening. Nigel Short was asked what he thought his IQ was. He was not sure, but (far too modestly) proposed 130 or 140. John Nunn, his second, suggested that with a little training, Nigel could knock his score up to at least 160. Speelman was not impressed by IQ tests generally, and everybody saw the inadequacy of any test which depended on how much practice you had had at the type of questions involved.
At this point, some bright spark (me) suggested that it might be a better measure of intelligence to do two tests and see how much the person improved. Quick as a flash, Nigel replied that this was a very bad idea since you could do deliberately badly in the first test! It took me a few seconds to grasp his meaning - that you could artificially inflate the difference in your scores and thus score better in the proposed test.
Everybody was fairly impressed by this quick and crafty answer and the conversation moved on. The story illustrates something important about the nature of the chess mind - how good it is at short cuts (no pun intended) and tricky ways round things. Mathematicians are usually less devious in their thinking - it is important to find direct ways to prove things.
There is a story about a Turkish reformer who wanted to discourage women from wearing the veil. Instead of attempting to forbid it directly (the mathematician’s approach), he issued a decree that all prostitutes must wear veils. This indirect ‘trick’ proved the workable, effective way to his objective and shows the sort of thinking which chessplayers are often rather good at.
In chess too, it is the result that counts, not how correctly it is derived. ‘Players’ like to try things out, and not to study other people’s work diligently. Chessplayers are good thinkers but not always good students, as many university dons have found to their annoyance!
I discussed what is meant by intelligence at the start of the book (just after the introduction), and later gave it as a typical characteristic of the chess genius, but so far I have not really answered the question: ‘how strong is the connection between chess ability and IQ?’. There are many reasons, some of them simply common sense, to believe that the two are strongly correlated. (A correlation of zero means that two things are entirely independent; a correlation of one means they are entirely related or dependent on one another. Mathematically speaking, all things are correlated somewhere between zero and one.) De Groot considered several of these reasons, and the next paragraph summarises some of his conclusions.
Spatial intelligence - especially the ability to perceive possibilities for movement - is clearly crucial to chess thinking, as is the capacity to build up a system of knowledge (knowing that) and experience (knowing how). This system must be stored (memory) and well managed - rules, analogies and operating principles must be constantly abstracted, adapted and improved (perhaps not always on a conscious level). Chess thinking often involves a complex, hierarchical structure of problems and sub-problems, and the capacity for retaining such complex structures of data (not getting confused), and for keeping objectives clear and well organised, all correlate with having a high IQ.
Before offering, very tentatively, my equation linking potential chess strength with IQ, I would like to say a little more about the IQ scale. Assuming, somewhat incorrectly as pointed out earlier (and it is true that from a false assumption you can deduce anything, but this sort of false assumption should be seen as just an inaccurate approximation), that intelligence follows the ‘normal’ distribution (mean 100, standard deviation 15), then how many really bright people would there be? The mathematical/statistical implications would be as follows:
16% above 115; 2.3% above 130; 0.13% above 145 and 0.003% above 160.
This would correspond to there being approximately the following numbers of people above the given levels in England:
1,150,000 above 130; 65,000 above 145 and 1500 above 160.
This should give you a fair idea of the way the normal distribution works, though remember that these are underestimates of the actual numbers. It is very difficult to generalise about the type of characteristics people have at different levels of intelligence. The following attempt to do so, an excerpt from Choice Mathematics (book one) by Kevin of the Teachers, is certainly quite provocative: ‘There appears to be a hierarchy of abilities and traits in those of high intelligence as follows, suggesting an order for teaching intelligence.
IQ (S.D. = 15) Attributes 185 High natural neuro-kinesthetic control; high curiosity drive; anti trivia; in a hurry 180 New creation 175 Knows intelligent (and right!) 165 Formalisation; beginnings of self confidence; less hiding 160 Interest in logic; paranoia; minor creation; recognises good work; art; music 150 Trivial formalisation 145 Below this level and often above is everywhere found a slavery to conditioning’
If this is true, then I guess all us slaves to our conditioning had better hope that the conditioning is good conditioning! Now that the vast majority of readers are feeling suitably outraged, it is time to present the ‘Levitt Equation’. I stress that this equation is subject to a number of reservations and should not be taken too seriously.
