Durin O’Linger — ‘The Pharmacist’ — is making the most of his unexpected chance

“The Pharmacist” is one such player.

“It’s tough not to daydream. But the big thing about daydreaming is you lose sense of where you are when you dream a little bit too much,” said pitcher Durin O’Linger on Thursday, at the conclusion of his first pro summer with the short-season Lowell Spinners. “Obviously, the goal is to make it all the way with the Boston Red Sox, but the big thing I did over the past two months is really enjoy where I am, because none of this was supposed to happen for me.”

O’Linger— a 5-foot-10-inch righthander from liberal arts Davidson College — emerged as something of a national phenomenon at the end of his college career, and he did so with no expectation of a professional future. The redshirt senior had emerged as the anchor of Davidson’s pitching staff, but with a fastball that typically sat at 84-87 miles per hour and a modest slider and changeup, there was nothing to suggest that his career would extend beyond the end of the college season in June.

“To be quite honest,” confessed Red Sox vice president of amateur scouting Mike Rikard, “he was a player we had no knowledge of whatsoever.”

Yet Rikard and the rest of the baseball industry became aware of O’Linger as he led Davidson through the Atlantic 10 Conference tournament and then three straight wins in an NCAA Tournament regional, two against top seed North Carolina in Chapel Hill. O’Linger pitched . . . and pitched . . . and pitched.

It started with a 140-pitch start over 8⅓ innings against St. Bonaventure on May 24, then continued with relief appearances on May 26 (three shutout innings, 51 pitches) and the conference championship clincher on May 27 (three innings, one run, 45 pitches). Over four days, O’Linger pitched in three games and logged 14⅓ innings and 236 pitches.

He wasn’t done. He started against UNC on June 2, earning the win while allowing three runs over six innings (94 pitches), then contributed two more scoreless innings on June 4 (34 pitches) in the regional clincher. Finally, O’Linger made one last start in the Super Regional against Texas A&M on June 9, his six-run yield over 7⅔ innings and 138 pitches representing his final college performance.

Over 17 days, O’Linger threw 502 pitches and 30 innings. Cries of pitcher abuse echoed from some corners, but the 23-year-old had been adamant before the start of the run with Davidson coach Dick Cooke: He wanted to milk every opportunity he had to pitch before he wrapped up his career and started pharmacy school at the University of Florida in the fall.

“He did not project at the professional level. He knew that. I knew that,” said Cooke. “He’s just intensely competitive. He gets out there and decides, ‘The moment I’m on the mound, I’m the best pitcher in the universe.’ That’s the approach he seems to take. We saw great evidence of that on a pretty big stage here at the end of our season.

“Knowing what he was pulling off and what we had a chance to do, knowing that it appeared to be the end of his baseball career, if I had taken him out of any of those games, we would have been in a fistfight on the mound.”

As members of the Red Sox’ amateur scouting department lined up their draft board in Fenway Park, Davidson’s Cinderella postseason run and O’Linger’s role in it captured the group’s attention. The group got caught up in the debate about his workload, but ultimately concluded not only that Cooke and O’Linger were right to take advantage of a unique opportunity, but also gained a growing appreciation for the pitcher.

“We were watching this really neat story with Davidson unfold and seeing this pitcher continue to dominate against every team,” said Rikard. “Finally, at some point, I just said, ‘Man, this guy is really good. We should add him to our after-the-draft list.’ ”

Organizations have more innings available than they have legitimate minor league prospects to fill them. At the conclusion of the draft’s 40 rounds, teams seek fillers — players with competitiveness, intelligence, and strong character traits that represent clubhouse assets at any level. O’Linger fit the bill — so long as he was interested.

Red Sox amateur scouting director Gus Quattlebaum, a Davidson alum, made an unexpected call to Cooke at the conclusion of their tournament run.

“He said, ‘Hey, we’ve been talking and we’re thinking about signing The Pharmacist,’ ” said Cooke — who pitched for three years in the Red Sox farm system from 1979-81.

O’Linger was ready to spend the summer as a pitching coach in a North Carolina college summer league before pursuing his education, but apprised of the Red Sox opportunity he jumped at the chance to sign for $5,000 and a plane ticket, leaving behind coaching and, with the blessing of the University of Florida, putting pharmacy school on hold.

“They said they hope they never see me, to be honest, and that they’re rooting for me,” said O’Linger. “But when everything is up, the spot will still be there for me.”

He appeared in 15 games this summer — 13 for the Spinners, for whom he went 4-1 with a 2.03 ERA, 49 strikeouts, and 14 walks in 48⅔ innings, and two as a fill-in starter for High A Salem, where he allowed 11 runs in 9⅔ innings. He pitched well enough that, after a winter at home in Florida training and trying to find a job (preferably one that allows him to use his biology degree), he’ll get a chance to compete for a spot somewhere in the Sox system in 2018.

For that, pharmacy school can wait. For now, O’Linger has a chance to be “The Pharmacist,” something that offers satisfaction in its own right, without requiring considerations of what the baseball future might hold.

“Ever since I came here at the end of June, it’s been a dream come true,” said O’Linger. “I’ll enjoy the ride as long as it lasts.”

Alex Speier can be reached at alex.speier@globe.com. Follow him on twitter at @alexspeier.