The new team multiple seasons charts on FanGraphs makes it simple to figure out who the best/most important players for the Mariners have been since 2001. Behold, easy and not especially deep analysis.
Here are the links for position players and for pitchers for the Mariners from 2001-2010. Based solely of fWAR from the past 10 years, here are the players the Mariners would field if they wanted a team that contributed the most during the soon-to-be-over decade:
In the field
1B John Olerud
2B Bret Boone
LF Raul Ibanez
CF Mike Cameron
DH: Edgar Martinez
Wow, that list seems obvious. Extremely obvious. There's only one fabricated position battle, which would be whether you'd give Gutierrez the nod over Raul in LF. Otherwise, there's a sizable drop off from the top at one position to the next. The Mariners clearly haven't been able to swap out one quality position player with another.
To further poke at the Gutierrez/Raul debate, I also tried subtracting the replacement runs from runs above replacement. That should get rid of some of benefits of added playing time, I think. (I could divide by games or innings played, but that isn't on the FanGraphs page, and this whole thing isn't intended to be too substantive.)
If you do that, Franklin looks better than Raul (41.8 RAR-Replacement runs vs. 18.6). If you do that for the whole team, David Bell, Stan Javier, Russell Branyan, and Desi Relaford look like good bench players. Does anyone remember David Bell for anything besides almost starting the All-Star Game in 2001?
Toeing the rubber
Gil Meche (I cheated here, sorry)
(I don't like huge bullpens for "best of" lists, so I'm stopping here)
This list, especially the starters, screams of piling up wins through extended playing time. I used to love Joel Pineiro (I remember him pitching remarkably well in his first game in 2000, when he was called up to start in a double header), but no one looks back at him fondly as one of the five best pitchers on the squad. The starters are three mostly-lovable pitchers and then "bleh"
My solution: divide runs above replacement by innings pitched. That should give you the best pitchers the Mariners sent out to the mound. It also produced chuckle-worthy results.
Top 12 RAR/IP pitchers
*small sample size (less than 50 innings)
**RIDICULOUSLY small sample size (less than 6 innings)
Jamie Burke: better than any Mariners closer of the past decade. Somehow Burke got +.3 RAR for giving up a run to lose a game in 2008. Well, reviewing the Mariners teams of the past decade isn't complete without mentioning Burke, Madritsch, or Jon Huber. Also, it isn't necessary.
Next in line to replace Burke and Cortes would be Freddy Garcia and David Aardsma.
The other main use of the FanGraphs team links would be to look at players who contributed a negative WAR during their run the past decade. Garrett Olson and Matt Tuiasosopo tie for being the crummiest Mariners to somehow get playing time in the past decade. Other amusing sub-luminaries/sub-Mariners include Shin Soo-Choo, Carl Everett, Miguel Olivo, and Ken Griffey, Jr. for position players, and Matt Thornton, Brian Fuentes, and Jose Paniagua for pitchers.
Not on the negative WAR list: Yuniesky Betancourt. Thanks, replacement value!