Equal but different

Probability Level 5

In a round robin tournament with $N$ teams, every 2 teams play in a head-to-head match. Points are awarded as follows: 3 points for a win, 1 points for a tie and 0 points for a loss.

What is the smallest value of $N$ , such that it is possible for all the teams to have the same number of points, but for (at least) two teams to win a different number of matches?