Men and women searching for a mate on online dating sites are hoping Cupid’s arrow will strike high, according to a new study that suggests users tend to chase potential partners who are more desirable than themselves.

The study, based on data from a free online dating site, also reveals that while men become more desirable as they age – peaking at 50 years old – women are deemed steadily less so.

“There is so much folk wisdom about dating, but very little hard evidence. And that comes across in all of the sayings we have around dating, one of which is this idea that someone can be ‘out of your league’,” said Dr Elizabeth Bruch, associate professor in sociology and complex systems at the University of Michigan and co-author of the study.

“This [research] was motivated by a curiosity about that statement and trying to put some kind of scientific teeth around that idea.”

Writing in the journal Science Advances, Bruch and co-author Mark Newman, also from the University of Michigan, describe how they untangled the nuances of modern heterosexual courtship by looking at data from almost 200,000 users during January 2014 across New York, Boston, Chicago and Seattle. The identity of the website, they say, cannot be revealed due to a non disclosure agreement.

Each user was ranked by their desirability based on how many people initiated contact with them, and how popular those people sending the initial message were.

“A lot of previous studies have studied desirability based on people’s rated attractiveness,” said Bruch.But this latest study is based on actual behaviour. “What we wanted to do was say, what is the overall market power of each person in this city who is using the dating site,” she said.

The results reveal that when it came to making the first move, men and women tended to contact people with a broadly similar level of desirability to themselves, but most tried to punch above their weight by offering an opening gambit to people more desirable than themselves.

While women, on average, sent messages to men 23% more desirable than themselves, men approached women 26% more desirable than themselves.

Bruch said the results are perhaps surprising. “Women have much higher reply rates to their first messages than men: men’s average reply rate is around 17%, whereas for women often more than half of their messages can get a response. So women can afford to be more aspirational than they are,” she said.

Men initiated more contact than women, and while both genders generally contacted a range of individuals, those approaching the more desirable people sent fewer messages. Similarly, less desirable individuals were more likely to respond, with reply rates falling as their desirability approached and surpassed the person making initial contact.

The most desirable person on the site, a 30 year old woman in New York, received on average one message every 30 minutes day and night throughout the month.

Although the data was anonymised and the team could not read the messages, data showed that senders tended to write longer messages to more desirable people.

However, the study did not look at what happened beyond first contact and reply, while the authors note the situation might be very different in offline dating.

Dr Bernie Hogan, an expert in online dating from the University of Oxford, welcomed the study but cautioned that “desirability” was based on responses to an online profile, not necessarily how someone really is. He also warned against assuming the same trends would be seen in other countries, and noted it was not clear what sort of relationship individuals were looking for.

Bruch said that when it comes to online dating, perseverance pays off, saying: “Even if the probability of getting a reply when you are messaging a more desirable partner is low, it is not zero.”