It would be really cool if someone did do some randomized research on this. Now I'm really curious. Given the STEM obsession at present, maybe it's been done.
it may sometimes happen that someone that didn't think of themselves as super strong in math, may do really well in a competition, realize they've underestimated themselves, and improve a lot. (I.e. the competition could "discover" unrecognized/undeveloped talent, which is subsequently developed.)
I'm a fan of wide IQ-testing for this reason. I like the idea of casting a broad net. DD was assigned to sit next to a super-mathy kid for a while this year who liked to quiz her on math not yet covered in school (not sure if he lacks social skills, is just super psyched about math, likes my DD, or what). Even through this, I think she realized she had more skill at math than she knew. Actually, this is kind of a cute story about the value of gifted programs, now that I think about it.
