Does Dr. Frank Jobe belong in the Hall of Fame?

Three hundred and six names fill National Baseball Hall of Fame’s roster, from men who invented the box score and first put numbers on uniforms to the recently elected trio of Tom Glavine, Greg Maddux and Frank Thomas.

But no owner of a bronze plaque in Cooperstown, N.Y., influenced baseball in the same way as Dr. Frank Jobe.

But does Jobe, who died Thursday at age 88, belong there?

Walk into any Major League Baseball clubhouse and the telltale scars that mark Jobe’s legacy aren’t difficult to find. The doctor pioneered ulnar collateral ligament reconstruction in 1974 on a pitcher, Tommy John, who became synonymous with the career-saving procedure.

The scope of what Jobe started is difficult to exaggerate.

A study last year by Bleacher Report sports medicine writer Will Carroll found that one-third of pitchers on opening day rosters in 2013 had undergone Tommy John surgery. That’s 124 pitchers whose careers otherwise would’ve ended up on the scrap heap, and that’s not counting the minor leagues, college and high school players it’s helped.

Stephen Strasburg had it. Same with Tim Hudson. Jordan Zimmermann. Chris Carpenter. Chad Billingsley. John Smoltz. The list goes on.

The surgery is so ubiquitous as to be seen as almost routine, at least by those who don’t have to undergo the procedure. But pitching careers that would’ve been finished pre-Jobe now return to their previous form (after about a year of rehabilitation, of course) with such regularity as to hardly draw note.

Last July, the Hall of Fame honored Jobe during the induction weekend. That didn’t include a plaque. A campaign that pushed for Jobe’s induction ended the effort last December.

Even in Cooperstown, transcendence is a difficult thing to find, names like Jackie Robinson excepted. There are smooth-swingers and scoundrels, men who built stellar farm systems and won pennant after pennant, home run kings and, wedged in there, 10 umpires.

Thirty-three executives are in the Hall of Fame. Twenty managers too.

Few, though, left a legacy that sprawls through every level of baseball like Jobe’s.

The contribution isn’t tied to a particular player or era or franchise. Instead, it lives through the careers of players who owe their livelihoods to the man who invented the way to reassemble their elbows. And so long as pitching remains an unnatural motion, the need to repair those damaged elbows and resurrect careers won’t disappear.

Jobe may be gone, but watch nine innings and, more than likely, you’ll see his legacy live on. A legacy that extends beyond the Hall of Fame.

nathan.fenno@latimes.com

Twitter: @nathanfenno