Waitlist is better than outright rejection. I know it isn't much consolation but the fact that you even made it on the waitlist is quite an accomplishment with this school.

Stanford is only slightly less selective than Yale. Yale only accepts about 9.7% of all applications (for JD) and Stanford only about 10% for JDs. Harvard is "much" higher at 15%. I can't find any stats for LLMs but I would imagine it is somewhat similar.