Baseball Player Acquisition and Game Theory
http://www.businessinsider.com/some-free-agents-lose-money-because-they-are-good-at-baseball-2010-11
There are two ways for baseball teams to pick up additional players. First, there is the draft. It consists primarily of young, new players who have not played professionally but potentially have the skill to succeed in major league baseball. This is a game of sorts for the teams, as the potential payoffs for a team are different based on player selection and different teams get different amounts of utility for the same player. There is also the acquisition of free agents. Free agents typically have played in the major leagues before but no longer have a contract with a ball club. Different teams bid for a player’s loyalty in a what is essentially a first-price sealed bid auction. Though a player typically accounts for factors other than just pay while making his decision, money can be a major motivator and can dominate one’s decision-making process.
These two different forms of player acquisition are related. When a player becomes a free agent, he is rated as either being Type A or Type B. A Type A player, who is considered one of the best in the league, costs the team selecting him a draft pick. Type B players, however, do not cost a team a draft pick and thus do not hurt a team’s chances of drafting a star player. This has caused some interesting outcomes within game theory. The payoff for drafting a Type A player is high, but the lost draft pick decreases that payoff for the organization. Furthermore, unlike the draft, the first-price sealed bid auction for the player does not guarantee the acquisition of the player and takes time. The possibility of a team wasting time and effort on a player they do not end up acquiring should further decrease the payoff.
Based on this reasoning, if an organization is faced with the choice between two equivalent players (one a Type A free agent and the other in the draft), the drafted player would have the higher payoff. Similarly, if a Type A player and a Type B player have comparable skill (say, one of the bottom Type A players and one of the top Type B players), the Type B player would be selected because he would not cost the team a draft pick. This explains the phenomenon of skilled free agents (of Type A) going unsigned or making less money than Type B free agents. As a result, player skill does not directly correlate to salary.
The payoff for drafting a Type A player is high, but the lost draft pick decreases that payoff for the organization.?
Yes, a draft pick could potentially get a team another very skilled player. Thus, if a team is faced with signing either a Type A player or a comparable Type B player, the Type B player will be selected because it will not cost the team the draft pick (and the opportunity to gain another good player).