This could be a fastest time in a Mario Kart time trial, or a number of headshots in 2 minutes, or a high score on a pinball game. The specific instance I ran into was players playing NBA 2k trying to score most 3 pointers in a 1v1 game.

I'd like the option to specify a unit (score, time, etc) as well as ascending or descending order, and to allow an average of multiple values. For instance, doing an event for Home Run Contest in smash and allowing each player to have 3 tries and to average the 3 scores to get their final score on which their placement is based. You could even add features like "drop highest and lowest" to get a better average of say, 5 scores.