Becky Hammon proved herself as an effective head coach at the NBA Summer League in Las Vegas. (John Locher/Associated Press)

In an ideal world, Becky Hammon would be celebrated only for her considerable ability as a basketball coach, nothing more and nothing less. The world we live in is far from ideal, and so Hammon must also be celebrated as an infiltrator of a male-dominated universe, a self-assured pioneer, a world-beater whether in high-tops or high heels. Becky Hammon is a woman and a winner. Someday, only one should matter. Right now, they both do.

Monday night in Las Vegas, two weeks after she became the first female head coach in the league’s brief history, Hammon coached the San Antonio Spurs to the NBA Summer League championship. Hammon, 38, joined the Spurs’ coaching staff last offseason, after the Spurs plucked her from the WNBA’s San Antonio Stars roster. Hammon played point guard in the WNBA and in Europe for 16 years, developing a keen mind — and kindling a deep passion — for the game. She became the first female assistant coach in NBA history at the knee of Gregg Popovich, the winner of five NBA championships and unquestioned king of current NBA coaches.

The first instinct is to feel grateful toward the Spurs for inching the sports world forward. The other appropriate reaction is to feel fortunate for the Spurs, to congratulate one of the smartest organizations in sports on another wise move: identifying and hiring an excellent assistant coach. The Spurs didn’t hire her because they wanted to advance society; that’s not how professional sports operate. They hired Hammon to win games.

“I’m really happy for her,” Stanford Coach Tara VanDerveer said. “It’s great when someone is given this opportunity and makes the most of it. It should not be such a big deal. It should not be rare. It is, because she’s the only one doing it.

“It’s something that is not just in basketball. Whether it’s business, if you discount half the population, how can you be competitive in a global market? In sports, it’s about winning. If someone can help you win, it shouldn’t matter whether they’re black, whether they’re female. If they help you win, that’s good. It looked like she helped [the Spurs] win, so that’s great.”

Hammon’s victory resonated beyond the sports world. Tuesday evening, presidential hopeful Hillary Clinton tweeted, “Congrats, @BeckyHammon—first woman head coach in the NBA Summer League, and the first woman to win it. (Coincidence?)”

VanDerveer, a member of both the Naismith Basketball Hall of Fame and the Women’s Basketball Hall of Fame, has coached for more than 35 years. She has seen women’s college basketball morph into a big-time sport, but men still fill 75 percent of the head coaching positions. The only interest she received from a men’s program came years ago, from a Division II school whose name she forgot. Has she wondered why men so often coach women, but never the other way around?

“I haven’t wondered,” VanDerveer said. “It’s just sexism.”

The black-and-white nature of sports can be a powerful weapon against prejudice. Critics argue women cannot command the attention of male athletes, or that they can’t understand the game at a level they did not play. The naysayers have no defense against the image of Hammon lifting the trophy, wearing a celebratory “Victory in Vegas” T-shirt.

The Spurs take Hammon seriously for the same reason the Golden State Warriors respect Steve Kerr, or the Milwaukee Bucks lend credibility to Jason Kidd. She is young enough to relate to them, and they know she’s a player. Hammon thrived with a sweet shot and a deep understanding of the game. She doesn’t have to prove anything to her players; she already proved it on the court.

“When she’s talking, they’re looking at her,” said Bobby Marks, a former Nets assistant general manager who attended the Las Vegas summer league. “They’re not looking into the stands or rolling their eyes. She commanded that huddle. Guys look up to her.”

At the end of one summer league game, Hammon stood in the middle of the huddle and drew up a final out-of-bounds play with the score tied and 2.5 seconds left: an isolation on the weak side, designed for point guard Shannon Scott to catch an inbounds pass while moving toward the rim. The play broke down a bit, but Scott still shook free with enough space to swish a game-winning floater from the elbow at the buzzer.

“There’s always pioneers in everything,” NBA Summer League Executive Director Warren Legarie said. “What we always value above anything else is competence and clarity. She belongs at this level. It’s not a gimmick. That’s the thing the world has to get over. She’s played the game. She understands the game. She knows how to teach the game.”

During another game, Hammon argued with an official, standing toe-to-toe and screaming until she drew a technical foul in the service of protecting her players. They rallied around her. “That’s what really solidified with her team, when they saw her just as their coach, not as some kind of symbol,” Legarie said. “That’s the transcendence here.”

Last summer, Hammon was the only woman who took part in Las Vegas. This year, Nancy Lieberman served as an assistant coach for the Sacramento Kings, and Lindsey Harding served in the same role on the Toronto Raptors’ bench.

“What it’s saying is, people are looking for good coaches,” said Legarie, who also represents a gaggle of NBA coaches and executives as an agent. “It doesn’t matter from where they come. That’s what the game is about. That’s what summer league is about. It’s a testing ground. . . . If you separate yourself here, the NBA sees you as a viable commodity for later.”

The Spurs’ championship made Hammon a more visible and viable candidate to become an NBA head coach. Kerr and David Blatt, the two head coaches in this year’s NBA Finals, received their first NBA head coaching experience at last year’s Summer League.

Tuesday morning, Marks caused a minor stir when he tweeted: “I know this is a bold statement. If I was running a team and had a head coaching opening. The first call would be to Becky Hammon.”

For some owners, though, the perceived risk of breaking a barrier will hinder Hammon. Marks noted the “insecurity” in many front offices, that breaking standard protocol and losing is a quicker way out of a job than losing by standard measures. There is no doubt sexism exists.

“I think the hardest group is probably some current male coaches who are afraid of change,” VanDerveer said. “Some people might be out of jobs. If you block out half of the population from jobs to begin with, you’ve blocked out half the competition. If in fact women are able to compete, they’ll do well. Those are the people saying women don’t know the game, they can’t communicate with the guys. I think it’s BS.”

Hammon proved that in Las Vegas. It’s true that Becky Hammon coaching the Spurs is a victory for women. But she’s only coaching because having Becky Hammon is a victory for the Spurs.