Jeff Nelson was drafted in the 22nd round of the 1984 draft by the Los Angeles Dodgers and was later acquired by the Seattle Mariners in 1986. He made his major league debut for the Mariners in 1992, pitching 66 games out of the bullpen to a 3.44 ERA and earning six saves along the way in 81 innings pitched. Nelson spent four years with the Mariners, where he earned nine saves total. It was with the Mariners that Nelson got his first taste of the postseason, where he is currently second all-time in games pitched behind Mariano Rivera. In 1995, Nelson and the Mariners faced off against the Yankees in the ALDS, where the Yankees blew a 2-0 series lead and lost the series. Nelson pitched 5.2 innings in three games, and getting seven strikeouts.
Results: 73 G, 0 GS, 74.1 IP, 4.36 ERA (115 ERA+), 3.31 FIP
Prior to the 1996 season, Seattle traded Nelson along with Tino Martinez and Jim Mecir to the Yankees in exchange for Russ Davis and Sterling Hitchcock. Nelson was an important piece of the Yankee bullpen in 1996, but was never the star because that bullpen featured John Wetteland and some guy named Mariano Rivera. Nelson's ERA might not reflect a great season, but his FIP and ERA+ show that he was pretty solid and could be counted on to get the ball to the Rivera and Wetteland duo in the back of the bullpen.
On May 1st, 1996, Nelson was brought in to protect a 6-5 lead against the Baltimore Orioles in the eighth inning. Although he did his job, this game eventually made it to extra innings before ending 11-6 on a Tino Martinez grand slam in the 15th inning. A full recap of the game can be found here. This game is noteworthy for Nelson because it was the first time he successfully attempted his signature pick-off move; one of only three times he had a successful pick-off in his career; and the only one that came with the Yankees.
The move was special because he would fake to third base and then try to catch the runner from first attempting to steal second base. His secret was his three-quarters sidearm delivery which let him get away with this pick-off move, instead of getting it called a balk by umpires. Anytime he sees this move or it's referenced, Yankees TV announcer, Michael Kay, still refers to it as "the old Jeff Nelson." (Fun fact: Former Yankees reliever, Boone Logan, actually wanted to ban the move because he felt it was unfair to lefty relievers.)
Nelson continued to pitch well and reliably for the Yankees in 1996, and was also the man on the mound when the Yankees clinched the American League East.
Nelson had a very solid postseason performance, except for one game in the ALCS against the Orioles. In two games in the ALDS against the Texas Rangers, Nelson allowed zero runs in 3.2 innings pitched. In the ALCS against the Orioles, Nelson pitched a scoreless inning in Game 1 before he took the loss in Game 2 after allowing three runs on five hits. However, Nelson bounced back to help the Yankees win the World Series, pitching 4.1 scoreless frames in three games of the Series.
What did he do after?
Nelson remained part of the Yankees bullpen for the next four years, and remained an integral part of it after the Yankees let Wetteland depart in free agency and named Rivera the closer. During this time, he helped the Yankees win three more World Series from 1998-2000, and was a solid part of the Yankees dynasty before Seattle signed him as a free agent before the 2001 season.
While pitching for the Mariners in 2002, Nelson found himself in a peculiar situation as he tried to sell his own bone chips from an elbow surgery on eBay. The auction site did shut down the bidding because of their "no body parts" policy. The money raised from the auction was to be split between Bear Creek High School (where Nelson's daughters attended school) and the Curtis Williams foundation. So as weird as that was, at least it was for a good cause?
The Mariners eventually traded Nelson and his expiring contract back to the Yankees in exchange for Armando Benitez (boo) in 2003. Nelson bounced around for a few years after that, spending time with the Rangers, the Mariners (third stint), the St. Louis Cardinals (for about three months of the 2005-2006 offseason), and the Chicago White Sox briefly during the 2006 season. In June of 2006, it was announced that Nelson would undergo surgery to repair a nerve on his pitching elbow, which effectively ended his playing career. On January 12, 2007, Nelson signed a minor league contract with the Yankees and retired later that same day.