Pittsburgh argued during Wednesday's hearing he should be paid $5.6 million, A decision by arbitrators Gil Vernon, Jeanne Wood and Steven Wolf is likely Thursday.
A 31-year-old left-hander, Watson had a 3.06 ERA in 70 relief appearances for the Pirates last year along with a 2-5 record. He was an All-Star in 2014, when he was 10-2 with a 1.63 ERA, and he had a 1.91 ERA in 2015.
Watson is eligible for free agency after this season.
Teams and players have split 12 cases this winter and the sides are on track for 15 hearings, the most since teams won 10 of 16 decisions in 1994.