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Your Lifetime Best displays the best score for the course regardless of the cup or tour it happened in. If the same course can be played in two cups in the tour, both courses will display the same score. The Tour Best for each ranked cup is reflected in that ranking, and any Tour Best that occurs outside of that specific ranked cup, as well as Lifetime Best, are not reflected in the ranking.
Note: The best score for the course during the currently active tour is displayed for the Tour Best.