Imagine seeing the mixed 4x400m relay on the track in Paris, checking out the split times, and finding that the women on most teams in the final were faster than the men.

Or imagine watching the mixed medley relay in the pool, in which each team assigns two women and two men to cover the strokes of their choosing, and watching women pass men in the butterfly leg.

Or imagine watching the first medal event of the Paris Olympics, the mixed team air rifle shooting, and seeing women post higher scores than men on eight of the top 10 teams.

No need to imagine the last of those scenarios. That’s what happened on Saturday in the first medal event of the Olympics. In qualification, only Kazakhstan and Mexico finished in the top 10 with the man on their two-shooter teams outshooting the woman. Kazakhstan’s male competitor, Islam Satpayev, posted the highest score, but the next five highest scores belonged to women. At the other end of the table, the six worst scores were all posted by men.

Satpayev cooled down ever so slightly in the bronze-medal match, but teammate Alexandra Le nearly matched her teammate’s shooting to help Kazakhstan reach the podium. In the gold-medal match, 17-year-old Huang Yuting was the most consistent shooter as she and her teammate, 19-year-old Sheng Lihao, held off South Korea.

This result isn’t a fluke. Researchers took an interest in results from the Tokyo Olympics and found virtually no difference between men and women in air rifle competitions, while men did slightly better in air pistol, trap and skeet competitions.

The International Shooting Sport Federation acknowledged as much in its transgender policy: “Although ISSF does wish to maintain two separate Male and Woman categories, field of play evidence confirms that men and women are typically shooting similar scores. Thus, the Woman category need not be ‘protected’ per se in the name of fairness. The gender category protection component is thus not a concern … to consider in shooting at elite level.”

Women first competed in Olympic shooting in open (mixed-gender) events in 1968. In 1976, Margaret Murdock tied for first in three-position rifle with Lanny Bassham, and though a review of the targets gave the gold to Bassham, he insisted on bringing his fellow American to the top step of the podium. He continued to say, many years later, that Murdock deserved a gold medal.

Still, only a few women competed in the open events in 1976 and 1980. Starting in 1984, women’s events were slowly added to Olympics, but one woman, China’s Shan Zhang, won an open-event medal in skeet in 1992. Skeet and trap were the last shooting events to add women’s only categories, in 2000. Now men and women only compete against each other in mixed team events.

In contrast, at American universities, men and women compete side by side in shooting competitions, leading to some intertwined histories. Mary Tucker, a silver medallist in mixed team air rifle in Tokyo, shared medal podiums at college with Tokyo gold medallist Will Shaner (her one-time college teammate at Kentucky before she transferred to West Virginia, alma mater of 2016 gold medallist Ginny Thrasher) and Alaska-Fairbanks shooter Rylan Kissell, with whom she teamed up in the mixed air rifle in Paris.

Some say that whether women need their own events or should have their own events are two different questions. It’s a conversation familiar to those who follow competitive events that focus mainly on the mental rather than the physical, like chess and poker.

“Even with the success of women in open events, girls’ and women’s chess events are a very welcome sight, as they help address the historic imbalance in gender parity,” says Jennifer Shahade, an accomplished poker player, the first female winner of the US Junior Open in chess and a two-time US women’s chess champion who traced the history of women in chess in her book, Chess Queens. The world chess championship, now held by Ding Liren, is considered “open” rather than “men’s” because women like Judit Polgar entered the competition and occasionally defeated the top men’s players in the world.

In the Olympics, athletes would be loth to combine a men’s event with a women’s event if it meant one fewer event in their sport. But Olympic shooting is an abridged version of the event we see contested in world championships, where there are many more categories. Perhaps combining men and women in air rifle would open the door to bring back one of the shooting events that was cut from the Olympics over the years, such as prone rifle or an event from a longer distance (the 100m running deer is probably not going to make a comeback).

It’s not just shooting where we see women’s results sometimes rival men’s though. Archery, like shooting, has a mixed team event in which men’s and women’s scores are added together, and the distance (70m) and target size (122cm, with a 12.2cm-ring worth 10 points) are the same for both genders. Men typically score higher, though Lim Si-hyeon’s women’s world record of 694 in the Olympic ranking round on Thursday was higher than the top men’s score of 686. (US archer Brady Ellison holds the men’s world record at 702.) In those ranking rounds, the 64 men competing averaged 658.9 points; the women averaged 646.8. (For those who prefer medians to means, the median men’s score was 662; the women’s median was 649.5.)

As of now, the only competition in which women compete head-to-head against men, in individual events rather than in teams, is equestrian. Whether shooting becomes the next event where men and women compete against each other as individuals is anyone’s guess. But of all the sports on the current Olympic programme, it’s the most likely candidate to do so.