Tendering a contract literally means offering a contract. So, a team that offers Zack Greinke, a free agent this offseason, a contract could be tendering him a contract. Players who have played out the first few years of their original contract (the one the player signed when drafted) become arbitration eligible. Essentially, in order to attempt to properly compensate young players who find themselves still years away from free agency, MLB put in a system in which the player and team present information to a third party who decided what that player's contract will be for the next season. It is done on a season-to-season basis, and some players can go through 4 years worth of arbitration before becoming eligible for free agency. Any player who is arbitration eligible must be tendered a contract by a specific date, which happens to be December 2nd this year. Any arbitration eligible player not tendered a contract becomes a free agent. Arbitration can be an expensive process for teams. Especially when a previously productive player is coming off of a less productive season because that player will most likely make more money in arbitration, due to his past performance. A team might want to retain that player, but not at the expected arbitration salary, so the team non-tenders the player, allowing him to become a free agent, then offer him a separate deal for less money.
The process can be complicated, especially given the fact that the arbitration process has many flaws incorporated into it. Since it is complicated, here is a simple rule. Teams non-tender players when the team would rather risk losing the player to another team than possibly pay them an exorbitant amount of money through arbitration.
Non-tendering a player can prove fruitful or fruitless. Sometimes the player in question will sign with another club and perform very well whereas other times non-tendering a player can be the best way to dump a declining or injury-prone player. Some names that came out on the non-tender list this offseason include John Lannan, Mark Reynolds, Ian Stewart, Jair Jurrjens, Jeff Karstans, and Brian Wilson. The common themes amongst these players are injuries, Karstans, Wilson, and Jurrjens, and declines in productivity, Lannan and Sterwart. If you want a more comprehensive list, and way to track players who have been non-tendered, tendered, et cetera, check out MLBtraderumors page here.
Brian Wilson, known as "The Beard", put up a few productive years out of the San Francisco bullpen. With Sergio Romo taking his spot in the back end of the Giants bullpen, combined with Wilson's recent Tommy John surgery made Wilson an obvious non-tender candidate. Wilson is very valuable, but not in the typical way. Any team with money that is in need of a veteran cog in the bullpen could take a chance on Wilson, given his low cost, and Wilson's desire to prove himself. A team that might not be in contention next season could look to sign Wilson in order to flip him for prospects at the trade deadline in July. According to PECOTA, Wilson could be worth one WARP per season for the next three years. Any team that can sign Wilson to a one-year deal worth no more than $6 million could end up with a solid bargain. Look for the big clubs like Boston, Baltimore, Los Angeles (both LA teams), and Detroit to take a chance on Wilson.
Now that you have a full understanding of non-tendering, when this time comes about next season you might be able to point to specific players who make good non-tender candidates and other that don't. Remember, oftentimes the most important pieces to a 25-man roster can come from the most remote of places, like the jungle of non-tendered players. http://www.baseball-reference.com/players/w/wilsobr01.shtml