While the greater male variance hypothesis, and tail effects in general, are always interesting, I’m not sure if it’s too illuminating here. It is not surprising that there are some weird outliers at the top of the IMO list, ‘weird’ in the sense of ‘outperforming’ what you’d expect given some relevant variable like GDP, intellectual freedom, HDI index, national IQ, or whatever. That’s simply what it means for the correlation between IMO scores & that variable to be <1. If the IMO list was an exact rank-order correspondence, then the correlation would =1; but no one would have predicted that, because we know in the real world all such correlations are <1, and that means that some entries must be higher than expected in the list (and some lower). There’s always a residual. (This is part of why tests and measured can be gamed, because the latent variable, which is what we’re really interested in, is not absolutely identical in every way to the measure itself, and every difference is a gap into which optimizing agents can jam a wedge.)
When North Korea places high despite being a impoverished totalitarian dictatorship routinely struggling with malnutrition and famine, it’s just the tails coming apart. If we are curious, we can look for an additional variable to try to explain that residual.
For example, on a lot of economic indexes like GDP, Saudi Arabia places high, despite being a wretched place in many respects; does that mean that whipping women for going out in public is good for economic growth? No, it just means that having the blind idiot luck to be floating on a sea of unearned oil lets you be rich despite your medieval policies and corruption. (Although, as Venezuela demonstrates, even a sea of oil may not be enough if your policies are bad enough.) SA does badly on many variables other than GDP which cannot be so easily juiced with oil revenue by the state. Similarly, at the Olympics, Warsaw Pact countries infamously won many gold medals & set records. Does that mean the populations were extremely healthy and well-fed and happy? No, illegal doping and hormone abuse and coercion and professionalized state athletics aimed solely at Olympic success probably had something to do with that. Their overperformance disappeared, and they didn’t show such overperformance in anything else you might expect to be related to athletics, like non-Olympic sports, popular pro sports/entertainment, or life expectancy. Or, as respectable as Russian chess players were beforehand, the Russian school of chess, particularly in the Cold War, could never have prospered the way it did without extensive state support (potentially literally, given the accusations of employing espionage techniques and other cheating*), as a heavily-subsidized, propagandized domestically & overseas, professionalized program with lifetime employment, major perks like overseas travel, safety from persecution due to politically-connected patrons, and the sheer lack of much better opportunities elsewhere. But many other areas suffered, and like so many things in the USSR (like the Moscow subway?), the chess served as a kind of Potemkin village. More recently, Nigeria boasts an unusual amount of Scrabble champions; is Nigeria actually bursting with unrealized potential? Probably not, because they don’t dominate any other competitive game such as chess or checkers or poker, or intellectual pursuits in general, and Nigerian Scrabble seems to be path-dependence leading to specialization; you can easily win the annual per capita income of Nigeria at Scrabble tournaments, and there is now a self-sustaining Scrabble community telling you it’s a doable career and providing an entryway. Weird, but there’s a lot of games and countries out there, and one is always stumbling across strange niches, occupations, and the like which emphasize the role of chance in life.
* see Oscar’s comment about NK IMO cheating, which I didn’t know about, but am entirely unsurprised by.
North Korea’s IMO overperformance looks like it’s about the same thing as Soviet chess or Warsaw Pact athletics in general. I don’t know what benefits they get (do their families get to change castes, and move to Pyongyang? immunity from prison camps? how useful is the overseas travel to them? is it a feeder into the bubble of the nuclear program? how much financial support and specialized study and tutors do they get?), but I would bet a lot that the relative benefits for a NK kid who wins at the IMO are vastly larger than for a soft suburban kid from a US magnet high school who has never attended a public execution or gone hungry, and at most gets another resume item for college. (I’ve seen more than one IMO competitor note that IMO is not really reflective of ‘real’ math, but is its own sort of involuted discipline; always a risk in competitions, and seems to have afflicted the much-criticized Cambridge Old Tripos.) This is what juices the residual: almost all countries exert merely an ordinary endogenous sort of IMO effort, and only a few see it as one of the priorities to invest a maximum effort into. NK, it turns out, sees it as a priority, like building statues, I guess. The only remaining question here about the NK IMO residual is the historical contingency: how did NK happen to make IMO one of its ‘things’? Is it merely its typical envy-hatred towards China, because China for its own reasons targeted the IMO?
You can shoehorn this into a distributional argument, but when you don’t know which of the moments is changing (mean? SD? skew?), or even what the distribution might be (filtering or selecting from a normal does not yield a normal), I don’t find it too helpful and borderline circular. (“Why is NK performance on IMO high? Because their IMO performance distribution has a higher mean. How do we know that? Because their IMO performance is high.”) Pointing at the imperfect bivariate correlation and analyzing the possible causes of a residual is much more informative. When you look at the state involvement in IMO, it explains away any apparent contradiction with what you believed about correlations between intellectual achievement and GDP or whatever.
