The Mathematics Of Beauty

January 10th, 2011 by Christian Rudder

This post investigates female attractiveness, but without the usual photo analysis stuff. Instead, we look past a woman's picture, into the reaction she creates in the reptile mind of the human male.

Among the remarkable things we'll show:

Fair warning: we're about to objectify women, big-time. The whole purpose of this blog is to analyze OkCupid's data, and without a little bit of objectification that's impossible. Men will get their turn under the microscope soon enough. As usual, none of this (with the exception of the celebrity examples) is my opinion. All data is collected from actual user activity.

Let's start at the beginning.

All people, but especially guys, spend a disproportionate amount of energy searching for, browsing, and messaging our hottest users. As I've noted before, a hot woman receives roughly the messages an average-looking woman gets, and 25× as many as an ugly one. Getting swamped with messages drives users, especially women, away. So we have to analyze and redirect this tendency, lest OkCupid become sausageparty.com.

Every so often we run diagnostic plots like the one below, showing how many messages a sampling of 5,000 women, sorted by attractiveness, received over the last month.

These graphs are adjusted for race, location, age, profile completeness, login activity, and so on—the only meaningful difference between the people plotted is their looks. After running a bunch of these, we began to ask ourselves: what else accounts for the wide spread of the x's, particularly on the "above-average" half of the graph? Is it just randomness?

What is it about her:

that gets more attention than her:

...even though according to our users, they're both good-looking?

Not all 7s are the same

It turns out that the first step to understanding this phenomenon is to go deeper into the mathematically different ways you can be attractive.

For example, using the classic 10-point 'looks' scale, let's say a person's a 7. It could be that everyone who sees her thinks exactly that: she's pretty cute.

But something extreme like this could just as easily be going on:

If all we know is that she is a 7, there's no way to tell. Maybe for some guys our hypothetical woman is the cat's pajamas and for the rest she's the cat Garfield. Who knows?

As it turns out, this distribution of opinions is very important.

Celebrity photos: to titillate and inform

Let's look at what the ratings distribution might be for a couple famous people. I imagine that for, say, the actress Kristen Bell it would be roughly like this:

Ms. Bell is universally considered good-looking, but it's not like she's a supermodel or anything. She would probably get a few votes in the 'super hot' range, lots around 'very attractive', and almost none at the 'unattractive' end of the graph.

Compare her to Megan Fox, who might rate like this:

On the far right, you have the many dudes who think she's the sexiest thing ever. On the far left, you have the small number of people who have seen her movies.

Unlike Ms. Bell, Ms. Fox produces a strong reaction, even if it's sometimes negative.

Real People

Now let's look back at the two real users from before, this time with their own graphs. OkCupid uses a 1 to 5 star system for rating people, so the rest of our discussion will be in those terms. All the users pictured were generous and confident enough to allow us to dissect their experience on our site, and we appreciate it. Okay, so we have:

As you can see, though the average attractiveness for the two women above is very close, their vote patterns differ. On the left you have consensus, and on the right you have split opinion.

To put a fine point on it:

  • Ms. Left is, in an absolute sense, considered slightly more attractive
  • Ms. Right was also given the lowest rating 142% more often
  • yet Ms. Right gets as many messages

When we began pairing other people of similar looks and profiles, but different message outcomes, this pattern presented itself again and again. The less-messaged woman was usually considered consistently attractive, while the more-messaged woman often created variation in male opinion. Here are a couple more examples:

We felt like were on to something, so, being math nerds, we put on sweatpants. Then we did some work.

Our first result was to compare the standard deviation of a woman's votes to the messages she gets. The more men disagree about a woman's looks, the more they like her. We found that the more men disagree about a woman's looks, the more they like her. I've plotted the deviation vs. messages curve below, again including some examples.

The women along the graph are near the 80th percentile in overall attractiveness. You can click the tiny thumbnails to expand them.

As you can see, a woman gets a better response from men as men become less consistent in their opinions of her.

Our next step was to analyze a woman's actual vote pattern of 1s, 2s, 3s, 4s, and 5s:

If You're Into Algebra

We did a regression on the votes for and messages to a sample of 43,000 women. To keep everything consistent, all the women were straight, between the ages of 20 and 27, and lived in the same city. The formula given in the body of the post was the best-fit we found on our second regression, after dropping the m3 term because its p-value was very near 1.

msgs are the number of messages the woman received during the observation period. The constant k reflects her overall level of site activity. For this equation, R2 = .28, which isn't great in a lab or on a problem set, but is actually very good in a real-world environment.

