# Sex and Statistics or Heteroscedasticity is Hot

on January 12, 2011 at 7:30 am

Ok Trends has another great post combining statistics, sex and even a little "game theory" (read that in whichever sense you prefer). The statisticians at OK Trends discovered that the number of messages a women receives varies widely even after conditioning on the women's attractiveness rating. Why do some 7's receive far more messages than other 7's? It turns out that it's much better to receive some 10's and some 1's than all 7's. Or as OK Trends beautifully expresses it:

A lot of this can be explained by a non-linear function of messages to attractiveness; that is if 2 men rate three women, A,B,C, as A:{0,10}, B:{5,5} and C:{10, 0} it's not that surprising that A and C each receive one message and B receives none.

But OK Trends argue that more is going on. In a regression of messages on number of rankings in each category (1 being lowest, 5 being highest) they find, not surprisingly, that more high rankings increase messages but also that more low rankings increase messages. That is they find that a ranking of {0,10} can be better than a ranking of {6,10}.  Ok Trends hypothesize the following explanation:

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.

I have my doubts. Rather I think there are certain types of beauty that greatly attract some men but repel others. Analagously, some people will pay hundreds of dollars for an ounce of caviar that other people won't eat for free. The reason some people love caviar, however, is not that other people dislike it. Instead, it just so happens, that the thing that some people love is the very thing that repels others. We see the same phenomena in art, some people love John Cage, other people would rather listen to nothing at all. ðŸ˜‰

Now if we mix in this kind of beauty–beauty over which there are violent disagreements–with the kind that most people do agree upon (think Haagan-Dazs vanilla ice cream) then I suspect that it will appear that lower rankings increase messages. But what is really going on is that high rankings–conditional on their also being many low rankings–actually signal an extra strong attraction. Someone who tells you that John Cage is their favorite composer is telling you more than someone who says Aaron Copland is their favorite composer.

Note that even if rankings were not public this theory would predict that the same women would receive more messages than their (non-public) rankings would suggest.

Which ever explanation holds, some advice follows: In the marriage market what you want is not so much to increase your attractiveness to the average person but rather to the one person who will  cherish your unique features. Thus–conditional on attracting a decent number of suitors from a reasonable pool etc.–what you want to do is accentuate your unique features even if doing so reduces your average ranking. In short, heteroscedasticity makes you hot.

FYI, OK Trends will analyze women's reactions to men in a future post.

1 Cyrus January 12, 2011 at 4:03 am

There is a much simpler explanation: men do read the profiles, and after controlling for female attractiveness, the text matters.

2 Some Random Economis January 12, 2011 at 4:34 am

Whatever the reason for the differences in variance, Alex is right to doubt OK Trend's explanation. No strategic thinking is needed to explain the result. All you need is for each man to have a reservation level of attractiveness. For the sake of argument, say that reservation is 7 for all men. A woman whose ratings are tightly clustered around 6 will get fewer messages than a woman with the same average but a more dispersed distribution. More ratings in the upper tail means more messages, strategy or not.

3 TheophileEscargot January 12, 2011 at 4:38 am

The sample pictures has a girl with a flower in her hair, with her hair carefully arranged, wearing a lot of jewellery to illustrate the "some-like some-hate" girl.

The "bland" girl is a cropped shot of a girl casually dressed, standing outside, with her hair a little untidy from the wind.

I suspect it's not the facial features that are causing the difference, I think it's the pose and background of the photograph.

Guys who don't like to wear formal dress or go to formal events might see the "some like some hate" girl as high maintenance, someone always fussing over her appearance, someone who wouldn't fit in with his casual social life, and rate her down. Guys who do like these things might rate her up.

Whereas the "bland" girl doesn't really convey any such information. Everybody stands outside sometime: we don't know if she prefers ballroom dancing or NASCAR racing.

The lesson might well be: try to convey some hints about your personality and interests in your photograph: you'll get more responses on average, even if some rate you down for not matching.

