# This Simple Mathematical Formula Proves That We Lie About Sex

A new study on kissing in the microbiology journal Microbiome contains an interesting statistical discrepancy that demonstrates the way men and women lie about sex.

The heart of the study is solid — It suggests that people who kiss frequently end up sharing their oral bacteria.

But a section of the study briefly addresses a statistic that proves some of the people in the study must have been misreporting their numbers. The study was of couples, and there was an equal number of men and women. Yet the average number of intimate kisses per day reported by the men was twice the number of those reported by the women. This is a statistical impossibility. Men and women ought to report the same average number of kisses, and you can prove that with maths. The fact that the numbers mismatch demonstrates that someone in the study was either exaggerating or downplaying the number of kisses they received, as the authors of the study helpfully point out:

We calculated all the average kiss frequencies and average periods past after the latest kiss. Strikingly, 74% of the men reported higher intimate kiss frequencies than the women of the same couple, resulting in a male average of 10 and a female average of five intimate kisses per day (Additional file 3). This probably results from male over reporting, as previously noted in an analysis of self-reports on sexual behaviour, including number of partners and frequency of intercourse, in particular among unmarried couples [8].

This difference comes up most often when we talk about the average number of sex partners people have. The media frequently reports that heterosexual men have more sexual partners than straight women.

This, as a matter of mathematical logic, must be wrong because every time a man has sex with a woman, a woman must be having sex with a man. The total amount of sex must be equal, and the total number of partners on either side must be equal. So the averages must be equal, too.

But people get confused when talking about the entire population. Some people have more sex partners than others, so it feels reasonable to say that on average men may have more sex partners than women. Across the entire population, however, this cannot be true. Sex researchers have been aware for a long time that the data they often publish is “wrong” because of this problem. They assume that a double-standard is in effect: men exaggerate and women under-report, because it burnishes men’s reputations to be thought of as a Casanova, and because women face criticism for doing the same thing.

Here’s a simple mathematical example to demonstrate that men and women actually have the same average number of sex partners. Imagine a tango dancing event with 10 men and 10 women. It’s a pretty terrible tango session, however: One woman dances with each of the 10 men, and the other nine women dance with nobody. The whole thing is being filmed so that researchers don’t need to ask the dancers how many people they danced with. The maths here is easy: Both genders have an average of one dance partner.

On the side of the men, the 10 men had one dance each, so 10 x 1 = 10, and 10 divided by 10 = 1.

On the side of the women, one woman had 10 dances and nine women had zero dances. So 1 x 10 = 10, and 9 x 0 = 0. 10+0 = 10, and 10 divided by 10 = 1.

Everyone has an average of one dance each.

This logic tells you all you need to know about sex: The average must be the sum of all the encounters divided by the number of people having them, and that because it always takes two to tango the average number on both sides must be equal.

Of course, it would actually be more useful to know the median (or middle) number of partners, or the mode (most recorded) number of partners.

In our dance example, the median and the mode for men are the same: 1.

For women, the median and mode are both zero.

The two numbers describe a slight difference in the dance history of the two genders. But despite our statistical outlier — the woman who had nine dance partners — we can still say that men and women have either zero or one dances each. Similar, but with a slight difference, and quite close to the average anyway despite the very popular outlying female dancer.

What is interesting about the data in the kissing survey is the excessive difference in the reported average (men reported double the number of kisses). And, sure enough, the researchers had to discard some of their data when they realised that the numbers showed one of the men was lying:

One report of an average of 50 intimate kisses per day over the last year (Additional file 3) was according to the opinion of the authors unrealistically high … and showed a large discrepancy with the self-reported kiss frequency of his partner of eight intimate kisses per day. Therefore, we excluded the kiss frequency of this couple from the correlation analysis with the kiss frequencies and MH indices in this study.