My chances?

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This is entirely untrue - in biology Yale is probably top-5 nationally, in math it’s top-10, in the physical sciences it’s top 15, all at the graduate level. At the undergrad level, there won’t be any big enough differences to distinguish between it and anywhere else (with the exception of tech schools like Caltech and MIT, where the culture of the university makes the academic experience in the sciences even more intense, in both good and bad ways).
The broader point - that Yale is fine to go for as a pure science major, and weaker as an engineering major, is probably true. It does have a substantially weaker reputation in engineering than some of the other top schools.</p>