4 DanC January 12, 2011 at 5:15 am

Women who are successful in dating are often attractive enough to gain attraction but not so attractive to be intimidating for the average male.

Some extremely attractive women do not date that much while less attractive (but still pretty) women have a busy social calendar. This seems to be especially true in the high school and college years. Years that, until more recent times, which were periods when long term relationships formed.

Perhaps some very attractive women are more selective, feeling that they can hold out for a "better" partner. At younger ages I think male insecurity plays a larger role.

Some extremely beautiful women tire of being told how beautiful they are, it becomes boring and superficial, and males who use this approach often seem childish,

In contrast, pretty women, the attractive enough girls, enjoy compliments on their looks if the message implies that the women is special to the male.

5 Roger January 12, 2011 at 5:52 am

Isn't this the same argument that we hear about why Fox and MSNBC are kicking CNN's behind.

Better to appeal to the fringes than the center – you would have more committed followers

6 Peter January 12, 2011 at 6:11 am

Rather I think there are certain types of beauty that greatly attract some men but repel others.

Guess I'm not the only man who has an unorthodox (ahem) standard of female beauty.

7 Barbara January 12, 2011 at 6:20 am

Really interesting post. Men show interest in beautiful women. Despite subjectivity, everybody can tell if a lady is nice or isn't.

8 Yan January 12, 2011 at 6:23 am

this is a real life demonstration of the voting paradox or the intransitivity of voting.

9 Ted Frank January 12, 2011 at 6:51 am

Both you and OK Cupid are reversing causation. It is almost certainly the case that the reason that the reason women with highly dispersed "1" and "5" ratings get so many contacts is not because, as OKCupid would have it, the "1"s cause people to write to the women, but because so many men write to the beautiful women, get shot down (or, more likely, ignored), and then take "spoiled grapes" revenge by assigning a 1-star rating to the woman. (A more noble explanation is that the men use the "1-star" designation to remind themselves not to write the woman again, but given the other options OKCupid has to signal that–"hiding" profiles, checkmarks over the contact button, notes–suggest that it is simple bitter revenge.) Thus, OKCupid's stats are going to be messed up: some "3.8-star" women are really a 3.8 and others are a 4.6 who have provoked a lot of immature men. The latter are going to have the dispersion result that OKCupid suggests "causes" many contacts when it's really that many contacts causes dispersion in the beauty ratings.

10 Alex Tabarrok January 12, 2011 at 7:16 am

Ted Frank's explanation is great but I believe that the number of rankings far exceeds the number of messages so I am not yet fully convinced.

Gabriel, not true. I recognize exactly the point you make in the paragraph beginning "A lot of this can be explained…". My alternative explanation beginning "Now if we mix in this kind of beauty…" recognizes the need to explain why low rankings add to messages and I even propose a test.

11 Albert January 12, 2011 at 7:28 am

In the previous post I meant to say in the first paragraph that G1 gets more messages than G2, not the reverse

12 Alex Tabarrok January 12, 2011 at 7:47 am

Cliff has it exactly right.

13 Jim January 12, 2011 at 8:01 am

"Isn't this the same argument that we hear about why Fox and MSNBC are kicking CNN's behind."

I suppose that's one way of putting it. Here are yesterday's numbers.

Fox 578
MSNBC 265
CNN 212

>Better to appeal to the fringes than the center

Significantly more people watch Fox than CNN and MSNBC combined.

All these people are "fringe," huh?

14 Six Ounces January 12, 2011 at 9:01 am

One dynamic you're forgetting is reciprocity. A man will assign himself a number. He will judge the probability that each woman would be interesed in him given his number. That probability need not be the same for women with equal numbers because 1) not all women of the same rating are equally attractive, 2) interests, backgrounds, education, hobbies affect the probabilities, 3) the narratives give clues about character and personality.

Unless he's the type who will lay down a volume of fire, a guy will message the women he subjectively thinks will write him back. He may take some risks on long shots, but he will generally conserve his efforts. A "form" message is less likely to get a response, and thoughtful, personalized messages take time to write.

