If someone is smart enough to play chess at the highest levels, wouldn't he/she be better off as a mathematician?
Many American chess players switch to poker or a different profession.
Edit: it just occurred to me that, since we are talking about "average" and not "median", this may as well be true, if a handful of mathematicians make a gazillion dollars a year. Very senior faculty members in the top research universities in the US are likely to make only $200-500k per year.