There was a time, not too long ago, when any Major League Baseball pitcher with 300 or more victories in his career and any position player with 500 or more home runs was sure to be elected to the National Baseball Hall of Fame.

All such players were among the Hall of Fame’s chosen few until recently.

Then came the “Steroid Era” starting in the 1980’s, a period that may not have ended quite yet, despite Commissioner Bud Selig claiming it is over.

Each of the players currently eligible for the Hall of Fame played during this “Steroid Era,” when drugs artificially enhanced the abilities and production of many MLB players. Those who are known to have used performance enhancing drugs, or are even suspected of such drug use, have been soundly rejected by the annual votes of MLB reporters since “Steroid Era” players began to appear on Hall of Fame ballots during the last decade.

The 2011 Hall of Fame vote, which was announced Jan. 5, was no exception to that trend. Roberto Alomar, a Puerto Rican all-star second baseman who had a lifetime batting average of .300 with eight MLB teams, and Bert Blyleven, a Dutch-born right-hander who won 287 games pitching for the Minnesota Twins and five other teams, were the only players selected. Neither Alomar nor Blyleven has ever been mentioned as using PHD.

But Rafael Palmeiro, once a sure bet for the Hall of Fame on this his first year of eligibility, was rejected by members of the Baseball Writers Association of America because the slugging outfielder for the Texas Rangers and Baltimore Orioles, who told a Congressional committee he had never used PHD, later tested positive for illegal drugs.

Palmeiro, a Cuban who hit 569 career home runs, became the second man with 500 or more home runs to be turned down by the Hall of Fame electors.

Mark McGwire, who hit 583 homers playing for the Oakland Athletics and then the St. Louis Cardinals, was rejected again on this, his fourth year of eligibility. Long suspected of drug use, McGwire refused to discuss the issue for years until finally admitting a year ago that he did use PHD.

McGwire, who never received as much as 24 percent of the vote in any of his first three years of eligibility, got only 19.8 percent of the 581 votes cast in 2010, while Palmeiro was on only 11 percent of the ballots.

A player must be named on 75 percent of all ballots submitted to enter the Hall of Fame and be on at least 5 percent of all ballots to remain eligible for the next year’s election. A player who takes part in 10 MLB seasons becomes eligible 5 years after playing his final MLB game. If, after 15 years, he is not elected to the Hall of Fame, he is no longer eligible. Bert Blyleven was elected this winter in his 14th year of eligibility.

It seems clear that Barry Bonds, Roger Clemens, Gary Sheffield and Sammy Sosa may have little, if any, chance of making it into the National Baseball Hall of Fame when they become eligible. Each of them has been named repeatedly as partaking of steroids and/or other forms of PHD. Clemens vehemently denies drug use.

Bonds and Clemens face federal trials this year stemming from investigations questioning whether they told the truth about using or not using PHD. Clemens is scheduled to face trial in July on serious charges that, if he is found guilty on all counts, could result in him going to prison for many years.

Bonds’ trial has been postponed time and time again. Where it was once a matter of perjury and obstruction of justice, Bonds now faces only the obstruction charge. Some experts say he will never serve time.

Bonds, who holds the career home run record with 762, and Sosa, who hit 609, will become eligible for the Hall of Fame next year. Sheffield, who hit 509 homers, becomes eligible in 2014.

Clemens, who pitched for the Boston Red Sox, Toronto Blue Jays, New York Yankees and Houston Astros, is ninth on the list of most career victories with 354 and third on the strikeout list with 4,672. He will also be eligible for the Hall of Fame next year.

The Yankees’ Alex Rodriguez may also be subject to a BWAA veto when he becomes eligible five years after retiring from MLB. The 35-year-old A-Rod, who has 613 home runs and a chance to break Bonds’ career record, has admitted that he used PHD a few years ago.

Not all leading achievers in recent MLB seasons are drug users, according to what is known.

Frank Thomas, who played 16 of his 19 MLB seasons with the Chicago White Sox and hit 521 homers, has long advocated for stricter drug testing in MLB. He will become eligible for the Hall in 2013.

Ken Griffey Jr., No. 5 on the home run list at 630, will be eligible in 2015, while Jim Thome, who played for the Cleveland Indians, Philadelphia Phillies, Chicago White Sox and Los Angeles Dodgers, is currently on the Minnesota Twins roster. He has 589 home runs. Griffey and Thome, two of MLB’s most popular players in recent years, have no PHD record.

Manny Ramirez, on the other hand, is the unpredictable character who was suspended for 50 games in the 2009 season because he failed a MLB drug test. He is currently a free agent after a career playing for the Cleveland Indians, Boston Red Sox, Los Angeles Dodgers and Chicago White Sox. He is 14th on the homer list with 555. His chances of making the Hall of Fame seem less than good.

Only 25 men have hit 500 or more home runs to this point in MLB history, and only 24 pitchers have won 300 or more games. Although more players are expected to hit 500 home runs in the future, there may never be another pitcher with 300 victories the way MLB is played and managed at present.

The first 15 players who hit 500 home runs are in the Hall of Fame. They include Hank Aaron with 755, Babe Ruth at 714 and Willie Mays at 660. At No. 25 is Eddie Murray with 504. He is the only one of those 15 Hall of Fame members with 500 home runs who played during the “Steroid Era,” as he was in MLB, 1977-1997, most notably as the Baltimore Orioles’ first baseman.

Of the 10 men who have hit more than 500 home runs in their career and are not yet in the Baseball Hall of Fame, it appears safe to say that only three of them, Ken Griffey Jr., Jim Thome and Frank Thomas, will make the Hall with ease.

Barry Bonds, Alex Rodriguez, Sammy Sosa, Mark McGwire, Rafael Palmeiro, Manny Ramirez and Gary Sheffield must overcome the stigma of PHD use or a big change of heart by a majority of MLB writers in order to get through the doors at Cooperstown, N.Y.

The first 20 pitchers who won 300 games or more are in the Hall of Fame, including Cy Young at 511, Walter Johnson at 417, Warren Spahn at 363, and Early Wynn and Lefty Grove at 300 each.

There are four 300-game winners, including Roger Clemens, who are not in the Hall of Fame because they have not yet become eligible. Greg Maddux, with 355 triumphs, and his former Atlanta Braves teammate Tom Glavine, who has 305 victories, plus Randy Johnson with 303, have no hint of PHD in their careers. Thus it should be clear sailing into the Hall for Maddux and Glavine in 2013 and for Johnson one year later.

Gordon White served 43 years as a sports reporter for The New York Times. His e-mail is sports@thepilot.com.