It's cliche, but there's more to a woman than looks. There are lots of 10s I have no interest in dating if it comes at much cost. At zero cost, I would have dated any but the ugliest women. There's social value in getting to know people regardless of their physical ranking. I went on a New Years date with one woman, and ended up in a long-term relationship with one of her friends. I got traded in the women's rest room.

A lot of women who rank highly for looks have severe psychological issues including commitment problems, eating disorders, narcissism, and vacuousness. I've dated 10s – real 10s, and they're nothing special.

I met a gorgeous Hollywood actress, and SHE asked me out to dinner. The conversation was vapid. After scolding me for holding the door for her when we walked in, she didn't lift a finger to split the dinner check. I stood her up for a second date the next morning.

In my younger days I would rate myself a 7 relative to other men. Now, after 20 extra pounds, I'd rank myself a 6. I'd take a random 7 over a random 10 any day – if I didn't already have a wonderful wife who is unrated. A good relationship is priceless.

15 Max Rockbin January 12, 2011 at 9:24 am

This is based on a regression on highly correlated factors. If there are a lot of 3 ratings, there is a high likelihood of more than average numbers of 2 and 4 ratings – and relatively few 1s. A lot of covariance MEANS YOU WILL GET WEIRD NUMBERS IN THE REGRESSION COEFFICIENTS. For example, you will get a negative coefficient for the 3 because it's already counted by the coefficients for the 2 and 4.

I think this whole article (except for the anecdotal stuff) is based on a bad regression.

16 Six Ounces January 12, 2011 at 9:25 am

Let me make a comparison of interest.

When I shop for products online, I read reviews. I'm initially attracted to products with a higher number of stars, but I will make a point of reading the reviews of people who rated the product low.

Those low rankings may be from people disgruntled by product qualities or other factors which don't contribute to my decision. Or, they might reveal actual problems. Every product has SOME shortcoming, so the low review adds information to the cost-benefit analysis. The information lowers my expectations and thus reduces disappointment.

High rankings and glowing reviews are often posted in haste, with exuberance, and possibly even from parties with a vested interest. Lower rankings are more likely to contain a more thoughtful, considered, balanced overall appraisal. 10s can only get worse with time and consideration. 1s can only get better. But, I believe, 10s are more likely to come down than 1s are likely to go up.

However, the value of the 1-star rankings does NOT come from the ranking itself, but from the information in the comments.

But suppose we can see no comments supporting rankings. Can we learn anything from greater variance in the rankings? This might be a similar fallacy to the "small school" mistake of Bill Gates.

17 Tim January 12, 2011 at 9:35 am

I think there's far more genetics involved than we're able to process. Genes for red-headedness are recessive and yet have managed to stay wildly successful, frequently popping up in children where neither parent is red-headed. I think we are able to "see" genetic traits that we can in no way put into words. And can be strongly repelled or attracted.

18 dirk January 12, 2011 at 10:43 am

In the example photos the polarizing girl looks more ready to go. I wonder if a sluttier look creates greater polarization as well as more messages. Not that that is inconsistent with Alex's theory, except that the "extra strong attraction" isn't so much extra attraction as it is extra hope of scoring fast.

19 Matt January 12, 2011 at 11:55 am

Okcupid's quickmatch feature makes it possible that the (1,5)'s are strategically rated 5's by some men, since rating them a 4 or 5 sends them a signal that someone thinks they're attractive, while sending a 1 or 3 does not. The ratings data is biased due to this functionality of 4 or 5 star ratings versus 1-3, which are just ratings.

