The blue cat icon symbolizes your Rating. The Rating determines your position in League and in the World Ranking.
Your Rating depends on your success in battles. It increases when you win in Quick Fights, Championship or place successful Bets. It can also decrease if you lose the battle.
IMPORTANT: Please note that there is a limit of Rating points that you can get on a certain Stage of the Championship. Until you promote to the next stage, you won't be able to get more than the certain number of Rating points. Your Prestige also increases the limit of Rating points you can achieve.