Your idea is good too, but simply showing your own score would be a great start for improvement.
If you consider leveling this up you could try something like multiple values in the top center. Maybe your score your current rank and the highest score overall or your personal Highscore.
I'm no expert in that field but maybe look up the style of oldschool arcade games. Back than you had to pay for every round you play to beat the Highscore. When there are GameDevs which had to figure out how to do it, than those from the arcade era.
