MyATMPinIs1234

EHarmony: The worst case of false advertising since The Never Ending Story?

I haven't been on any dating websites, but I frequently see commercials on TV for a site called Eharmony.com. They profess to have a sophisticated algorithm that will match you with your soulmate. Unfortunately, Math disagrees.

I doubt Minister Thomas Bayes set out to prove that finding true love is next to impossible in his work, Essay Towards Solving a Problem in the Doctrine of Chances (1764), but the application of his theorem has the potential to crush the hopes of lonely people everywhere.

You might wonder, as I did when I watched the EHarmony commercial, if I fill out that whole profile and they find a match for me based on 29 dimensions of compatibility, what is the probability that this match is actually my soulmate? Fortunately this is a straight-forward math problem.

But first, the assumptions:

1) The Eharmony algorithm is 95% sensitive. Given a soulmate, they will identify them as such 95% of the time.

2) The Eharmony algorithm is 95% specific. It generates only 5% false positives.

3) Your soulmate(s) are 1 out of every 1000 people.

(I'm probably being way too generous, but you'll see it doesn't matter. Specifically, this would mean you have something like 40k soulmates in the USA)

And now, the calculation (Bayes' Theorem):

P(SoulMate | Matched) = P(Matched | SoulMate) x P(SoulMate) / P(Matched)

P(Matched | SoulMate) = .95 (the sensitivity of the test)
P(SoulMate) = .001 (1 out of 1000)
P(Matched) = Valid Matches + False Positives = .95(.001) + .999(.05) = .0509

P(SoulMate given EH Match) = .95 * .001 / .0509 = 1.9%

So don't get your hopes up too much for the date, because if Eharmony says you are a match, they have a 1.9% chance of being right. The chances of getting laid are much higher, but dependent on a completely different set of variables.