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I would say greed only matters when you are the only one (or one of very few) bidding. If you want a player to stay for a lower cost than other teams are offering, you should be looking more at the loyalty. Low greed works well for you while players are signing their first contracts, or up for arbitration. You might be able to get your low-greed superstar shortstop for $4 million for 7 years in his 4th MLB season, whereas his value to the market could be $6-7 million per year or even more. A high-greed player may want $8-10 million/year.
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