Apologies to Elroy Face and Firpo Marberry who were the last two cut from the poll, for space reasons.

I picked Rivera.  When he pitches, he gets locked in to some kind of wavelength of calm and focus.  A lot of closers get very, very pumped up, chomping at the bit and screaming obscenities.  I don't think I've ever seen him panic, not even when he messes up.  I remember Mo giving up a homerun last season (I think it was to Eduardo Peres, of the D-Rays).  He merely looked back, watched it go out and calmly said "stupido" and kind of shook his head.  His real strength is his ability to get it done, year after year, in low key situations and in high pressure situations. Torre doesn't ever have to worry about him.  A guy like that is a gift to a manager because he isn't a question mark.

P.S.  I mentioned before how I love the A's names.  Rollie Fingers is the best damn name ever.  A guy with that name is either a pitcher or a jazz pianist.

"Greatest" means the relief pitcher who did the most to help his team to win.  Rivera is an easy choice by this definition. 

PRAR              Best Five Seasons       Total Best Five   Career Total     ERA+

Eckersley           94  89  81  78  75            417                    1243              116     
Gossage             99  94  77  68  68             406                     840              126
Marshall             95  87  87  84  69             422                      568              118
Rivera                 81  80  79  76  73            389                      754              197
Wilhelm              98  74  67  62  60            361                      954              146
Hoffman             83  81  67  60  58            349                      698              146
Fingers               77  71  69  66  58            341                      749              119
Lee Smith          75  67  67  60  55            324                      756               132
Sutter                80  76  74  56  49            335                      533               136
Henke                 63  62  61  53  53            292                      535              156
Quisenberry        76  72  67  59  58           332                      452              146

From age 28 to 32 Marshall pitched 111, 116 (1.78), 179 (2.66), 208 (2.42), and 109 (3.29) innings without making a single start.  Then he did nothing but recuperate for the next two seasons and at age 35 and 36 pitched 99 and 143 innings with a 2.45 and 2.65 ERA respectively.  Not surprisingly, that was all she wrote.

Yes, Eckersley was also a great starting pitcher.  Does that count for anything in this poll?  If we are only considering his career as a reliever then he is at a considerable disadvantage since he pitched only a small portion of his career as a reliever.  For his career in total......he is the best of this bunch.

If we're using ERA it's Rivera and Henke.

It occurs to me that these pitchers are so great that one of the most vivid memories many of us - well, me anyway - have of most of them are of those rare and shocking occasions when they actually failed to get the job done.

Rich Gossage against George Brett in the 1980 ALCS and Kirk Gibson in the 1984 WS
Dennis Eckersley against Gibson in the 1988 WS and Roberto Alomar in the 1992 ALCS
Lee Smith against Steve Garvey in the 1984 NLCS
Mariano Rivera against Luis Gonzalez in the 2001 WS

Uh...
Trevor Hoffmann against Michael Young in the 2006 ASG?

If you're going to look at the numerical side of things, you have to take account of post-season performance.  In Rivera's case, that is almost as important as his regular season.  He's thrown 111 innings in the post-season, and been absolutely dominant- 8-1 0.81 ERA, 69 hits, 15 walks, 87 strikeouts.  Eckersley threw 36 OK innings in the post-season, Marshall 12. 

Torre's strategy  has often been to save Rivera during the regular season so that he could deliver the mail in the playoffs.  It has worked very well. 

I'm an old time Gossage fan myself.  Endurance, attitude up the wazoo, pitched as a setup man after his closing days were over thus proving that giant ego wasn't all he was about.  For long term he'd be the one I'd want.  Short term, must win situation I'd lean toward Eck although he did have a couple of very high profile blown saves (seems a rule with the big guns, but then they get the most chances too).  Smith & Sutter don't belong in the argument imo (to me Sutter being in the HOF and Goose out is a joke) although I can understand putting them on the poll.

Postseason is interesting.
Goose: 19 games, 2-1 with 8 saves 2.87 ERA 1.6 IP/G teams won 5 of 8 series 62.5%
Fingers: 30 games, 3-4 with 10 saves 2.35 ERA 1.9 IP/G teams won 6 of 9 seires 66.7%
Rivera: 72 games, 8-1 with 34 saves 0.81 ERA 1.55 IP/G teams won 17 of 24 series 70.8%
Eck: 27 games, 1-2 with 15 saves 2.05 ERA 1.1 IP/G teams were 5-5 in series 50.0%

Note: skipped Eck's one postseason start.

Very surprised to see Rivera has averaged, in post season, the same IP/G as Goose. Torre deserves a lot of credit for following the Cito method (ie: manage one way during the season, differently in the post-season). 

Note: the only other getting a vote (to this point) was Mike Marshall (only 2 postseason series, 12 IP 0-1 1 save on just 1 run allowed, now that is bad luck).

Hoffman to date has zero votes which is understandable when your name comes after Eckersley and before Rivera. But for the sake of honourable mention, he's been lights out for an extremely long time and isn't really showing much hope of him slowing down. He's done a phenomenal job and yet you don't hear of him nearly as much as you should.

I still voted Rivera, but Hoffman is extremely underrated and definitely deserves some mention.

Interesting point VBF. After 100+ votes, Hoffman is the ONLY one on the list now to have NO votes. And it's possible that before the end of this season, certainly by early next, he will become MLB's all-time leader in saves. (He needs just 10 more.) One of the most under-the-radar all-time record pursuits ever.