Even cherry-picking to the last 6 years, the Sox are one of the top 5 MLB teams to follow, if you weight rings very highly:
1 ring, 6 POs, Best record: LAD (2 WS showings)
1 ring, 6 POs, 2nd best record: HOU (3 WS showings)
1 ring, 6 POs, 3rd best record: ATL (1 WS)
0 rings, 5 POs, 4th best record: TBR (1WS)
1 ring, 2 POs and 8th best record: BOS (1 WS)
1 ring, 2 POs, 12th best record: PHI (1)
0 rings, 5 POs, 5th best record: NYY (0)
0 rings, 5 POs, 6th best record: MIL (0)
0 rings, 4 POs, 9th best record: STL (0)
0 rings, 3 POs, 7th best record: CLE (0)
0 rings, 3 POs, 10th best record: MIN (0)
0 rings, 1 POs, 11th best record: SEA (0)