4) Jeff Brigham
Jeff Brigham was the second piece of the offseason deal with the Marlins that also netted the Mets Elieser Hernandez. Brigham was supposed to add depth to the bullpen and was a guy the Mets envisioned shipping back and forth from AAA Syracuse to the majors considering the fact that he was able to be optioned.
Billy Eppler had a vision where the bullpen would remain fresh with the Mets sending relievers up and down but also productive enough to win ballgames. Why he opted to go with optionable relievers instead of just signing a proven one without options is beyond me, but it's part of why the bullpen struggled in the middle innings. Brigham was right in the middle of that.
The right-hander had a 5.26 ERA in 37 appearances and 37.2 innings of work. He got off to a decent start for the Mets but the more he was used, the more he struggled. He wound up making just five appearances in the second half as he was ineffective whenever he was called upon.
Brigham didn't show one bit that he was worthy of being part of the 2024 bullpen, so the Mets have no incentive to tender him a contract. If Brigham enjoyed his time with the Mets and they want him back as depth, a minor league contract would likely be on the table. There's no reason to give him more than that.