As far as I understand, the tails coming apart and the moment attribution are two different, superimposed problems. The tails coming apart is “Nigeria has the best Scrabble players in the world, but the persons with the richest English vocabulary in the world are probably not Nigerian”. The moment attribution is “the best Scrabble players in the world are Nigerian, but Nigerians are probably not the best Scrabble players in the world”. In the first case, we are talking about the distribution of country scores for two correlated variables, in the second we are talking about the distribution of individuals within a country for a single variable.
Also, thank you for bringing up Nigerian Scrabble, that would have made a somehow funnier example than NK’s math olympiads.
The tails coming apart is “Nigeria has the best Scrabble players in the world, but the persons with the richest English vocabulary in the world are probably not Nigerian”
No. The tails coming apart here would be “gameplaying of game A correlates with national variable B but the top players of game A are not from the top country on variable B”.
I say it’s borderline circular because while they aren’t the same explanation, they can be made trivially the same depending on how you shuffle your definitions to save the appearances. For example, consider the hypothesis that NK has exactly the same distribution of math talent as every other country of similar GDP, the same mean/SD/etc, but they have a more intense selection process recruiting IMO participants. This is entirely consistent with tails coming apart (“yes, there is a correlation between GDP and IMO, but it’s r<1 so we are not surprised to see residuals and overperformance which happens to be NK in this case, which is due to difference in selection process”), but not with the distributional hypothesis—unless we post hoc modify the distribution hypothesis, “oh, I wasn’t talking about math talent distributions per se, ha ha, you misunderstood me, I just meant, IMO participant distribution; who cares where that distribution difference comes from, the important thing is that the NK IMO participant distribution is different from the other countries’ IMO participant distributions, and so actually this only proves me right all along!”
More recently, Nigeria boasts an unusual amount of Scrabble champions; is Nigeria actually bursting with unrealized potential? Probably not, because they don’t dominate any other competitive game such as chess or checkers or poker, or intellectual pursuits in general, and Nigerian Scrabble seems to be path-dependence leading to specialization; you can easily win the annual per capita income of Nigeria at Scrabble tournaments, and there is now a self-sustaining Scrabble community telling you it’s a doable career and providing an entryway.
It might not just be specialization on Scrabble. English is the official language in Nigeria. I think it’s plausible that Nigerian elite English education focuses more strongly on learning a lot of words then US English education.
There are many countries besides Nigeria where English is an official language, elite language, or widely taught. And language proficiency apparently has little to do with Scrabble success at pro levels where success depends on memorizing an obsolete dictionary’s words (apparently even including not really-real words, to the point where I believe someone won the French Scrabble world championship or something without knowing any French beyond the memorized dictionary words).
To noodle a bit more about tails coming apart: asymptotically, no matter how large r, the probability of a ‘double max’ (a country being the top/max on variable A correlated r with variable B also being top/max on B) decreases to 1/n. The decay is actually quite rapid, even with small samples you need r>0.9 to get anywhere.
A concrete example here: you can’t get 100%, but let’s say we only want a 50% chance of a double-max. And we’re considering just a small sample like 192 (roughly the number of countries in the world, depending on how you count). What sort of r do we need? We turn out to need r ~ 0.93! There are not many correlations like that in the social sciences (not even when you are taking multiple measurements of the same construct).
Some R code to Monte Carlo estimates of the necessary r for n = 1-193 & top-p = 50%:
The comparison to chess is maybe more accurate than you think. See stuff like: Beginnings: The first IMO was held in Romania in 1959. It was initially founded for eastern European member countries of the Warsaw Pact, under the USSR bloc of influence, but later other countries participated as well.[2] (source https://en.wikipedia.org/wiki/International_Mathematical_Olympiad) Also classic geometry is (to my knowledge) taught more generally in many eastern European countries (and make up 1/6-1/3 of the imo).
Also the note about incentives being larger in North Korea also applies to much of eastern Europa to a lesser degree, where qualifying for imo is seemingly enough to get access to any university (source: Sankt Petersberg university gave an open offer at Baltic Way (a regional math competition), and i know someone who used something like that to get into Moscow university)
(Romania, Serbia, Poland, Russia, Ukraine Hungary are the eastern european countries with consistently good results)
A comparison to many Olympic sports also fits here as well. Just look at the success of Bulgaria in weightlifting throughout the 80s and 90s. Strong incentives, culture, coaching, and some cheating all played a role, just as I am guessing they do for IMO success.
Also the note about incentives being larger in North Korea also applies to much of eastern Europa to a lesser degree, where qualifying for imo is seemingly enough to get access to any university
I think that’s the case anywhere; qualifying for IMO is a pretty big deal.
