The Arena Tournaments offer two distinct scoring modes as described below:

In High Score events, the leaderboard shows each player's single best round score. For example, if you play three rounds of Word Drop and score 200, 210, and 195, your score of 210 would be ranked on the leaderboard.
You may continue to play more rounds and if you score above your high score, this new score will replace your previous best. If your round score is lower than your best, your previous highest score will continue to be used.

In Total Score events, all of the player's round scores are added together to form a single score that is reflected on the leaderboard. For example, if you play three rounds of Word Drop and score 200, 210, and 195, your leaderboard score will be 610 (200 + 210 + 195).

Each additional round you play will add to your total score, so play often and score high!