"Both men and women pursued partners about 25 percent more 'desirable' than themselves," said the report in the journal Science Advances.

Hardly anyone reached out to people who ranked significantly lower than themselves. 

People's desirability was determined using a ranking algorithm based on how many messages they received from other popular users on a dating site in New York, Seattle, Boston and Chicago.

"If you are contacted by people who are themselves desirable, then you are presumably more desirable yourself," said the study.

Using this PageRank algorithm, which is employed by web search engines, researchers could establish a person's "league", which they scientifically coined "hierarchies of desirability".

For some at the pinnacle of the dating game, the flurry of messages from would-be suitors was dizzying.

"The most popular individual in our four cities, a 30-year-old woman living in New York, received 1,504 messages during the period of observation, equivalent to one message every 30 min, day and night, for the entire month," said the study.

While researchers did not reveal the end to this lady's love story, they did find that the majority of daters on the site tended to reach out to people who were ranked higher than themselves.

Read also: Indonesian men among the world's luckiest in online dating, study says

They also tended to send lengthier messages to people deemed higher on the desirability ladder.

In most cases, these long-shots fell short.

When there is a big gap in desirability between online daters, "there is a pronounced drop in the probability of reply," said the report.

And only in Seattle were there signs that long letters were more successful than short messages at getting a potential mate to respond.

People have probably been pining for unattainable love interests since the dawn of time.

But taking a scientific look at the phenomenon gives cause for hope, according to lead author Elizabeth Bruch, a sociologist at the University of Michigan, Ann Arbor.

"I think a common complaint when people use online dating websites is they feel like they never get any replies," she said. 

"This can be dispiriting. But even though the response rate is low, our analysis shows that 21 percent of people who engage in this aspirational behavior do get replies from a mate who is out of their league, so perseverance pays off."

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