This required a bit more math and is harder to explain with a simple line-chart. Basically, we derived a formula to predict the amount of attention a woman gets, based on the curve of her votes. With this we can translate what guys think of a woman's looks into how much attention she actually gets.

The equation we arrived at might look opaque, but when we get into it, we'll see it says some funny things about guys and how they decide which women to hit on.

The most important thing to understand is that the ms are the men voting on her looks, making up her graph, like so:

And those ms with positive numbers in front contribute to messaging; the ones with negative numbers subtract from it. Here's what this formula is telling us:

The more men who say you're hot, the more messages you get.

How we know this—the .9 in front of m5 is the biggest positive number, meaning that the guys who think you're amazing (voting you a perfect '5') are the strongest contributors to your messaging income. This is certainly an expected result and gives us some indication our formula is making sense.

Men who think you're cute actually subtract from your message count.

How we know this—because the .1 coefficient in front of m4 is negative. This tells us that guys giving you a '4', who are actually rating you above average-looking, are taking away from the messages you get. Very surprising. In fact, when you combine this with the positive number in front of the m1 term, our formula says that, statistically speaking:

If someone doesn't think you're hot, the next best thing for them to think is that you're ugly.

This is a pretty crazy result, but every time we ran the numbers—changing the constraints, trying different data samples, and so on—it came back to stare us in the face.

What We Think Is Going On

So this is our paradox: when some men think you're ugly, other men are more likely to message you. And when some men think you're cute, other men become less interested. Why would this happen? Perhaps a little game theory can explain:

Suppose you're a man who's really into someone. If you suspect other men are uninterested, it means less competition. You therefore have an added incentive to send a message. You might start thinking: maybe she's lonely. . . maybe she's just waiting to find a guy who appreciates her. . . at least I won't get lost in the crowd. . . maybe these small thoughts, plus the fact that you really think she's hot, prod you to action. You send her the perfectly crafted opening message.

"sup"

On the other hand, a woman with a preponderance of '4' votes, someone conventionally cute, but not totally hot, might appear to be more in-demand than she actually is. To the typical man considering her, she's obviously attractive enough to create the impression that other guys are into her, too. But maybe she's not hot enough for him to throw caution (and grammar) to the wind and send her a message. It's the curse of being cute.

The overall picture looks something like this:

Finally: What This Could Mean To You

I don't assume every woman cares if guys notice her or not, but if you do, what does all the above analysis mean in practical terms?

Well, fundamentally, it's hard to change your overall attractiveness (the big single number we were talking about at the beginning). However, the variance you create is under your control, and it's simple to maximize:

Take whatever you think some guys don't like—and play it up.

As you've probably already noticed, women with tattoos and piercings seem to have an intuitive grasp of this principle. They show off what makes them different, and who cares if some people don't like it. And they get lots of attention from men.

But our advice can apply to anyone. Browsing OkCupid, I see so many photos that are clearly designed to minimize some supposedly unattractive trait—the close-cropped picture of a person who's probably overweight is the classic example. We now have mathematical evidence that minimizing your "flaws" is the opposite of what you should do. If you're a little chubby, play it up. If you have a big nose, play it up. If you have a weird snaggletooth, play it up: statistically, the guys who don't like it can only help you, and the ones who do like it will be all the more excited.

427 Responses to “The Mathematics Of Beauty”

  1. mark says:

    A physical/mental rating system would certainly help. Most of the time, I rate a girl based on what she writes in her profile. Guys like me invalidate all of the conclusions of this survey, since it is incorrectly trying to separate physical attractiveness out of a composite scoring system.

  2. Sarah says:

    Would love to see a follow up that addresses quality of messages based on this logic and criteria. If people disagree about your attractiveness, then you’re likely to get more messages– but what kind of quality of messages?

  3. sconzey says:

    @Maya: If I remember correctly from a previous post on this subject, the “attractiveness” data comes from a specific anonymous “attractiveness” survey; and not from the star-ratings.

    Guys: great post; fascinating, and — in retrospect — embarrassingly obvious.

  4. Dave says:

    I’d like to concur there. The studies’ premise is that the 5 star rating is explicitly linked to the images only, when I’d imagine a large subset of men give those ratings using information from the profile and not simply pictures alone.

    How can you disaggregate that data?

  5. ZaviareMykols says:

    @Maya: I would suppose this can even be projected past merely pictures and to simply towards ratings of any sort. Those that are the middle will be contacted less because of their lack of unique qualities that cause people to become polarized about their profile.

  6. J says:

    I’m with Maya here in that I’m confused: are my star ratings supposed to be reflecting just looks? I’ve been using star ratings to categorize potential dates, rating them by overall interest rather than just looks.

