There's a blue circle behind the flags before you beat the race after you beat the race it changes to a blue wreath behind the flags, as far as I know that's the only way I know I did the race, I dont pay any attention to the explanation marks
Actually I can confirm the wreath does hold true. You must beat the event in the lowest level option for that event and the wreath will show up.
At least it's worked like that for 30 races in a row so far for myself. Press the left on the dpad to get to the lowest level option then hit R1 to start.
Question is what do the crowns mean above the race, that seem to have a random placement. My only guess is that it means I have the best score for that event in my crew
The wreath aroun the event is confirmed, Because I just got the Platinum trophy
