I don't think a 650 would have gotten me into Yale.
They are looking for students who are stronger on the GMAT, since they have such a small class, but I think it would have made me more competitive than the 590.
Still, I gather they are looking for students who are at the top of their game So, consider how you could make yourself absolutely outstanding in your extracurricular activities or professional choices as well.
Students who did not get into Harvard or Stamford consider Yale, so they score 680's and above. Students are scoring 720s and higher, but a 680 or 700 would definitely get you noticed. As for my profile, I am a high-school teacher and teacher coach in an urban school district and my career plans were rather unique for the not-for-profit sector.
If there is anything else you need to know, please ask.