I received a comment from a prof on the LRWPROF list after posting this. That person wrote: “We don’t have a “best brief” competition, but we do have a 1L criminal law moot court with best oralist and best team awards for the oral argument rounds. It’s a competition students sign up for that takes place early in spring semester. It’s a closed-universe problem, and the top 16 teams from the brief-writing phase move on to oral rounds. The prizes are $500 for the winning team and $250 for the runner-up team. The prize money comes from an endowment established in memory of a former criminal law professor, but I don’t know who established it (I could find out). The best individual oralist just gets glory and bragging rights. The competition is run by a student board chosen from the top eight teams (previously from the top 4 teams), with a faculty advisor (currently me).

“Let me know if there’s any other info I can provide.”