It's definitely my experience that it's hard to find people with high levels of mathematical knowledge who don't have a 4-year, technical-field bachelor's degree. It's of course possible this is merely a correlation, but I would at least
hypothetize that the students who've finished a four-year degree in an area like mathematics, computer science, electrical engineering, or physics, have more mathematical sophistication than they would have had if they had not finished that degree and taken/passed the mathematics classes it required.
It's not impossible to self-teach, but as far as I can tell, self-taught people usually don't self-teach mathematics, at least not successfully. Among self-taught programmers without CS degrees, for example, it's quite common to find people who are skilled coders, but much less common to find people who have a strong mathematical grounding.
Heck, if you want someone who really knows statistics and data mining, to take one example, I haven't met many people without grad-school experience who fit the bill. Masters degree is good, some PhD experience is better (finishing a PhD doesn't matter as much; ABD is fine).