    I would be willing to use the stars however OkCupid expects me to, because I love these social science experiments we’re getting out of them. But if that’s the intent, nobody told me!

  7. Ever says:

    I’m a woman, so it’ll be interesting to see how the men are starred. Personally, I rate them based on their profile, and if they happen to be cute, then all the better! But it really comes down to whether or not I like what they say, and what their values are, etc. It’s sad, but unsurprising, to see how much people (women especially) are judged on their looks more than their personality.

    Oh, and I’d be very interested to know what the statistics are for people who don’t have pictures on their profiles, like me. I’m a little hesitant to put one up, and this isn’t helping.

  8. Gregg says:

    @Maya But doesn’t that have the same effect as what this article says? While you might be turned off by someone who really likes god, wouldn’t that in turn make them more desirable to a church go-er? Same thing for reading, some people just don’t like to read or deal with people who they see as maybe intellectual or pretentious.

  9. greg says:

    In the sidebar “If You’re Into Algebra”, it’s indicated that m3 is dropped because it’s of low significance. This is a classic mistake; by dropping the term, you shift the impact of m3 to the other variables, increasing the overall error of the result. In other words, by dropping a term you actually made your coefficients less accurate instead of more accurate.

  10. Aaron says:

    This is very interesting, but isn’t it assuming that people are reliable in how they use the stars and that they only use them to measure looks? For example, a guy could be lazy and only use 1s and 5s. Or perhaps someone uses the stars just to put a feeler out there to see if she gives him 4 or more stars too. I just don’t think the users are reliable enough to take the data seriously. Is there a way to adjust for the different ways that people use the rating system by doing a survey on how users actually use the star system?

  11. fayaway says:

    Signed, sealed and delivered. This has confirmed my long time suspicions. Thanks OKC for telling the cold, hard truth. I dig it.

  12. Nick says:

    As always, interesting post! But you make some assumptions I don’t agree with there and oversimplify to much. First, you’re assuming looks and the rating girls get are more or less the same. But they’re not.The reason why Kristen Bell and Megan Fox are rated differently is not because some people think Megan Fox is ugly (I’m sure they don’t), but because she’s not their type or they strongly disagree with what she stands for.

    My explanation of why “unattractive traits” lead to more messages is a different one. Many people belong to some kind of sub-culture. Showing that you belong to one makes you very attractive to some users and very unattractive to those who dislike this sub-culture. When guys message girls, they obviously pick the ones that stand out.The polarizing girls obviously stand out. So they get more messages.

    I also don’t think that a polarizing trait like tattoos should be considered in the same way as being overweight. In your recommendation you equate them. I highly doubt emphasizing (instead of just not hiding) the fact that you’re overweight gets you many 5 star ratings, you’re not gonna polarize, you’re just lowering your ratings. I don’t think there’s a significant group of people that considers overweight people to be more attractive than average, but there definitely is a signficant group of people that considers tattooed people to be more attractive than average.

  13. Alexander Horschack says:

    From one anthropological perspective, it’s possible that the function of this pattern in a grand-scheme-of-things sort of way is to ensure that everyone looking for a mate is more likely to find one. If everyone thought that the same individuals were 5s, 4,s, 3s, 2s, and 1s, then we’d end up with loads and loads of people spending their entire lives consuming but without giving anything back (in the form of babies), amounting to a societal cost. This assumes that tens or hundreds of thousands of years worth of evolution wasn’t able to prepare our DNA and instinct and all of that for the relatively recent trend in overpopulation and its consequential resource depletion, in which case fewer babies might be to our benefit.

    In any case, this pattern allows for more people to end up as 5s overall and to experience all of the happiness and advantage in life that status offers, simply by diluting strong negative reactions by spreading them out in small batches assigned to each 5 candidate (an idea similar to political gerrymandering).

  14. William says:

    Back in the day, there used to be TWO star ratings per profile. One was for looks, and one was for personality. Now that there’s only ONE star rating per profile, I’ll find a girl who I think is a total knock-out, for instance, but she’s a smoker, and she gets one star. These statistics would be more valid if they were analyzed on the OLD system.

  15. tigerkite says:

    It makes enough sense. The Sex Pistols would have sold a lot less records if they were less noisy and made their lyrics tame, even if they were repulsive to lots of people in the process.

  16. Jan says:

    Another, much simpler interpretation of the data you have shown:

    1. Only ‘hot’ triggers messages, ‘cute’ doesn’t.
    2. To be hot to someone you better are an extreme, even if it makes you ugly to others.

    Perhaps you could add an analysis which men message the girls (for ugly/hot and cute)? I think probably the hot-raters are the majority.

