There is no number available. In multiplayer games, it's a button with a checkmark in it next to the name, green, yellow, red (orange) for different "classes" of completion rate.
AFAIK it's the completion %% of the last 100 MP games. "Complete" means, you arrived at the main game menu or the next game. Any quitting of either participant causing the game to stop, any abortion due to disconnects is an "Incomplete".
Edit:
After a few essays, I'm confused. There are no buttons visible in Match Play, but in Alternate Shot. Shouldn't it be vice versa? Have conditions changed that much?