I don't think it matters in FA. Elite relievers get paid regardless of what role they were in. It may matter in arbitration.
Maybe. But here are the top paid relievers in MLB. See:
https://www.spotrac.com/mlb/rankings/relief-pitcher/
Rank. Name, Team - 2019 salary - notes
1. Chen, Mia - $20m - Signed a deal before the 2016 season when he was a starter logging near 200ip a season. Just became a reliever this year, so he doesn't really count.
2. Jansen, LAD - $19.3m - Signed before the 2017 season, after saving 47 games in 2016 (and 127 from 2014-2016).
3. Melancon, SF - $19m - Signed before the 2017 season, following 51 saves in 2015 and 47 saves in 2016.
4. Davis, Col - $18m - Signed before the 2018 season, following 27 saves in 2016 and 32 saves in 2017.
5. Chapman, NYY - $17.2m - Signed before the 2017 season, following 36 saves in 2016, and 143 saves between 2013-2016.
6. Kennedy, KC - $16.5m - Signed before the 2016 season, when he was a starter, so like Chen, he doesn't really count here as he just became a reliever and his contract was a starter's contract.
7. Britton, NYY - $13m - Highest paid non-closer. Naturally...signed by the Yankees, who can afford such luxuries.
8. Chatwood, ChC - $12.5m - Signed before the 2018 season, when he was a starter, coming off 25 starts in 2017.
9. Martinez, StL - $11.7m - Signed before the 2017 season, coming off 195.1 innings and 31 starts in 2016. He then threw 205 innings in 2017, so his contract is a starter's contract.
10. Miller, StL - $11m - Signed before the 2019 season, as a non-save reliever.
11. Robertson, Phi - $10m - Signed before the 2019 season, as a non-save reliever.
Ok so of these top 11, four were starters when they signed their contracts (Chen, Kennedy, Chatwood, Martinez), three were non-save relievers (Britton, Miller, Robertson), and four were save-heavy closers (Jansen, Melancon, Davis, Chapman).
Note too that the three non-save relievers all have Yankee ties. Either their current contract was from NY (Britton), or they made big money with NY and then again with another team (Miller, Robertson).
Type: Ranking in the top 11
Starters: #s 1, 6, 8, 9
Non-save relievers: #7, 10, 11
Save-heavy closers: #2, 3, 4, 5
Taking the salaries for the top save-heavy closers and the non-save relievers, here's the averages:
- Save-heavy closers: $18.4 million
- Non-save relievers: $11.3 million
It's not that Barnes wouldn't get paid big bucks if he hit the FA market after this year. It's that he wouldn't get paid NEARLY as much as if he were a traditional save-heavy closer. Because for some reason, teams still value those guys more.