It's the highest rated opponent you have beaten in a rated game.
What Defines "Best Win"?
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On my stats page, there is a stat called "Best Win" that claims my best win was against an 1195 player. Since then, I've defeated two 1400 players — one in fewer moves — but this stat has not changed. I have not found a way to change this manually or suggest an update, so I was wondering what or who determines which game is a player's "best win."