KöMaL 2014 B4660

In a championship, every team plays every other team exactly once. 3 points are awarded for winning, 0 for losing, and 1 for a draw. In the case of equal scores, the order of the teams is determined at random. The championship is in progress at the moment. Team $A$ is leading the points table. If team $A$ scores exactly $x$ points in the remaining rounds then they will win the championship. However, if $A$ scores more than $x$ points, they will not necessarily win. (It is possible for $A$ to score more than $x$ .) How many rounds remain to be played in the championship?