The Levitt Equation
The meaning of the ‘~’ symbol can be taken as ‘given many years of intense effort, will tend to equal approximately’. That is to say that a player with an IQ of Y, after many years of tournament play and study will tend to have a chess Elo rating of about 10Y + 1000.
It is easy enough to translate this into
British Chess Federation (BCF) grades, should anybody prefer to use the English system rather than the international one. Using the standard conversion:
Elo = 8 x BCF + 600
and combining this with the ‘Levitt Equation’, one gets (after some basic algebra):
BCF ~ (1.25 x IQ) + 50
This no longer has the round numbers of the original, and thus loses some of its appeal. What do these equations imply? Assuming, for the sake of speculation, that the formula is correct, there would be many conclusions:
1) To become World Champion (about 2800 standard these days) you would need an IQ of about 180. I suspect many of the World Chess Champions do have IQs of this order. Could this be why darts commentators get so excited by this number?
2) A person of ‘average’ intelligence, IQ = 100 by definition, could expect to reach about Elo 2000 (or BCF 175). As a group, chessplayers are likely to be above average IQ, since chess will appeal more to those who are initially successful at it, so perhaps the ‘average chessplayer’ could expect to reach (after sufficient work) a slightly higher level.
3) Strong grandmasters (Elo = 2600+) are likely to have an IQ above 160.
4) In England, only a tiny fraction of those with sufficient talent to reach 2500 actually do so. The majority never spend enough time at the game to even begin to fulfil their potential. On the 1st January, 1996 there were eighteen English players 2500 or above on the Elo list. This compares with the estimate of some 24,000 with IQ over 150 in the population as a whole (so the fraction is less than one in a thousand). Assuming, again somewhat incorrectly, that genetic intelligence is uniformly distributed across the planet, one could use the fraction who ‘make it’ as an indicator of the degree of chess culture in the respective country. Iceland, with all the necessary assumptions, would have just over 100 people with IQ greater than 150. Yet at least half a dozen of these have reached 2500. Call it one in twenty - this is more than fifty times better than England. Perhaps it is simpler to forget about IQ and just compare the number of grandmasters and the size of the population, but Iceland does show what can happen if you hold a major World Championship match in a small country. It seems that after making allowance for the limitations imposed by ‘nature’, there is still enormous scope for ‘nurture’ to make a difference.
You cannot, of course, use the equation to deduce a person’s IQ from their chess rating since the precondition of the necessary years of effort and study may not apply. One could try writing the equation with the ‘<‘ symbol (meaning ‘less than’) rather than the ‘~’. I.e. Elo is less than (10 x IQ) + 1000. Then no preconditions are needed, but I feel this equation would be misleading since most players probably could go higher than this equation would imply is possible, given sufficient motivation. Perhaps Elo < (10 x IQ) + 1200 would be harder to falsify.
There are a number of possible objections to the Levitt equation:
1) You do not like the whole IQ concept, perhaps because you think it is impossible to bring human intelligence down to one dimension (a number). I have some sympathy with this.
2) You think it ‘politically incorrect’ to rate humans with a number. I have no sympathy with this view. If it were possible to do it accurately then I think it could certainly be a good (useful) idea, the trouble (and danger) is that it may not be possible to do it accurately. People do not generally object to measuring height with a number, so why get all emotional about intelligence? As a friend of mine (who wishes to remain nameless) put it, ‘people with small ones often say that size doesn’t matter’. And yes, he was referring to intelligence!
3) You do not think the numbers in the equation are right, in that you think chess requires either more or less intelligence than the numbers imply. You could be right in either direction, I do not know. At least the numbers (10 and 1000) are simple to remember. I think they are about right, in as much as it is possible for such numbers to be right.
4) You think that if there was a formula, it would not be of the simple, linear type. Almost certainly correct - but it is just an approximation.
5) You might agree with the Venezuelan Ministry of Education’s findings that study of chess in schools leads to an increase in IQ scores. This could complicate matters, but only if you are concerned with implausible levels of accuracy.
6) Other objections. Yes - there are one or two other major problems, as will be explained in the final section of this chapter.
Extract from Genius in Chess (J. Levitt, 128 pages, Batsford, 1997, £12.99 ISBN 0 7134 8049 1)