  17. Sharon says:

    Do y’all have actual data showing that overweight women get more attention when they show their actual size? Granted, I live in Brooklyn, but I’m not expecting tattoos and piercings (freak, which is a strong positive for a lot of people) to play out the same as fat (not so much).

  18. Kevin says:

    @Maya
    Exactly what I was thinking. Having the written profile available is a bad idea for Quickmatch if you guys want to use the ratings to assess physical attractiveness.

  19. Ray says:

    “This happens all the time in China.” – Did I really just read that? Wow.

  20. Michael Joseph says:

    It’s funny, we just did a teleseminar last night at IvyLeagueLoveCoach.com recommending people check out this blog! Great fresh info for dating.

  21. Tim Thraeryn says:

    What Maya said. In addition, I’ll often rate women I sleep with as “5”s and women with whom I have shitty IM conversations “1”s, attraction be damned.

  22. Jen says:

    Interesting analysis. Don’t you think it’s possible that those pictures that cause disagreement among users re: attractiveness are just more interesting/controversial and thus provide more fodder for conversation? If only you had ratings of how interesting/boring photos were and not just how attractive…

  23. kxrm says:

    This just proves my thought all along that it isn’t ugly that is a detractor, it’s average.

  24. Eric says:

    A great post ruined by the fact that you never define how you think you know how attractive a woman is. I assume it’s quickmatch and star votes. Which is presented with a profile as well as a picture. To assume that stars = physical beauty rests solely on the assumption that guys are completely shallow. Which, we are. But you should list your assumptions at the top if you are at all trying to present something informative.

  25. Paul says:

    Another terrific post about why we might choose a partner, because it has the ring of truth to it and liked how Cupid explained why in scientific terms what we resist persists.

    Anyway, in my life love is a decision first, then it moves to an experience. But, maybe I’m just unique in doing that. The first two questions I ask regarding whom to get to know – Is this who I am? and What would love do now?

  26. OpenOaks says:

    Given the bold caveat that “we’re about to objectify women” I’ll also risk backlash by pointing out a glaring flaw: the report implies that “attractiveness” in women may be judged by head shots. That flies in the face (pun intended) of how most men actually function. Only Megan Fox (singularly unattractive) gets to show off a little (singularly unattractive) cleavage — not a hip, leg, tummy, or bottom to be seen.

    This approach ignores much of what constitutes “attraction” for men. I realize your data do not capture body type effectively (a significant oversight and time-waster on all dating sites), and that body type is frequently misreported, anyway. However, a significant number of self-aware and thoughtful men are looking for a woman who is more than a pretty face, in many ways.

    Personally, I find NONE of the photos in this report “attractive.” The first graphed, leftmost “tiny thumbnail” comes close — but none would inspire me to send a message. In part, that’s due to the lack of data about how these women actually LOOK. All I know is how their FACES look.

    I encourage every person to post at least one relatively full body shot — regardless of body type. To do otherwise is to limit the number of qualified inquiries from truly interested parties.

  27. Bryan says:

    Exactly what Maya says above. You should use the data from MyBestFace if you’re going to be examining looks alone.

  28. Kevin says:

    What about measurement error? Could it be that a non-trivial portion of rsepondents mistake “1” as the value for “hot” and respond accordingly? How are the hotness scales measured?

  29. Addison says:

    I fully agree with Maya. I will click on a woman’s profile and if she’s really cute but she has 5 words per section, it most likely means she could give two craps about the site and isn’t really that great of a communicator in the first place.

  30. singalongblog says:

    @Maya, I think the results should still hold whether you include profiles or just pictures. You would still get the distribution differences. It probably smoothes out given enough users anyway because some people would rate purely on the picture, others on the use the profile.

    @oktrends, First, awesome analysis! Second, here is a suggestion for another data analysis project…

    We know that received unsolicited message frequency seems to be a function (in part) or attractiveness, race, gender, religion, and politics. What I’d be curious about is whether or not you could tease out information about the things people can do to boost their unsolicted message frequency.

    Proposal: Calculate message count on a weekly or biweekly basis and look at people who had significant changes in their message rate across time. Then go back and look at what things they did to their pics and profiles that might account for the changing rate over time.

  31. SVM says:

    Oh, sly, pouty redhead, let me immerse myself in your pool of love!

  32. BK says:

    Were all of the messages to the bimodal girls positive? Maybe those women are getting a response from both ends of the spectrum. “OMG, you’re ugly as sh#$%t, why are you even on here?” along with “Wow, you’re gorgeous, let’s go out.” This would account for an increase in messaging, but not necessarily the desired response. You’re assuming that messaged = positive, but is it?

