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I apologize if this question comes across as dumb, but I was wondering how important "connections" are when it comes to securing a judicial clerkship (and by connections, I mean knowing the actual judge on a personal level)?

I mean knowing the actual judge on a personal level

I'll put it this way: Add up the time you actually spend talking to him/her in a year. Average it out since you were in high school. Not the time when you are at the same neighborhood party or whatnot, but the time actually spent engaged in face-to-face communication. If it's more than 100 minutes per year, you probably know the judge well enough for it to make a difference.

(The point is: Yes, connections can make a big difference. But people tend to to grossly overestimate how good their connections are.)

I'd say it's less than 100 minutes per year, but both of the judges I have in mind are very close friends with my father (who's currently a criminal defense attorney).. but I guess you already answered my question - connections matter haha