The salary of a star players often increases substantially when they become free agents

A monopsony is the market structure characterized by the presence of a single buyer. This implies that the buyer has the power to bargain.

When the players are playing as a team, they are given equal salaries as other team members. The players who are not so good also receives the same amount of money. However, when they become "free agents", they're free to choose the team they wish to get associated with.

The salary of the star player increases when they become free agents. When a player becomes the free agent, he may choose the team he wants to get associated with at his expected salary. Hence, he isn't the seller of his service, but he acts as a buyer and equates as to which team can pay his salary. He's got the power to negotiate and select his team.