  33. stillsosexy says:

    Other than perceptions of ‘looks’ another variable is ‘the look’. Notice the coy, sideways glancing, come-hither look for those rated highly attractive. Not a coincidence, I think!

  34. Dennis says:

    So in some of the biological literature regarding female choice and mating systems, the variance of male success factors heavily. Do you have any way to look at this with your very interesting experimental system? Does the variance of a male’s response rate show any interesting trends?

  35. Amber says:

    Regarding categorically using descriptors such as “ugly” to characterize individual women (based on her photos) my thoughts are that men often call women “ugly” because they think that a woman’s sexuality is too pronounced.

    The Megan Fox example illustrates this perfectly. I’ve have actually heard men call her ugly, which is completely ridiculous. If Paris Hilton were stripped of her reputation and fame and pictured in blue jeans and a black leather jacket, I doubt half as many men would call her ugly as currently do.

    So, I don’t agree that if a man says a girl is “ugly” that they think she is “ugly.” What they means is that she comes on too strong, is not ladylike enough, etc, so it follows that women that are pictured as utterly feminine (Kristen Bell) only appeal to those men for whom pure femininity holds charm.

    But average Joe likes a combination of femininity and certain characteristics that are less-than feminine. Tattoos, piercings, a sharp nose, bird legs, bold eyebrows, dyed black or red hair, etc.

    So I don’t believe it necessarily follows that the more a group of men disagree with a woman’s “looks” on a scale of pure attractiveness. There is little subjective about pure attractiveness, there is general agreement across cultures and ages — which has been illustrated in multiple studies. What’s funny is that men often use the descriptor ugly to mean that they think she is an ugly person, despite her objective attractiveness.

    So, Paris Hilton is ugly no matter what she is wearing. :)

  36. greg says:

    I think you hit the nail on the head this time, good job OKcupid!

  37. another stat says:

    I think you are overlooking the fact that 4s and 5’s as well as 1’s and 2’s are not independent variables.

    the negative coefficient for m4, is not unrelated to m5.

    if someone suddenly has a whole bunch of people thinking she is a 4, she had better have many thinking she is a 5.

    likewise for 1 and 2

    it isn’t that a “1” will get you a lot of messages,
    in fact if you have as many 2 ‘s as 1’s (which i would guess to be the case because raters are not mean), then the sum of 1 and 2 is

    you need to normalize for the covariance

  38. Justin says:

    Maybe my game theory degree will come in handy after all

  39. Yrro says:

    Sounds about right. Whatever it is you do, be *interesting*.

    Oh, and people message girls with tattoos because they think they’ll put out. Just saying.

  40. Waleed says:

    Maya: They used to have a separate star rating for looks. Maybe they are using the old ratings.

  41. Jon says:

    Your “What Men Think of Your Looks vs. Your Messages” plot is very smooth. In reality, there should be quite a bit of scatter. Can you post the scatter plot in addition to the fit curve?

  42. singalongblog says:

    Another question… In earlier posts oktrends differentiated between messages that lead to conversations versus unanswered messages. Did you account for that distinction in the results you present above? And if not, might that distinction help reduce the differences between consensus and controversial people?

  43. lee says:

    I am no longer a member of this site, but when I was I voted based MOSTLY on their profile. If they were attractive they received an additional star. I assumed most people voted that way.

  44. Caleb says:

    It’s true. I rate based on 1) personal opinion of attractiveness, 2) profile content, and 3) religion.

    When it comes to the “message count”… I have a feeling it’s because the general consensus is that cute girls aren’t going to sleep around, whereas sexy girl (stereotypically) will. So I suspect the statistic is closer to: One in every four men is actually looking for love on this site, three out of four are trying to get laid.

  45. Phil says:

    I *love* these blogs, one of the best reasons to be on this site. But 125 messages a month, I’d be lucky to have received 125 “unique” messages since joining this site. Help the guys out, the girls seem to be doing just fine.

  46. ErikTheRed says:

    There also seems to be a positive correlation between “flirty” looks or at least pictures where the subject is “paying more attention to the camera” and higher message count, at least from the very limited sample shown here.

  47. vrb1955 says:

    How about this . Beauty only skin deep . Ugly is to the bone . Some of the most so called “beautiful people” on this site have the ugliest souls. I like the the guy that is easy on these old eye and has a beautiful soul.

  48. Malatesta says:

    I assume you’re already contemplating something similar about response rates for guys…

  49. ski-horse-cook says:

    Isn’t the title misleading? This appears to be the mathematics of selection.

    As for the math.. I have more thinking to do.

  50. p-man says:

    this is amazing work. a lot of things i’ve wondered about are perfectly explained here. women with an edge are sexy, it’s a fact.