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The other first baseman who will be competing with Davis if neither ends up getting traded will be Lucas Duda. Duda should end up on the Mets' major league roster regardless, but it's the starting first base job he would be battling for.
After spending the 2011 and 2012 seasons as a right fielder and part of 2013 as a left fielder, it has become clear that Lucas Duda's position going forward will be at first base, whether it is with the Mets or another team.
Duda batted .223 with 15 home runs and 33 RBI in 318 at-bats this past season. He was the starting left fielder until he got injured in June and was replaced by Eric Young Jr. in left field for the rest of the season. When Duda eventually returned in late August, it was as a first baseman. Originally, he was on the bench, but after Davis got hurt, Duda took over at first base for the rest of the season.