Puts pressure on free agents how? I know it is widely stated, but that doesn't mean it's based in fact (as opposed to people suggesting, 'don't blame the heroic player for being greedy, it's the evil union' -- same logic that leads to such vitriol for Scott Boras). Maybe they would talk to the player if it was something outrageous, like signing for the league minimum or something, but I really don't think the union is sitting on the players' shoulder and telling him to take $10 million more to play for the team he hates rather than the team he actually wants to go to. (Also, fairly sure MLBPA members just pay set dues; the union doesn't get a percentage of their contract) This is getting slightly off the topic of Greinke though