They will be out there throughout the playoffs, on the pitching mound each day, though they will not be easy to see. They range from about 7-9 cm in length. Some are thick, others thin and faded. They tell the story of the modern pitcher.

About a quarter of active major league pitchers have had elbow surgery to repair a damaged ulnar collateral ligament, or UCL. Some have had it multiple times. The operation — known as Tommy John surgery, after the first pitcher to undergo it — leaves players with a crescent-shaped scar inside the elbow.

The scar is the physical mark of both the epidemic and an individual player’s history. Each scar, like rings on a tree stump, reveals the past: which doctor performed the operation, how long ago the player had it and whether he had it more than once.

“The funny thing is,” said David Altchek, the New York Mets’ doctor, “nobody ever sees it except the batter.”

The scar, of course, depends partly on the surgeon. Even two members of the same pitching rotation, of about the same age, can have very different scars. The New York Mets’ two aces, Matt Harvey and Jacob deGrom, were operated on by different surgeons who used different techniques.

Dr. James Andrews, a renowned orthopedic surgeon, performed Harvey’s operation using the Modified Jobe technique, a variation on the method used by Dr. Frank Jobe, the surgeon who pioneered the procedure and operated on John. It requires a longer incision, about 9 cm, because it involves moving the ulnar nerve to reach the damaged ligament and then drilling holes in the bone to graft the new ligament. The surgeon needs extra room to maneuver around the tissue carefully.

Altchek performed deGrom’s operation using the Docking technique, a method he developed in the early 1990s as a less invasive, less complex alternative. He makes a shorter incision, only about 7 cm, because he does not move the nerve. He drills fewer holes in the bone to which the new ligament is docked.

Altchek can complete Tommy John surgery in about 30 minutes; Andrews takes about an hour. But the Modified Jobe technique is the only method Andrews will use. Like several other top surgeons, Andrews learned the operation from Jobe. Some of Jobe’s disciples say they still hear his voice in their heads, guiding them through parts of the procedure.

“I’ve done it 3,000, 4,000 times,” Andrews said. “You need to do what you’re used to, going through the learning curve, how you handle all the tissue. It doesn’t matter how you do it, as long as you do it the same way. Depends how you were trained.”

After those thousands of operations, Andrews has noticed that the length of the scar has reflected the size of the player. As professional baseball players have gotten bigger and stronger, the scars have gotten longer. Andrews needs even more room to maneuver inside the elbow of a power pitcher like Harvey, who is about 6 feet 4 inches and 215 pounds.

“On the inside of the arm there, that skin doesn’t scar very nicely,” said Neal ElAttrache, the doctor for the Los Angeles Dodgers. “The skin is a little bit more thin and is under more tension. The scar is not a pretty fine line, no matter how you put the stitches in. It’s just not that pretty of a scar to begin with. The only saving grace is that it’s on the inside of the elbow, which is not immediately visible.”

After Jose Fernandez of the Miami Marlins had the operation, he looked at his long, unsightly scar and asked ElAttrache, in jest, “Hey, have you been drinking?”

The bigger pitchers who require longer scars also tend to throw harder, which may explain, in part, why the injury is so prevalent. As a pitcher’s velocity climbs, so does the amount of stress on the ligament.

“Those are forces you just can’t escape,” ElAttrache said. “There is no ulnar collateral ligament that is strong enough to throw a ball over 90 miles per hour. So the shielding of the ligament with perfect body mechanics and perfect muscle forces all have to be working perfectly. If they’re not, that sudden exposure to that kind of force will tear the ligament.”

Some pitchers watch their peers throw and try to guess which ones will tear the ligament: maybe the one with the jerky delivery, or the one with the 100-mph fastball. Even for doctors, an exercise like that is futile.

Major League Baseball has assembled a task force to study the issue, but there is still much that is not known, like what causes the injury, how to prevent it and the best way to handle someone who has had it.

The success rate of the operation is higher than Jobe first expected in 1974 — roughly 80 percent now. But a recent study, conducted by a group including ElAttrache and Altchek, examined 235 major league pitchers who had the operation from 1999 to 2014 and found that 13.2 percent of them had to have it a second time.

When Josh Johnson, a San Diego Padres starter, went in for his second operation, having torn his UCL again about 6 1/2 years after his first operation, he was told, “Well, that’s a pretty good run for that one.”

ElAttrache warns his patients, “If you ruptured the ligament God gave you, you can tear the one we’re going to give you.”

Daniel Hudson said he paid little attention to the statistics. Through his rehabilitation, he had no setbacks and was on a pace to return about 12 months after the operation, as expected. Then, during his first official rehab start, his elbow locked up in the second inning. He cried for an hour when he was told he needed to have Tommy John surgery again.

The second time a player has the operation, it can take twice as long, and the incision is longer because the surgeon needs room to navigate the scar tissue and nerve again. If the tunnels drilled in the bone from the first procedure are compromised, the surgeon also has to devise a new way of grafting the new ligament.

“The first time, it is such a beautiful and elegant operation,” said Christopher Ahmad, the New York Yankees’ doctor. “The second time, it’s rough and tumble. There’s no ‘I’m going to give you a cosmetic, beautiful scar.’ That’s all out the window. Now it’s all about getting a good ligament reconstruction. We don’t care what it looks like on the outside.”

Every pitcher seems to regard his scar differently because experiences with the operation vary greatly. Joba Chamberlain, for one, has changed organizations three times since he had surgery in 2011. He had a smiley face tattooed on his scar as a metaphor.

“My scar can never frown,” he said.

Shawn Kelley proudly credits his two operations as the reason he is still in the majors. When doctors call asking him to participate in studies, he happily obliges. When he went in for his second operation, he requested that the doctor not harm his scar.

“Trace it perfectly,” Kelley told the nurse.

When Tommy John himself cocks his arm as if he is going to fire a fastball, the scar on the inside of his left elbow is hardly visible. About 40 years after the incision was made, the scar is a thin white line that curls neatly up his arm.

It was the handiwork of Jobe, who operated on John’s elbow, in the same spot, three times. He performed the second operation in 1974, after John blew out his UCL. Jobe gave John about a 3 percent chance of pitching again, but only if they tried experimental ligament reconstruction surgery.

John went on to pitch for 14 more years in the majors. Curious about his scar, John once asked Jobe why he had used the same incision.

“It’s kind of like taking a trip,” Jobe told him, trying to explain as simply as possible. “If you find a good route and there’s good food on the way, you tend to go the same way.”