## Average 2.8 M sexual partners

Check out these news-story titles: How the average Brit has slept with 2.8 million people. Ave Brit shagged 2.8 m people. Someone is going to need a bigger bed. Here’s one story:

**Brits have had ‘indirect sex’ with 2.8 million people **(AFP) – Sep 23, 2009

LONDON – The average British man or woman has slept with 2.8 million people – albeit indirectly, according to figures released Wednesday to promote awareness of sexual health. A British pharmacy chain has launched an online calculator which helps you work out how many partners you have had, in the sense of exposure to risk of sexually transmitted diseases (STIs).

The ‘Sex Degrees of Separation’ ready reckoner tots up the numbers based on your number of partners, then their previous partners, and their former lovers, and so on for six ‘generations’ of partners. The average British man claims to have actually slept with nine people, while women put the figure at 6.3, giving an average of 7.65.

‘When we sleep with someone, we are, in effect, not only sleeping with them, but also their previous partners and their partners’ previous partners, and so on,’ said Ms Clare Kerr, head of sexual health at Lloydspharmacy. ‘It’s important that people understand how exposed they are to STIs and take appropriate precautions including using condoms and getting themselves checked out where appropriate.’

Now my side of the story. Lloyds has created a “statistically transmitted disease.” This disease is transmitted via sexual contact but these sexual contacts are based on a model — a statistical model. Lloyds goes out six generations beyond your immediate partners. This choice is totally arbitrary. The more generations out, the bigger the number. Lloyd’s model gets a big number by being unrealistic.

Lloyd’s model ignores five big items: the prevalence, communicability and remoteness of the disease, the order in which the sexual contacts occur, and the inappropriateness of the average.

**After taking into account the five things Lloyds ignored, I estimate the Lloyd’s number is ten thousand times as big as any sexually-relevant number.** Instead of 2.8 million, I estimate 280 sexually-relevant partners.

(1) PREVALENCE: If only 20% of adults have STDs, then the number of sexually-relevant partners is less by a factor of five.

(2) COMMUNICABILITY and (3) REMOTENESS: The Lloyds model assumes that everyone who has sex with someone having a STD will catch that disease. This is unrealistic. Suppose there is a 10% chance of catching an STD from a partner that has it. The chance of acquiring an STD from someone six generations away is miniscule. Averaging over the varying degrees of separation might give a total number of sexually-relevant partners that is less by a factor of at least a hundred.

(4) ORDER: To measure vulnerability to sexually-transmitted diseases, the issue is not how many sexual partners your partners had, but which events occurred first so that diseases could be transmitted to you. The Lloyd’s reckoner assumes that order is irrelevant. I’m guessing that taking into account all possible orderings to get the number of indirect sexual partners that could transmit disease could give a total number of sexually-relevant partners that is less by a factor of two or three.

(5) AVERAGE: The Lloyd’s reckoner uses averages. This number-of-partners distribution is highly skewed. There are more “rabbits” than virgins and some rabbits are very “promiscuous.” Those promiscuous rabbits will pull the mean quite a ways above the median. Assuming you and your sexual partners are not highly promiscuous, this choice is likely to persist through your chain of sexual partners. In such a case, the median is more appropriate. If the median is 70% of the mean, then the seven-generation estimate is 0.7 to the seventh power of the original: 0.08 – a ten-fold reduction. If the median is 50% of the mean, then the seven-generation estimate is 0.5 to the seventh power of the original: 0.008 – a hundred-fold reduction.

Summary: Making all these adjustments gives a total number of relevant partners that is less by a factor of 10,000: going from 2.8 million to 280. If we’re going to have a statistically-transmitted disease, it should be modeled realistically.

More technical details here and here. OK numbers people. What do you make of Lloyd’s reckoner and these adjustments?