4. In a ball game competition, there are eight teams participating, and each pair of teams has to play a match. A team gets 2 points for a win, 1 point for a draw, and 0 points for a loss. If a team wants to ensure it enters the top four (i.e., its points must exceed those of at least four other teams), then the minimum points the team needs are $\qquad$
4. 11.

Since there are eight teams, there will be $\frac{8 \times 7}{2}=28$ matches, totaling $28 \times 2=56$ points.

If the top five teams draw with each other and each win against the bottom three teams, and the bottom three teams draw with each other, then there will be five teams each with 10 points, and the other three teams each with 2 points. Therefore, scoring 10 points does not guarantee a place in the top four.

If a team scores 11 points but is in fifth place, then the total points of the top five teams is at least 55. Thus, the total points of the bottom three teams is at most 1. However, the total points from the three matches among these three teams should be 6, leading to a contradiction.

Therefore, scoring 11 points definitely ensures a place in the top four.