They have long been a beacon of hope for Mariners fans, providing visions of a prosperous future amid the ballclub’s ongoing struggles.

They had a flashy nickname — “The Big Three — to go with dominating stats at the minor-league level and the hype that gets heaped on flashy prospects. Particularly for an organization without much else to cling to.

According to the master plan, they would all break into the rotation in proximity of each other — right about now, in fact — and combine with Felix Hernandez and Hisashi Iwakuma to form one of the most formidable starting staffs in the game.

That dream might still come to fruition, eventually. But right now, as another season threatens to slip away from the Mariners, the Big Three are all on the outside, looking in.

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More specifically, all three are on the disabled list, a reality that speaks volumes of the fragility, and volatility, of pitching prospects. It also whispers of the kind of buzzard’s luck that has befallen the Mariners in recent years:

• Danny Hultzen, 24, the No. 2 overall pick in the 2011 draft, is out for the season after shoulder surgery last October to repair a torn anterior capsule and a partial tear of the rotator cuff, as well as to clean up damage to the labrum. It’s an ominous development considering the difficult road back from shoulder surgery — one many pitchers never successfully accomplish.

• Taijuan Walker, the Mariners’ first pick in the 2010 draft, is still trying to come back from the shoulder problems that sidelined him for much of spring training. After two impressive rehab starts in the minor leagues that had him on the verge of joining the Mariners’ rotation, Walker, 21, was scratched from a scheduled start in Tacoma on April 15 when he couldn’t get loose. Now he has been cleared to play catch as his rehab resumes.

• James Paxton, 25, got off to a sensational start with the Mariners that built upon last year’s 3-0 record and 1.50 earned-run average in four September outings. But Paxton strained his left lat muscle in his second start, April 9. Though he is also set to resume playing catch, Paxton is expected to be out until at least late May.

It’s hardly unique to the Mariners. Baseball is currently undergoing an epidemic of pitching injuries, particularly Tommy John surgeries. And the ratio of phenoms who get sidetracked on their way to stardom, from Mark Pryor to Rick Ankiel, has been well-documented.

There’s even an acronym for this phenomenon, coined by Baseball Prospectus founder Gary Huckabay in the late 1990s: TNSTAAPP. It stands for There’s No Such Thing As A Pitching Prospect.

That goes in bulk, as well. The A’s took four pitchers among the first 36 picks of the 1990 draft and immediately people began touting “The Four Aces.” They were Todd Van Poppel, Don Peters, Dave Zancanaro and Kirk Dressendorfer, only two of whom made the majors, with lackluster results.

Similarly, the Mets’ vaunted “Generation K” from the mid-1990s — Jason Isringhausen, Paul Wilson and Bill Pulsipher — succumbed to injuries and never flourished in New York. Only Isringhausen had a substantial career, and it was as a closer.

Again, that’s not to say that the Mariners’ Big Three still won’t break out, but the odds against all three thriving have always been high. That’s just history, and reality, speaking. Will Carroll, who writes the “Under The Knife” column for Bleacher Report and is author of “Saving The Pitcher,” notes that it is the cluster of injuries with the Mariners, rather than the fact they got hurt, that jumps out to him.

“When you look at the sheer numbers of injuries among pitchers in general, and the massive number in young pitchers, it’s not that unusual,’’ he said. “If they were spread out, rather than clustered, you wouldn’t really notice.”

Carroll also points out that he regards the Mariners as one of the most enlightened organizations in MLB when it comes to dealing with pitchers. He has given out the Martin-Monahan Award for the past 10 years to baseball’s best medical staff, and last year he awarded it to the Mariners, in part for their ability to keep pitchers healthy.

But baseball as a whole has done a lousy job of that, Carroll believes. He points to the fact that more than $1 billion in contracts were on the disabled list last year.

“If any other business was losing that kind of money on anything, let alone its prime assets, they’d be doing research or sending specialists to study the issue,’’ he said. “In baseball, they kind of shrug their shoulders. They’re doing absolutely no research — except for some individual teams — and that stuns me.”

The Mariners, meanwhile, will continue to wait for their Big Three to make an impact. There might be no such thing as a pitching prospect, but there’s still plenty of room for faith and hope.

The throwing wounded
Pitcher Age Height, Weight Injury
RHP Taijuan Walker 21 6-4, 230 Soreness in his throwing shoulder
LHP James Paxton 25 6-4, 220 Strained lat muscle
LHP Danny Hultzen 24 6-3, 210 Rehabbing from rotator cuff surgery

Larry Stone: 206-464-3146 or On Twitter @StoneLarry