At least the big Brittish schools this doesn’t clearly hold based on the experience of people i know. Granted the evidence i have is consistent with them only caring about silver or better.
Also my impression for the Russian schools was that not speaking Russian was a problem they were happy to work around (which certainly isn’t true everywhere)
While the greater male variance hypothesis, and tail effects in general, are always interesting, I’m not sure if it’s too illuminating here. It is not surprising that there are some weird outliers at the top of the IMO list, ‘weird’ in the sense of ‘outperforming’ what you’d expect given some relevant variable like GDP, intellectual freedom, HDI index, national IQ, or whatever. That’s simply what it means for the correlation between IMO scores & that variable to be <1. If the IMO list was an exact rank-order correspondence, then the correlation would =1; but no one would have predicted that, because we know in the real world all such correlations are <1, and that means that some entries must be higher than expected in the list (and some lower). There’s always a residual. (This is part of why tests and measured can be gamed, because the latent variable, which is what we’re really interested in, is not absolutely identical in every way to the measure itself, and every difference is a gap into which optimizing agents can jam a wedge.)
When North Korea places high despite being a impoverished totalitarian dictatorship routinely struggling with malnutrition and famine, it’s just the tails coming apart. If we are curious, we can look for an additional variable to try to explain that residual.
For example, on a lot of economic indexes like GDP, Saudi Arabia places high, despite being a wretched place in many respects; does that mean that whipping women for going out in public is good for economic growth? No, it just means that having the blind idiot luck to be floating on a sea of unearned oil lets you be rich despite your medieval policies and corruption. (Although, as Venezuela demonstrates, even a sea of oil may not be enough if your policies are bad enough.) SA does badly on many variables other than GDP which cannot be so easily juiced with oil revenue by the state. Similarly, at the Olympics, Warsaw Pact countries infamously won many gold medals & set records. Does that mean the populations were extremely healthy and well-fed and happy? No, illegal doping and hormone abuse and coercion and professionalized state athletics aimed solely at Olympic success probably had something to do with that. Their overperformance disappeared, and they didn’t show such overperformance in anything else you might expect to be related to athletics, like non-Olympic sports, popular pro sports/entertainment, or life expectancy. Or, as respectable as Russian chess players were beforehand, the Russian school of chess, particularly in the Cold War, could never have prospered the way it did without extensive state support (potentially literally, given the accusations of employing espionage techniques and other cheating*), as a heavily-subsidized, propagandized domestically & overseas, professionalized program with lifetime employment, major perks like overseas travel, safety from persecution due to politically-connected patrons, and the sheer lack of much better opportunities elsewhere. But many other areas suffered, and like so many things in the USSR (like the Moscow subway?), the chess served as a kind of Potemkin village. More recently, Nigeria boasts an unusual amount of Scrabble champions; is Nigeria actually bursting with unrealized potential? Probably not, because they don’t dominate any other competitive game such as chess or checkers or poker, or intellectual pursuits in general, and Nigerian Scrabble seems to be path-dependence leading to specialization; you can easily win the annual per capita income of Nigeria at Scrabble tournaments, and there is now a self-sustaining Scrabble community telling you it’s a doable career and providing an entryway. Weird, but there’s a lot of games and countries out there, and one is always stumbling across strange niches, occupations, and the like which emphasize the role of chance in life.
* see Oscar’s comment about NK IMO cheating, which I didn’t know about, but am entirely unsurprised by.
North Korea’s IMO overperformance looks like it’s about the same thing as Soviet chess or Warsaw Pact athletics in general. I don’t know what benefits they get (do their families get to change castes, and move to Pyongyang? immunity from prison camps? how useful is the overseas travel to them? is it a feeder into the bubble of the nuclear program? how much financial support and specialized study and tutors do they get?), but I would bet a lot that the relative benefits for a NK kid who wins at the IMO are vastly larger than for a soft suburban kid from a US magnet high school who has never attended a public execution or gone hungry, and at most gets another resume item for college. (I’ve seen more than one IMO competitor note that IMO is not really reflective of ‘real’ math, but is its own sort of involuted discipline; always a risk in competitions, and seems to have afflicted the much-criticized Cambridge Old Tripos.) This is what juices the residual: almost all countries exert merely an ordinary endogenous sort of IMO effort, and only a few see it as one of the priorities to invest a maximum effort into. NK, it turns out, sees it as a priority, like building statues, I guess. The only remaining question here about the NK IMO residual is the historical contingency: how did NK happen to make IMO one of its ‘things’? Is it merely its typical envy-hatred towards China, because China for its own reasons targeted the IMO?
