I thought that Peter might be a bit pessimistic about Jansen reaching 500 saves for his career, but then I looked at some season results for total saves for a team. Getting to 24 saves without being the designated closer would be difficult, give that team total saves generally hover around 40 for the Tigers in recent years. I also looked at some of the Yankee totals during Mariano Rivera's heyday, and they did get to 50 once. I recalled Bobby Thigpen's 57 saves for the White Sox in 1990 (Thigpen was on my Rotisserie league team that season.); the team recorded 68 saves total. My impression is that, if a team records a very high number of saves, it's likely that one designated closer accounts for the high team number.
There have been a few teams with two pitchers recording 25 or more saves in a season, although this is very unusual.
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I think there is a possibility that Jansen will get his 24 saves, even if he and Vest share responsibilities as the primary close, although I think this a long shot. If there is three-way sharing of the role, I can't see Jansen getting 24 saves.
Please note that none of this meets any standard for being a rigorous analysis.
Mike Coveyou