Good question.
Let's stick with the teams named (with payroll rank: 2010 - 2015. It's too cumbersome to type out the values):
4 playoff appearances
Detroit: 6, 10, 5, 5, 5, 4
STL: 13, 11, 9, 10, 13, 11
3 playoff appearances
NYY: 1, 1, 1, 1, 2, 2
TEX: 27, 13, 6, 11, 8, 8
OAK: 28, 21, 29, 27, 25, 27 (absolutely remarkable)
TB: 21, 29, 25, 28, 28, 28 (equally remarkable)
ATL: 15, 15, 16, 16, 14, 23
CIN: 19, 19, 17,13, 12, 14
SF: 10, 8, 8, 6, 7, 5
2 playoffs:
BAL: 17, 18, 19, 15, 15, 17
PHI: 4, 2, 2, 3, 3, 9
NAT: 23, 22, 20, 12, 9, 6
PIT: 30, 27, 26, 20, 27, 25 (pretty damn impressive)
LAD: 12, 12, 11, 2, 1, 1
"Question Marks"
LAA: 8, 4, 4, 7, 6, 7
TOR: 22, 23, 23, 9, 10, 10
CLE: 24, 26, 21, 21, 26, 26
SEA: 9, 16, 18, 24, 18, 12
BOS: 2, 3, 3, 4, 4, 3 (I know where you're going with this)
So the "conclusion" could be that the Red Sox suck the most because they've had the fewest playoff experiences per dollar than any of the mentioned teams. Well, one could also say that the Yankees and the Dodgers suck more - but that's just one metric, with an arbitrary 5-year assessment (2010-2104)
Total Payroll: 2010-2104 (avg/year)
NYY: $1,038,632,704 ( 207,726,541)
PHI: $ 834,881,137 (166,976,227)
BOS: $ 810,814,337 (162,162,867)
LAD: $ 745,770,878 (149,154,176)
LAA: $ 682,085,607 (136,417,121)
DET: $ 671,513,188 (134,302,638)
SFO: $ 628,116,061 ( 125,623,212)
$/playoff appearance 2010-2014
NYY: $346M
PHI: $417M
LAD: $373M
LAA: $682M
DET: $168M
SFO: $209M
BOS: $811M
Judging by that criteria, and that criteria alone - the NYY are an infinitely better run club than the Red Sox...not even in the same ballpark. By that criteria, the Red Sox and the Angles are the worst-run teams since 2010, and Detroit is the best (of the big-market teams). Does anyone really think that?
The criteria is valid as far as it goes (e.g., the Red Sox were 1 game away from the playoffs in 2011 - and that 1 game would have changed this arbitrary way of looking at things substantially), and is certainly applicable when comparing the front offices of the Red Sox with, say, the Rays (with their draft picks)...but it ignores the development of the farm system and direct comparison with the competition on a non-arbitrary basis (for example, Philadelphia's payroll was really high when they made the playoffs...and what do the Yankees have to show for spending over $1B?) For that matter, given the Dodger payroll of the past couple of years, or the Angels even further back...are they considered better-run clubs than the Red Sox?