Chances are you didn’t hear of Michael Olmsted during his relatively brief Red Sox tenure. On Saturday, the hulking 25-year-old right-hander was signed by the Brewers as a minor league free agent.

The Sox would have loved to have kept Olmsted from leaving, but they couldn’t do so because they lacked something that the Brewers could offer to the reliever: A 40-man roster spot.

Olmsted has had a somewhat remarkable career path. He was a ninth-round pick out of junior college in 2007 by the Mets, blew out late in 2008, missed all of the 2009 season and then got released by New York early in 2010. He signed to pitch in the minors in Japan, but had to ask for his release to return home that year when his mother became critically ill. The next year, early in 2011, he went to an independent league signout, but before going that route, Sox VP of player personnel Allard Baird was sufficiently impressed with Olmsted’s arm strength, stuff and size — at 6-foot-6, and more than his listed 245 pounds, Olmsted has a physical presence like few others on the mound — that he signed him on the spot.

Olmsted pitched well in his return to minor league ball in 2011, with a 1.39 ERA and 48 strikeouts in 32 1/3 innings. Still, at 24, he was beating up on Rookie Level and Single-A opponents.

But this year, as a 25-year-old, he was just as dominating in High-A Salem and Double-A Portland, forging a 1.52 ERA with 92 strikeouts and just 15 walks in 59 1/3 innings. In 14 Double-A games at the end of the year after his promotion, he didn’t give up a single earned run and he struck out 31 batters in 20 innings. The Sox saw a pitcher whose fastball — which sat in the mid-90s — and wipeout slider offered an easy projection for a power reliever. The combination of performance and stuff, many members of the front office understood, meant that if the Sox didn’t add him to their 40-man roster this winter, the team would likely lose him, whether as a minor league free agent or through the Rule 5 draft.

Still, the team couldn’t create that spot. Though the Sox currently have 37 players on their 40-man roster — thus leaving three open spots, though that number will decline to two open spots once the deal with David Ortiz becomes official — they’ll have to add a number of players to the roster later this month to protect them from the Rule 5 draft. Players such as right-handers Allen Webster, Alex Wilson, Josh Fields and Steven Wright, along with catchers Christian Vazquez and Dan Butler, will have to be added to the 40-man roster if the team doesn’t want to risk losing them for $50,000 through the Rule 5 process.

But the Sox are at a point where it’s difficult for them to add any more relievers to the 40-man roster. Indeed, the team likely will part with other relief arms this winter, just as they did with Olmsted.

Already, the team has 23 pitchers on its 40-man roster, including 15 — Alfredo Aceves, Scott Atchison, Andrew Bailey, Daniel Bard, Pedro Beato, Craig Breslow, Chris Carpenter, David Carpenter, Rich Hill, Mark Melancon, Andrew Miller, Franklin Morales, Clayton Mortensen, Sandy Rosario and Junichi Tazawa — whose primary roles in 2012 were as relievers. Given the number of needs that the Sox still have to address (first base, two outfielders, a starting pitcher, possibly a shortstop), and the possibility of adding Wilson and Fields to the 40-man, the Sox are likely to be moving some of the arms inventory at some point this offseason, whether via trades or by removing players from the 40-man roster.

The Sox didn’t want to lose Olmsted. They tried to sign him to another deal. But without a 40-man spot for a right-hander who hadn’t pitched above Double-A — even one who may not be far from the big leagues — the Sox lost a pitcher whom they like. It almost certainly won’t be the last time that happens this winter.