It’s hard to argue that there’s been a more popular player in Red Sox history than David Ortiz.

Few fans even knew his name when he signed an under-the-radar deal with Boston prior to the 2003 season. Despite the fact that Ortiz had already compiled three straight double-digit home run seasons in Minnesota, he was an afterthought on a stacked Sox roster. He began the year ostensibly as a left-handed power option of the bench.

In June of ’03, manager Grady Little decided to make a switch at designated hitter, benching the polarizing Jeremy Giambi for Ortiz. The rest, they say, is history. Ortiz clocked 31 homers that year and 208 in his first five seasons with the club, leading Boston to two coveted World Series championships.

Now, at age 37, Ortiz is somehow still producing at a high level at the plate. An 0-for-5 night Wednesday snapped a 27-game hitting streak dating back to last year, but he’s off to a roaring start overall in 2013, as he brought a .381/.412/.714 line into Thursday’s game.

At this point in a star player’s career, it’s natural to start thinking Hall of Fame candidacy. In the case of Ortiz, enshrinement in Cooperstown is not a farfetched ideal, though it’s not exactly clear cut, either. There are a few key roadblocks that could very likely keep Ortiz out, namely the fact that he became a slugging superstar during the height of the steroid era.

But there are many factors to consider when it comes to Ortiz – one of the greatest power hitters of his generation – and whether or not he makes the Hall of Fame.

The Home Runs

There are only four members of the 500-home run club who are eligible for the Hall of Fame, but are not in. All four of them – Barry Bonds, Sammy Sosa, Mark McGwire and Rafael Palmeiro – have been heavily linked to steroids. Take out the “cheating” angle, and 500 home runs becomes an absolute lock for Cooperstown.

Ortiz currently sits with 405 dingers and is under contract with Boston for the next 11 months of regular season baseball. If he stays healthy, it’s reasonable to predict that he’ll finish the 2014 season with 460 homers.

Of the nine players with home run totals between 460 and 500, two – Fred McGriff and Jose Canseco – are not in nor never will get in the Hall of Fame. Let’s take a look at how Ortiz’s career numbers stack against McGriff’s and Canseco’s:

Ortiz: 7,717 PA, .286/.380/.549, 405 HR, 1,343 RBI, 1,135 R, 11 SB
McGriff: 10,174 PA, .284/.377/.509, 493 HR, 1,550 RBI, 1,349 R, 72 SB
Canseco: 8,129 PA, .266/.353/.515, 462 HR, 1,407 RBI, 1,186 R, 200 SB

Of the three, Ortiz is clearly the best and “most efficient” hitter. He gets on base at a similar clip as McGriff, but out-slugs him by 40 points. Meanwhile, Ortiz his “counting statistics” in less than 8,000 plate appearances; McGriff needed 2,400 more trips to the plate to put up relatively similar numbers. Canseco provided a threat on the basepaths to go along with his gargantuan power, but his on-base and slugging percentages don’t stack up to Ortiz.

By the time Ortiz ends his contract with the Red Sox after 2014, he should be right up there with McGriff in terms of career numbers, with maybe 1,000 less plate appearances. Of course, McGriff is not in the Hall of Fame, and his support has decreased since he first appeared on the ballot in 2010.  That does not bode well for Ortiz.

The DH Stigma

Edgar Martinez received 36.5 percent of the Hall of Fame vote in 2012, marking the highest vote total ever for a designated hitter. With a ridiculous .312/.418/.515 triple-slash line, Martinez is, without question, the greatest DH of all time.

There’s nothing really left to expand upon here. If Hall of Fame voters haven’t voted for Martinez based on the fact that he never provided any value in the field, then so be it. But if Martinez doesn’t get in on that logic, than Ortiz shouldn’t, either.

But of course, voters tend to look beyond the box score …

The Accolades

Game 4 against the Yankees in 2004 … then, Game 5. 54 homers in 2006. Countless walk-offs. Two world championships. This.

“Big Papi” has become a bit of a legend in Beantown over the years. Sometimes for his antics in the clubhouse, but mostly for his tendency to produce in the clutch, time and time again. He’s one of the most important players the Red Sox have ever had, and is perhaps the signature face of the greatest era in franchise history.

Unlike Martinez, who never won a ring and flew fairly under-the-radar up in the Northwest for his entire career, Ortiz has been at the center of an epic rivalry between the Sox and New York Yankees for the past 10 years. Whereas Martinez quietly wore out opposing pitchers in the American League West, Ortiz headlined SporsCenter commercials.

All of this should help Ortiz’s Hall of Fame candidacy amongst voters who consider that stuff (which seems to be a lot). Not just the fame and the popularity, but the fact that he achieved that while winning a pair of titles.

The Steroids

Nobody, outside of Ortiz and maybe a doctor somewhere in the Dominican Republic, knows whether or not Ortiz has ever taken illegal steroids. But according to a 2003 New York Times investigation, Ortiz and teammate Manny Ramirez – who has had his fair share of run-ins with PEDs – were listed as having tested positive.

It’s very likely that Ortiz did take steroids at some point in his career, if only because seemingly everyone else was doing them in the early 2000s. That’s an issue for Hall of Fame voters, plain and simple.

Again, there’s nothing much left to expand on at this point. Time will tell how voters “evolve” on the issue of steroids. Many voters have already decided to vote for who they feel are the best players of their generations, steroids or not. Others, especially the old voters, don’t want to put their stamp of approval on a player they viewed as a cheater.

The Conclusion

Ortiz has a lot of things going for him statistically. For instance, did you know that he has a slightly better home-run-per-at-bat ratio (16.30) than Hank Aaron (16.38)? And if Papi somehow reaches 500 home runs, there will be no historical precedence to not allow him in the Hall of Fame.

Of course, there’s the steroids. Then again, there’s the two World Series titles and his playoff heroics. Good vs. evil at its best.

My prediction: Ortiz doesn’t get to 500 homers, and while the Hall of Fame voters loosen up a bit on letting steroid users in, Ortiz doesn’t make it to Cooperstown at the end of the day. He’ll still go down as one of the greatest hitters ever to play his home games at Fenway Park.