While waiting to see if the Jays sign a free agent (I'm betting they sign big names before the CBA negotiations are finished)(I see someone I've never heard of is tweeting that Edwin is going to sign with the Astros. I figure if I haven't heard of the person and they have few followers, I'm not believing them), let's continue with the polls.
I'm going to skip Edgar Renteria and Arthur Rhodes.
Renteria was a pretty good shortstop. He had a 16 year career, hit .286/.343/.398 with 140 home run in 2152 games. You don't play 2152 games in the majors unless you are pretty good,but to make it to the Hall with those number, you would have to be great defensively. FanGraphs has him at a 0.2 UZR/150 for his career, but he does own 2 Gold Gloves. He played in 5 All-Star games, won 3 Silver Slugger awards, got MVP votes twice (finishing 15th in 2003) and came in second in Rookie of the Year balloting in 1996. He played for 7 different teams, Cards for 6 years, Marlins for 3, Giants and Braves for 2 each, and Red Sox, Reds and Tigers for a season each.
His career bWAR was 32.1 and his highest second mark was 5.6. I'm thinking Hall of Pretty Good.
Rhodes had a 20 year career (once you have that LOOGY union card, your life is made). He pitched in 900 games (25th in MLB history), starting 61. Finished with a career 4.25 ERA, 33 career saves. Total bWAR of 15. He played in 1 All-Star game and got MVP votes once (finishing 20th in the vote). He played for the Orioles (9 years), Mariners (5), Reds (2), Phillies, Cards, A's, Rangers, Indians and Marlins (all 1). His only case for being in the Hall is that he played 20 years, which is great and all, but he's not a Hall of Fame player. I wouldn't put him in the Hall of Pretty Good either.
Ivan Rodriguez, on the other hand, played 21 years in the majors, hit .296/.334/.464 with 311 home runs and was a terrific defensive catcher. He threw out 46% of base stealers career.
He had a 68.4 career bWAR.
He played in 14 All-Star games, won 1 MVP and got MVP votes 6 times. He won 13 Gold Gloves. He has 7 Silver Slugger awards. He was 4th in Rookie of the Year voting in 1991, when he was just 19.
Ivan also played in 40 playoff games, and has 1 World Series ring, he was a Marlin in 2001, and was MVP of the NLCS.
When he started his career he was great defensively and good offensively, then, he suddenly became amazing offensively, for a short period of time. He had a 5 year stretch of hitting 20 plus home runs, and a 3 year stretch of 35, 27 and 25 home runs.
Of course there was whispers of PEDs. In fact more than whispers....Jose Canseco wrote that he 'personally' injected Rodriguez with steroids. Rodriguez denied it. I wouldn't take Canseco's word on anything. I think it would be crappy to keep him out of the Hall because of Jose's claim.
I think Ivan's defense makes him a good candidate for the Hall, even if you discount his offense some.
You can see his stats here.
A lot of debate about the Hall of Fame relates to comparing a candidate against others elected and excluded. The chart below shows all players who played the majority of their career after 1945 (excluding active players, and those on the ballot or yet to hit the ballot) according to how long they played and how productive they were. TRC+ is wRC+, just for all runs rather than just batting runs. This is not meant to be definitive, but a high level starting point showing how players with similarly productive and lasting careers have fared.
Catchers don't fit well into this framework since they start fewer games and not all aspects of catching are currently reflected in most public value systems. Among catchers, Pudge is most similar to Carlton Fisk, Gary Carter and Yogi Berra. Broader comparisons include Tony Gwynn, Tim Raines, Buddy Bell, Dwight Evans, Roberto Alomar and Ernie Banks.