Doubling your chances for a date on Saturday night

It's one of the most famous jokes from Woody Allen's early career as a standup comedian (though the exact wording and the original source are, as usual with famous quotes, somewhat obscure); as quoted in the New York Times (1 December 1975, cited by Fred Shapiro in The Yale Book of Quotations), bisexuality "immediately doubles your chances for a date on Saturday night." The AZ Quotes site (giving no source) phrases the line this way:

"I can't understand why more people aren't bisexual. It would double your chances for a date on Saturday night."

No one seems ever to have pointed out that Woody's point seems to be not just strictly inaccurate but profoundly and grotesquely false. Analysis suggests that bisexuality would not double your chances for a date on Saturday night, it would roughly halve them. Given the statistics referenced here on Language Log recently, we can set out the reasoning fairly rigorously.

For concreteness, we consider a straight male named Nigel in the United Kingdom who is determined to lock in a date for next Saturday night and starts working at the problem from Monday morning. (It is not essential that he be called Nigel. In fact the name is reportedly dying out in Britain, so it is not even particularly plausible that he be called Nigel. But ignore that. He's just a fiction.) Let's say Nigel typically runs into about 20 women a day, and plans to ask every single one of them, with no ethnic or other prejudices and no advance inquiries about who is married, single, straight, lesbian, etc. By Friday night he will have asked a hundred women out.

We'll assume arbitrarily that when straight women are asked out, ten percent will say yes. (Nothing in what follows hangs on the 10% figure being reasonable; it's there just to permit us to compute actual counts of Nigel's probable positive answers under differing scenarios.) As revealed in the aforementioned figures from the Office of National Statistics, two of the women he asks are likely to be lesbians. We'll assume they will not want a date with a guy, so Nigel has a 9.8% chance of getting a yes.

Now assume Nigel adopts the philosophy suggested by Woody Allen's remark: he broadens his horizons, and tries dating people without regard to whether they're male or female. This will make no difference if he continues to ask out only women, so obviously he has to ask men as well. But if he only has time to strike up the necessary conversations at a rate of 20 a day, and he does not discriminate any more, his new policy is going to involve asking (on average) about 50 men and 50 women during the working week. We'll assume for now that the 10% figure for positive answers is constant for the population.

Given that 2% of the population will identify as LGB, one of the women he asks will be a lesbian, and we're assuming she will say no. (Occasionally Nigel will be luckier, and will find he has asked an LGBT woman who is bi, and I'm not taking that into account here. It makes only a tiny difference.) And of the men he asks, only one will be gay or bisexual. We can surely assume that all straight men are going to say no (or some elaboration of no, such as "Whaddya talkin' about? Geddaway from me, ya effin' pervert"). His candidates are now 49 straight women and the one gay or bisexual man, i.e. 50 people who just might be interested (I'm assuming here that gay men are prepared to date straight men). With a 10% chance of a positive answer from these 50 candidates, he now has only a 5% chance of getting a date. His chances have halved.

So let's make a more generous assumption about willingness to consider a date. Gay and bisexual men are reputed to be, if not total wicked horndogs, at least much more interested in dating (and having sex, which is what this is really about) than straight people. So maybe we can up the response percentage for gay and bisexual men. Suppose we double it, to 20%. In that case (let's consider ten weeks of date-seeking so as to avoid talking about fractional people), out of every 1000 invitees he could expect 490 to be straight women from whom he can expect an average of 49 positive responses, and 10 to be gay men of whom he can expect 2 to accept, so that's 51 per thousand, i.e. 5.1%. That's only a little better than half the 9.8% chance that he would have if he asked solely women. Even the outlandish assumption that 99% of date proposals to gay or bisexual men result in a yes will only get Nigel's hit rate up to 58.9 per thousand = 5.89%. No twofold improvement in dating luck.

Naturally, if we take it to the limit and assume that 100% of gay or bisexual men will accept, then since Nigel is statistically certain to get one such man among the 50 in his 100 invitees, he is certain to get a yes. But first, this makes Woody Allen's claim absurdly understated: the chances have not doubled, they have gone up by a factor of infinity to complete certainty. And second, it also has a weird consequence that Allen surely didn't intend to play a role in the reasoning: it means that asking women is a complete waste of time, since by focusing on asking men Nigel can pretty much guarantee getting a positive answer at some time during the week. But he'll always be dating men.

I'll consider one other possible change in assumptions that Allen could plausibly have had in mind if we take his claim seriously (thanks to Jim Donaldson for remind me to cover this case): perhaps he was positing not just a more catholic view of candidates among the people one meets, but a more energetic approach to asking people out. Don't just ask twenty women each day, but ask all of them and additionally ask the same number of men. What would be the result? Asking 100 women gets Nigel a 9.8% chance of a date with a woman, but the same number of propositions to men adds only 0.2% if they share the 10% yes rate, or 0.4% if they are twice as likely to accept: maybe a 10.2% chance overall.

Bumping that up to asking 100 women and, say, 1000 men is unreasonable just on grounds of time commitment: to chat up those 1,100 people in a week of five 16-hour days (80 hours), he'd have to ask people out at a rate of more than one every five minutes, from dawn until late evening, leaving no time for work or meals. And even that would only get him a probable 9.8 women saying yes and 2 to 4 men (10% to 20% of the probable 20 gay men encountered), for 11.8% to 13.8%. Still absolutely no sign of doubling.

As far as I can see, maintaining anything like familiar sociological and sexological assumptions, there is no plausible way to make Allen's claim come out anywhere near true. I actually don't have a date lined up for next Saturday, October 14th, so believe me, if Allen's suggested strategy had any plausibility at all, I would have it under consideration. Under a wide range of reasonable assumptions (since there is nothing essential about my adopting the conjecture of an even split of women and men in the candidate pool, or a typical 10% constant positive response rate) the result would be approximately the opposite of what he said: a policy of developing a bisexual orientation would, given basically constant energy put into asking people out, would roughly halve your chances of a date next Saturday night.

Please note that comments below are open only to (a) statisticians, (b) sexologists, (c) bisexuals, (d) Woody Allen scholars, (e) total wicked horndogs, (f) people who do have a foolproof plan for doubling your dating chances, and of course (g) Edinburgh residents interested in a possible early supper and a movie next Saturday night.