NEW YORK — There was just one witness to the moment Kenny Sailors helped revolutionize the game of basketball — his brother, Bud — but by all accounts no one has ever doubted their story.

The moment came on a hot May day in 1934. The two were tussling, one on one, under an iron rim nailed to the side of the family’s windmill, a wood-shingled, big-bladed landmark that their neighbors on the Wyoming high plains recognized for miles around the way sailors of the usual kind know a lighthouse from miles out at sea.

Kenny, a 13-year-old spring-legged featherweight, was dribbling this way and that on the hardpan, trying to drive to the basket, when Bud began taunting him, as older brothers will.

“Let’s see if you can get a shot up over me,’’ Bud said. A high school basketball standout, he had five years on his brother and, at that time, almost a foot in height.

Kenny took the challenge, doing what people at a disadvantage often do: He improvised. He squared up, planted his feet, and leaped.

“I had to think of something,’’ he said in an interview a lifetime later.

What he thought of was the jump shot, an innovation that would eventually be seen as comparable to the forward pass in football.

Kenny Sailors, who died at 95 on Saturday in Laramie, Wyo., would never say flat out that he had invented the shot on that day or any other. No one can say for sure who did. The early 20th century produced enough far-flung claimants to that distinction to fill out a starting five and warm a decent-size bench — players like Glenn Roberts, Bud Palmer, Mouse Gonzalez, Jumpin’ Joe Fulks, Hank Luisetti, and Belus Van Smawley.

But people of reliable authority have said that if you had to pick the one whose prototypical jump shot was the purest, whose mechanics set in motion a scoring technique that thrilled fans and helped transform a two-handed, flat-footed, essentially earthbound affair into the vertical game it is today, giving rise, quite literally, to marksmen like Oscar Robertson, Jerry West, Rick Barry, Michael Jordan, and Kobe Bryant, it would be Mr. Sailors.

Mr. Sailors developed the shot in high school, perfected it in college as a three-time All-American, and was one of the few of his era to make a living off it in the professional ranks.

He did so in the face of skeptics. The game back then was all about quick passing to find the open man and shooting from the chest, with two hands, feet on the floor. Watching Mr. Sailors play, a coach told him, “You gotta get yourself a good two-hand set shot,’’ and benched him.

But Mr. Sailors ignored the advice, to the delight of fans in Laramie, where, as the point guard, he led the University of Wyoming Cowboys on an improbable ride to their only NCAA championship, in 1943, making the college powerhouses of the East and the big-city reporters who covered them sit up and take notice of Western basketball.

If anyone can be said to have immortalized Mr. Sailors, it was Life magazine photographer Eric Schaal. He was courtside at Madison Square Garden in January 1946, when, in a game between Wyoming and Long Island University, his camera caught Mr. Sailors airborne.

In the picture Mr. Sailors, in black high-tops, is suspended a full yard above the hardwood and at least that much over the outstretched hand of his hapless defender. The ball is cradled above his head, elbow at 90 degrees, his right hand poised to fling the shot with a snap of the wrist that will have it backspinning to the rim along a high arc.

The photograph, appearing in one of America’s widest-circulating magazines, made an impact coast to coast.

“A shot whose origins could be traced to isolated pockets across the country — from the North Woods to Ozarks, from the Appalachian Mountains to the Pacific — was suddenly by virtue of one picture as widespread as the game itself,’’ journalist John Christgau wrote in his book “The Origins of the Jump Shot.’’ “Everywhere young players on basketball courts began jumping to shoot.’’

Jerry Krause, research chairman of the National Association of Basketball Coaches. concluded in his own study that Mr. Sailors was the first player to develop and use the shot consistently.

And Ray Meyer, the venerated coach of DePaul University, assured Mr. Sailors in a handwritten letter, “You were the first I saw with the true jump shot as we know it today.’’

Kenneth L. Sailors was born on Jan. 14, 1921, in Bushnell, Neb., to Edward Sailors and the former Cora Belle Houtz. His mother had gone west in a covered wagon and grown up in a sod house. She gave birth to Kenny by herself. The parents divorced when the boys were young, and Ken and Bud — Barton on his birth certificate — were reared by their mother on a 320-acre farm outside Hillsdale, a stockyard town in southeastern Wyoming. An older sister, Gladys, had married and left home.

The brothers’ historic game of one on one remained vivid in Kenny Sailors’ memory. “The good Lord must have put in my mind that if I’m going to get up over this big bum so I can shoot, I’m going to have to jump,’’ he said in an interview on NPR in 2008. “It probably wasn’t pretty, but I got the shot off, and it went in. And, boy, Bud says: ‘You’d better develop that. That’s going to be a good shot.’ And I started working on it.’’

Kenny became a champion miler and long jumper and a basketball star at Laramie High School, building leg power that would eventually give him, by his measure, a 36-inch vertical lift — an invaluable asset for a 5-foot-10-inch point guard.

The jump shot puzzled the Laramie coach, Floyd Norman. “Where’d you get that queer shot?’’ Kenny Sailors recalled him asking.

Mr. Sailors followed his brother to the University of Wyoming. (Early on he was a teammate of future sports broadcaster Curt Gowdy). He soon had sportswriters groping to describe his jump shot. “A shot-put throw,’’ one wrote.

In the 1942-43 season, under coach Everett Shelton, Mr. Sailors led the team to a 31-2 record and Wyoming’s only national championship, defeating Georgetown, 46-34, at Madison Square Garden. Mr. Sailors was chosen the tournament’s most outstanding player.

“His ability to dribble through and around any type of defense was uncanny, just as was his electrifying one-handed shot,’’ The New York Times said.

That year he married Marilynne Corbin, a cheerleader nicknamed Bokie, then enlisted in the Marines and served in the South Pacific.

Discharged in 1945 with a Bronze Star and captain’s bars, Kenny Sailors, with a year of eligibility left, rejoined the Wyoming team midseason and led it to a 22-4 record, earning his third All-America honor and a contract with the Cleveland Rebels of the Basketball Association of America.

The jump shot was still alien to the pros, and the Rebels’ coach, Dutch Dehnert, was skeptical. “You’ll never go in this league with that shot,’’ he told Mr. Sailors before benching him.

But Dehnert was soon gone in a coaching change and Mr. Sailors, with his jump shot, returned to the lineup. He was named a second-team All-Pro in his rookie season.

Professional stardom eluded him, though. In three seasons in the BAA and two in its successor, the National Basketball Association, he played mostly on losing teams, including the Providence Steamrollers in Rhode Island (where he signed an endorsement deal with Bennett’s Prune Juice, receiving all-you-can-drink cases of it as a bonus). He led the original Denver Nuggets in scoring one year, exploded for 37 points in a game with the Baltimore Bullets, and finished with the Boston Celtics, retiring from professional basketball at 30.

Mr. Sailors later bought a dude ranch in Jackson Hole, Wyo. A Republican, he served a term in the Wyoming Legislature and lost two bids for the House of Representatives and another for the Senate.