You can shoehorn this into a distributional argument, but when you don’t know which of the moments is changing (mean? SD? skew?), or even what the distribution might be (filtering or selecting from a normal does not yield a normal), I don’t find it too helpful and borderline circular. (“Why is NK performance on IMO high? Because their IMO performance distribution has a higher mean. How do we know that? Because their IMO performance is high.”) Pointing at the imperfect bivariate correlation and analyzing the possible causes of a residual is much more informative. When you look at the state involvement in IMO, it explains away any apparent contradiction with what you believed about correlations between intellectual achievement and GDP or whatever.
As far as I understand, the tails coming apart and the moment attribution are two different, superimposed problems. The tails coming apart is “Nigeria has the best Scrabble players in the world, but the persons with the richest English vocabulary in the world are probably not Nigerian”. The moment attribution is “the best Scrabble players in the world are Nigerian, but Nigerians are probably not the best Scrabble players in the world”. In the first case, we are talking about the distribution of country scores for two correlated variables, in the second we are talking about the distribution of individuals within a country for a single variable.
Also, thank you for bringing up Nigerian Scrabble, that would have made a somehow funnier example than NK’s math olympiads.
No. The tails coming apart here would be “gameplaying of game A correlates with national variable B but the top players of game A are not from the top country on variable B”.
I say it’s borderline circular because while they aren’t the same explanation, they can be made trivially the same depending on how you shuffle your definitions to save the appearances. For example, consider the hypothesis that NK has exactly the same distribution of math talent as every other country of similar GDP, the same mean/SD/etc, but they have a more intense selection process recruiting IMO participants. This is entirely consistent with tails coming apart (“yes, there is a correlation between GDP and IMO, but it’s r<1 so we are not surprised to see residuals and overperformance which happens to be NK in this case, which is due to difference in selection process”), but not with the distributional hypothesis—unless we post hoc modify the distribution hypothesis, “oh, I wasn’t talking about math talent distributions per se, ha ha, you misunderstood me, I just meant, IMO participant distribution; who cares where that distribution difference comes from, the important thing is that the NK IMO participant distribution is different from the other countries’ IMO participant distributions, and so actually this only proves me right all along!”
It might not just be specialization on Scrabble. English is the official language in Nigeria. I think it’s plausible that Nigerian elite English education focuses more strongly on learning a lot of words then US English education.
There are many countries besides Nigeria where English is an official language, elite language, or widely taught. And language proficiency apparently has little to do with Scrabble success at pro levels where success depends on memorizing an obsolete dictionary’s words (apparently even including not really-real words, to the point where I believe someone won the French Scrabble world championship or something without knowing any French beyond the memorized dictionary words).
To noodle a bit more about tails coming apart: asymptotically, no matter how large r, the probability of a ‘double max’ (a country being the top/max on variable A correlated r with variable B also being top/max on B) decreases to 1/n. The decay is actually quite rapid, even with small samples you need r>0.9 to get anywhere.
A concrete example here: you can’t get 100%, but let’s say we only want a 50% chance of a double-max. And we’re considering just a small sample like 192 (roughly the number of countries in the world, depending on how you count). What sort of r do we need? We turn out to need r ~ 0.93! There are not many correlations like that in the social sciences (not even when you are taking multiple measurements of the same construct).
Some R code to Monte Carlo estimates of the necessary r for n = 1-193 & top-p = 50%:
https://i.imgur.com/Yzz2VYA.png
The comparison to chess is maybe more accurate than you think.
See stuff like:
Beginnings: The first IMO was held in Romania in 1959. It was initially founded for eastern European member countries of the Warsaw Pact, under the USSR bloc of influence, but later other countries participated as well.[2] (source https://en.wikipedia.org/wiki/International_Mathematical_Olympiad)
Also classic geometry is (to my knowledge) taught more generally in many eastern European countries (and make up 1/6-1/3 of the imo).
Also the note about incentives being larger in North Korea also applies to much of eastern Europa to a lesser degree, where qualifying for imo is seemingly enough to get access to any university (source: Sankt Petersberg university gave an open offer at Baltic Way (a regional math competition), and i know someone who used something like that to get into Moscow university)
(Romania, Serbia, Poland, Russia, Ukraine Hungary are the eastern european countries with consistently good results)
A comparison to many Olympic sports also fits here as well. Just look at the success of Bulgaria in weightlifting throughout the 80s and 90s. Strong incentives, culture, coaching, and some cheating all played a role, just as I am guessing they do for IMO success.
I think that’s the case anywhere; qualifying for IMO is a pretty big deal.
At least the big Brittish schools this doesn’t clearly hold based on the experience of people i know. Granted the evidence i have is consistent with them only caring about silver or better.
Also my impression for the Russian schools was that not speaking Russian was a problem they were happy to work around (which certainly isn’t true everywhere)