The fourth member of that fraternity, Rafael Palmeiro, has received 11 and 12.6 percent of the votes in his first two years of eligibility. Those numbers confirmed Palmeiro's concerns over how his suspension seven years ago for the use of performance-enhancing drugs would affect his candidacy.
There still seems to be little gray area concerning the Cuban-born first baseman with the sweet left-handed swing.
Palmeiro's 20-season career ended with 569 home runs and 3,020 hits.
Palmeiro's career also ended during the 2005 season with a 10-day suspension for violating MLB's Drug Policy, giving him the blemish of being the first star of the sport's so-called PED era to be suspended.
In a sport in which you normally get three strikes, the 2010-11 votes left Palmeiro feeling as though he only got one.
"I thought I would get more votes," Palmeiro said. "But I'm grateful for what I received, and that keeps me on the ballot. Voters are putting too much weight on the one incident.
"I wish they would look at my whole career. If they want, why don't they just throw out the last season of my career? I would still have Hall of Fame numbers. I've put up my numbers, and they aren't going to change."
Will his vote totals? Mark McGwire, the other incumbent candidate with a self-admitted PED past, has received more support during his five years on the ballot -- but significantly, his votes have wavered little, between 19.5 percent and 23.5 percent every year.
In addition, the competition has gotten about as formidable as it could possibly be, with the introduction of Barry Bonds, Roger Clemens, Craig Biggio, Sammy Sosa, Mike Piazza and Curt Schilling to the ballot for the first time.
A candidate must receive 75 percent of the vote from eligible Baseball Writers' Association of America members to gain election to the National Baseball Hall of Fame. Shortstop Barry Larkin (86.4 percent) was the lone 2012 inductee, while pitcher Jack Morris (66.7 in his 13th year of eligibility), infielder Jeff Bagwell (56) and Lee Smith (50.6) are the leading returning candidates.
Until the arrival of this year's first-time candidates, Palmeiro was considered the most valid test case for the durability of a PED smudge because, in the view of some, he put up stronger numbers than did McGwire.
McGwire, the Dodgers' new batting coach, did briefly hold the single-season record of 70 homers and retired with a total of 583 -- but had 1,043 other hits as a lifetime .263 hitter.
Only two players with fewer than McGwire's 1,626 career hits have gained Cooperstown entrance through the front gate of BBWAA election (as opposed to via Old Timers or Veterans Committees): Jackie Robinson and Ralph Kiner. So evaluating McGwire's ballot scores -- percentages of 23.5, 23.6, 21.9, 23.7 and 19.5 - can become a bit murky.
On-field performance puts Palmeiro in an obviously more elite company.
When his suspension came down on Aug. 1, 2005 -- months after the alleged violation, after the test results were appealed and the case went through an arbitration process, and two weeks after he'd collected his 3,000th hit -- Palmeiro knew his legacy was in danger.
Conceding the test results, but claiming not to know how the incriminating supplements entered his system, Palmeiro said at the time, "Why would I do this in a season when I was going to get to 3,000 hits? It makes no sense. I would not put my career on the line. I would not put my reputation on the line and everything that I've accomplished throughout my career. ... I'm not a crazy person. I'm not stupid. This is something that's an unfortunate thing. It was an accident. I'm paying the price."
Whether the Hall of Fame vote will continue to bring him sticker shock is up to the hundreds of tenured (10-plus years) BBWAA members who do the voting. Plenty of those voters could be conflicted. While recognizing the hazards of profiling, they continue to think of Palmeiro as someone who never exhibited any of the traits typically associated with PED use.
Palmeiro's career timeline was devoid of spikes. Consistency was one of his key attributes: He had 10 seasons of 37-plus homers, 10 seasons of 100-plus RBIs, 11 seasons with 30-plus doubles.
"Era domination" is viewed as one of the crucial elements of Hall of Fame worthiness, and few players ever stood out as Palmeiro did from 1993 through 2003. In that 11-season span, he hit 433 homers and drove in 1,266 runs, with a .555 slugging average that was supported by 364 other extra-base hits.
And despite the impressive power, Palmeiro had the plate discipline of a slap hitter -- only once did he strike out more than 96 times, and his walks exceeded his strikeouts in eight of his 20 seasons.
Hall of Fame juries can deliberate for as long as 15 years, and the one hearing Palmeiro's case is still in its early stages.