This is an interesting idea. Something that I have been thinking in the context of qualifying the quality of a nation's education program is how these things should be considered given that division of labor is the standard mode of operation. Germany for instance has a highly tracked education system, and consequently it has some world class scientists as well as some very talented mechanics but I suspect neither group is very good at the other's specialty. A country can have poor average math scores but be globally competitive in mathematics as long as some collection of people are trained well. The US for instance is largely terrible at mathematics (on average), but we have also produced a large number of world class mathematicians and scientists because we eventually dedicate serious resources toward training a small subset of the population to do these things well.