I'm a little late to the party talking about Lebron "taking his talents to South Beach", but Planet Money recently did a podcast on Lebronomics that I think over simplfied the concept diminishing returns.
So in short Lebron James went to Miami so he could play with Chris Bosh and Dwyane Wade two other super star free agents. Alex Blumberg the show's host said that the impact of Lebron on happiness of local fans was smaller because Miami already had a superstar. He made the analogy to chocolate bars. If you are hungry the first chocolate bar is awesome, the second one is Ok, and the third makes you sick.
This demonstrates the concept of diminishing returns. That is the additional happiness from another player or a chocolate bar decreases which each subsequent one you add. However, diminishing returns don't necessarily start after the first player.
Players have the biggest impact on the probability of winning championships if the team already has some good players. For example teams close to making the playoffs will often trade for more expensive players. The Texas Rangers just added ace pitcher Cliff Lee, because they have a good chance to make the playoffs, they got him from the Seattle Mariners who have almost zero chance of making the playoffs. Cliff Lee provides more value to Texas than Seattle.
At the sports economics conference I went to last week one economist pointed a flaw in one presentation was that it assumed that a players value is constant for all teams. I agree, Lebron's value to the team may be higher in a place with another superstar in place.