> If you look at the top 10 distance runners, they're all from Ethiopia and Kenya. But as you look further down the list into the top 100, you start to see Amer

> If you look at the top 10 distance runners, they're all from Ethiopia and Kenya. But as you look further down the list into the top 100, you start to see Americans and others. Furthermore, the Americans' times are really close to the Ethiopians and Kenyans. > Because it doesn't say anything about the individual people, who vary much more than the difference in averages. It's not clear it says anything about the difference in averages. Say someone is born in Syria with great genetic potential to be a distance runner, you might expect they are unlikely to "live up to that potential" because of all the obvious things that get in their way. Is it not possible that individuals who are biologically very well suited for distance running in Kenya have a better chance of ending up as distance runners than they do in America, because Kenya specializes in distance running and America does not, and because America actually specializes in other comparable things that are more remunerative? Or perhaps that in Kenya, amateur athleticism is a relatively lucrative career compared to outside options whereas in America it is not. Let me model this mathematically; say countries are homogeneous such that all persons born in the country j are characterized by a two parameter model that for the sake of argument we'll take to be normal: mean_j and sd_j. A draw from this distribution assigns natural talent theta_i to each person i. If they choose to train and run, we see theta_i, so the observed outcome is: y_i = D_i theta + (1 - D_i) 0. Thus training to run is a treatment (D_i); if you are treated you reveal your talent theta, if you are control, you don't run and no one knows. Then the characteristics of the population as a whole are characterized by mean, standard deviation, and n (population) and the observed distribution is just the distribution of y_i. In all countries D_i = f_j(theta_i, p_j); p_j refers to the fraction of the country that runs; in a country where everyone runs, the function is constant 1. In a country where runners are a random sample f_j has no theta_i term. You could imagine other functions that are positively or negatively correlated with talent. An easily implementation of this would be to draw a bernoulli variable with p_j and some correlation rho_j with theta_i; you can do this with a copula or the analytic formula for biserial normal-bernoulli correlation, but let's say the detals of the function are irrelevant. Finally, competition reveals max(y_i) for a country, and thus for the planet. It is easy to find a world where the identity of the winning country j is the country that has the highest mean. It's also possible that the identity reflects mean-sd-n (e.g. all countries have the same average but some have more variation; or more births = more outliers). But it's also easy to assign viable p_j or f_j(theta_i) p_j such that the "wrong" country wins because of cultural factors. It's true the model is a toy model (countries aren't homogeneous, talent may well not be normal, theta is not perfectly revealed and training has varying degrees of quality, individual race times have stochasticity), but even accepting the toy limitations wherein every cultural factor goes through f_j(theta_i) and p_j, it's clear we don't have a bead on mean_j. So, like, what now?