Honestly, they tend to skew strongly in favor of people with strong academic backgrounds. Unlike Harvard (and to some extent, Stanford), which place a greater emphasis on GPA/LSAT, Yale Law tends to treat GPA and LSAT as threshold issues – and it’s often things like extensive academic work or additional degrees (masters, PhDs, etc.) that make the difference. I base this not only on my personal experience, but also on extensive discussion with the former director of admissions – Jean Webb (Jean | inGenius prep).
Frankly, this isn’t surprising, given that the admissions process at YLS centers very strongly on the professors (who ultimately make most of the decisions).
Long story short – write a senior thesis, get some publications if you can, it certainly won’t hurt. Also – write your 250 on an intellectual or academic hobby…those are overwhelmingly popular among accepted students.