This is a question that practically every male has asked himself at one point or another in his life. Unfortunately, there is rarely a hard and fast answer to the query. In reality, it's probably due to a number of physical and psychological factors that we could never measure.
But that's boring. So I'm doing this my way.
Let's take a look at the figures:
Number of people on Earth: 7,000,000,000
We start with the largest demographic in which I am interested--namely, the population of this planet. Don't get me wrong, I'm not against the idea of interstellar romance, I just don't see it as a reasonable assumption to make.
...who are female: 3,500,000,000
I assume that, given the title of this article, this kinda goes without saying. Also, (I may get a little side-tracked here, sorry in advance) the population is half and half, deal with it. If you're one of those people who INSISTS that it's a 49%/51% split, nobody likes you, I'm serious (you probably also complain about how Big Ben isn't called Big Ben and you liked Owl City before Fireflies, you're wrong on all three). You need to pipe down and just have a serious think about where your life is going, seriously. Anyway, it's a 50%/50% split; accordingly, roughly half of the Earth's population must be discounted. Sorry, guys.
in Europe and USA: 685,601,000
I restrict the geographical area of interest to countries I am likely to live and/or work in and therefore meet my potential partner.
...currently aged 13 to 18: 45,399,083
I would like to restrict my search for love to those whose age is approximately equal to my own (although I fully understand that when we're 90 years old, a 5-year age gap would feel like nothing). To make things still worse, roughly 1% of these girls will have died since the census I'm using was taken; thus, the true number of so-far eligible bachelorettes is 44,945,092
...who are beautiful (to me): 1,487,838
Personal attraction, both physically and personality-wise, is the most important factor (maybe other than the living-on-Earth thing) in any relationship. Of course, beauty is a largely subjective trait which varies from person to person.
I'm not going to argue about what makes you beautiful (you don't know you're beautiful (God, I'm going to get crucified for that one)) but what I hope we can all agree on is that it will probably be normally distributed amongst the population.
Without going into the specifics of precisely which traits I admire, I will say that for a girl to be considered really beautiful to me, she should fall at least two standard deviations above the standard. From basic statistics theory, the area to the left of the normal curve at z = 2 (for those of you who haven't done basic calculus, they have to be like an 8 out of 10).
...and intelligent: 236 053
Again, intelligence can mean different things to different people, yet I am once again squirming out of trying to explain personal opinion to you people by noting that it, like most other characteristics, has a pretty much normal distribution across the population. Let's assume that I will settle for someone a mere one standard deviation above the normal (like a 6 ½ out of 10); in that case, a further 50.0002% must be removed.
...and not already committed: 118 027
I could find no hard statistics on the number of above-noted girls who are already married (that would be weird), engaged (slightly less weird) or otherwise committed to a significant other (still a little weird), but a little basic observation (no binoculars, I promise) leads me to assume roughly 30% of my remaining candidates to already be in some form of relationship.
...and also might like me: 82,618
Naturally, finding a suitable girl who I really like is no guarantee that she'll like me back.
Assuming, as previously mentioned, that personal attractiveness is normally distributed, there is a mere 50% chance that any given female will consider me even marginally attractive. In practice, however, people are unlikely to consider pursuing a relationship with someone whose looks and personality just barely suffice. I'll then make the (rather conservative) assumption, then, that a girl might go out with someone if, and only if, they were at least one standard deviation above her idea of average. (I'm not giving you any more scores out of ten; it's pretty simple). In that case, referring to our previous calculation, only 15.8655% of females would consider someone with my physical characteristics and personality acceptable as a potential romantic partner (on an unrelated note, I've worked out that 84.1345% of women are fools).
We have arrived at a pool of 13,107 acceptable females. At first glance, that may not seem like such a low number (indeed a high number to those of you who know me), but consider this: assuming I was to go on a blind date with a new girl about my age every week, I would have to date for approximately 50,000 weeks before I found one of the 13,107.
That's very nearly 1,000 years.
I hate to say it, but I think it's become clear to everybody reading this that the reason I'm lonely is because I'm exactly the kind of guy who sits down and spends hours doing this kind of stuff. Also the 1,000 years thing.
I'm going to die alone.