Barry Bonds, the all-time home run king, was on the ballot for the first time but received far short of the 75 percent of the vote necessary for induction. (M. Spencer Green/AP)

Baseball is a game that reveres numbers, and their numbers offer indisputable evidence they were among the best to ever play. Barry Bonds clobbered more home runs than anyone in a single season or a career, and was honored as his league’s most valuable player a record seven times. Roger Clemens won 354 career games and was named winner of the Cy Young Award as his league’s best pitcher seven times, another record.

Yet on Wednesday, Bonds and Clemens were denied entry to the Baseball Hall of Fame, a sharp rebuke not only to those two stars, but an apparent condemnation of the steroids-tainted period in which they played the game.

In their first time eligible to receive the sport’s top honor from the Baseball Writers Association of America, both men — whose careers ended with suspicions they used performance-enhancing drugs, despite their denials — received fewer than four out of 10 votes, well short of the 75 percent needed for induction.

For the first time since 1996, the baseball writers elected no one to the Hall. Among those rejected were Sammy Sosa, the slugger who sits eighth on the all-time home run list and who joined Clemens and Bonds on the ballot for the first time. Mark McGwire, who sits 10th on the all-time home run list, failed again, receiving his lowest percentage in seven years of eligibility.

McGwire has admitted steroid use. Sosa was widely suspected of it.

The vote was the latest emphatic, if expected, pronouncement that the vast majority of the 569 writers who cast ballots are not ready to elect even the best performers if there are fears they used drugs. (The Washington Post does not participate in the voting.)

“It means that the period in baseball from about the time I left until the present is a pretty dirty, if that’s the right word, period,” said Fay Vincent, who served as baseball’s commissioner from 1989 to 1992. “Everybody, including many who were probably clean, are subject to that judgment, and any judgment has got to be a cloudy one.”

The results extended the debate about how baseball, a sport that cherishes its history, should remember those players who defined and dominated an era from the 1990s through the mid-2000s in which baseball’s own investigation – undertaken just as the careers of Bonds and Clemens were ending — showed the use of performance-enhancing drugs was widespread.

“It’s a tough period for evaluation,” Hall of Fame President Jeff Idelson said. “That’s what this chalks up to.”

News of the vote was embraced by some and brought swift rebuttals from others. Clemens, who has defiantly and publicly expressed his innocence, took to Twitter to express his reaction.

“After what has been written and said over the last few years I’m not overly surprised,” Clemens wrote in a link from his account. “Thanks to all the teams I’ve worked with and to fans and friends for all the fantastic letters, voice mails and texts of support over the last few years.

“To those who did take the time to look at the facts . . . we very much appreciate it.”

Hall of Fame relief pitcher Dennis Eckersley tweeted, “Wow! Baseball writers make a statement. . . . Feels right.” Jeff Borris, Bonds’s longtime agent, told the Associated Press that it’s “unimaginable that the best player to ever play the game would not be a unanimous first-ballot selection.”

Michael Weiner, the executive director of the players’ union, called the result “unfortunate, if not sad.”

“To ignore the historic accomplishments of Barry Bonds and Roger Clemens, for example, is hard to justify,” Weiner said in a statement. “Moreover, to penalize players exonerated in legal proceedings – and others never even implicated – is simply unfair.”

Both Bonds and Clemens have been directly linked to baseball’s steroids period.

In 2003, Bonds became embroiled in the scandal surrounding the Bay Area Laboratory Cooperative (BALCO), to which his personal trainer, lifelong friend Greg Anderson, had ties. Bonds maintained his innocence, but in 2007 – the year he hit the last of his record 762 home runs – he was indicted on perjury and obstruction of justice charges in relation to his grand jury testimony in the BALCO case. In 2011 he was convicted on one count of obstruction of justice.

Clemens was a prominent figure in baseball’s independent investigation into steroid use, led by former senator George Mitchell, in 2007, when Clemens recorded the last of his 4,672 strikeouts, a total that ranks third all-time. The following February, Clemens appeared before a congressional committee and denied ever using performance-enhancing drugs even as Brian McNamee, his former trainer, offered detailed accounts of injecting Clemens with steroids.

Members of Congress eventually recommended that the Justice Department investigate whether Clemens lied under oath. A procedural misstep by prosecutors initially led to a mistrial. Last June, Clemens was acquitted of six counts of lying to Congress – enough to clear his name legally but not, apparently, to clear it in the minds of Hall of Fame voters.

Vincent said those voters have “a very murky, opaque decision. . . . I think it’s the right decision. But it reflects very badly on that whole era in baseball.”

Bonds, Clemens, Sosa and anyone receiving more than 5 percent of the vote will be eligible in the future, for as long as 15 years. Idelson said there are no plans to change the procedures for voting.

“It’s evident that the voters took this exercise probably more serious than any other ballot that they filled out, and that’s because there’s so many questions in voters’ minds,” Idelson said. “It takes time for history to sort itself out. I’m not surprised we had a shutout today.”