20 mpowell January 12, 2011 at 12:13 pm

I don't like the way they ran their study because simply doing a linear regression on the ratings is not necessarily the best way to look at it. And I prefer Alex's explanation to OK cupid's, but I'd adjust it some. Looking at those photos, I see more personality and engagement with the camera from the women with heteroscedasticity. Those photos force viewers to form a real opinion on whether they want to talk/meet/interact with the woman. With these women, the 1s correspond to viewers deciding they don't want to meet the person not that they really think the woman is ugly. The 5's think the woman is attractive and are excited to meet her. If you have a more bland photo people will judge your physical appearance more objectively giving less variance in the rankings but also will be less inclined to message you because your photo doesn't tell them much about who you are. Of course, this would also overlap with the set of women who have physical features that will bring out strong negative and positive reactions from men.

21 dirk January 12, 2011 at 12:31 pm

mpowell says "more personality and engagement with the camera" and I say "sluttier". Tomato, tomato.

22 ohwilleke January 12, 2011 at 1:13 pm

The analysis tends to assume that more messages are good, but that isn't necessarily so, although it might be. After all, most men on this website are looking for one match, not a harem.

While it could be that different results come from a diversified audience of raters and reflect someone ensconced in a niche not shared by all, another possibility is that pictures that produce mixed results do so are in some way ambiguous or lack data on a point that is important to rating men. For example, clothing or accessories can be visual homomyns that have multiple symbolic messages – is a rainbow a signal of support for bisexual gay pride, or is it an expression of childhood innocence? Is a retro outfit ironic, or a sincere indication that the person wearing it is behind the times? Consensus pictures, in contrast, may contain sufficient and consistent information.

High levels of messaging, which are after all a means of getting information, may reflect a need for additional information in order to clear up ambiguity that the general communication does not. In the same way, people are less likely to click of a link in a blog if it is accompanied by a blockquote that tells you what the link says (call it a "footnote link") than one is if it does not (a "look and see for yourself link")

23 anonymous January 12, 2011 at 1:37 pm

A man will assign himself a number. He will judge the probability that each woman would be interesed in him given his number.

Really? With most guys, it's like, "hey, half a dozen situps and I'm ready to date a supermodel…"

24 Hugh Ristik January 12, 2011 at 9:56 pm

Rather I think there are certain types of beauty that greatly attract some men but repel others.

I agree with Alex's hypothesis.

Let's speculate that people message you when you are 1+ SD above average on their population distribution of attractiveness. Then what is your goal? Your goal is NOT to maximize your average attractiveness to members of your desired population. Your goal is instead to maximize the percentage of your desired population who perceive you as above the 1+ SD cutoff on their individual attraction distribution.

Of course, if it was possible to get above 1 SD attractiveness to everyone, then you are fine. But that's hard, due to heterogeneity of preferences. Often people encounter tradeoffs, where to get above 1 SD to some people, they will have to drop below to others. Even though your desired population may agree on who is average in attractiveness to them (where people's preference vectors cross), their opinions may diverge about who is 1-2+ SD in attractiveness to them.

I am willing to bet that this polarization effect is even stronger for men than for women, based on the teachings of pickup artists (PUAs). From Brad P's Fashion Bible:

In women, sexy stereotypes are polarizing. You will get some strong positive reactions and a few strong negative reactions. Typically, a well developed sexy stereotype will turn on about 80% of women and turn off the other 20%. That goes for "normal girls" too.

Being polarizing is good because you will get an immediate strong reaction. The girl will
love you or hate you right off the approach. The reason why this is good is because you
don't need every girl to like you. It's more important to get strong attraction from some
women then to get acceptance from all women.

You will get laid more and get more dates by getting strong reactions than by getting

Sometimes it's worth sacrificing average attractiveness to increase the variance of your attractiveness.

25 andy January 12, 2011 at 11:10 pm

"some people love John Cage, other people would rather listen to nothing at all"

That was good ðŸ™‚ ROFL

26 Careless January 13, 2011 at 7:48 am

In the example photos the polarizing girl looks more ready to go. I wonder if a sluttier look creates greater polarization as well as more messages.

That was my reaction to most of the pictures as well.

27 cabbage soup diet February 26, 2011 at 12:42 am

I enjoyed this post a lot. It was certainly creative and not what I was expecting when I clicked on the title ? a title I might add, which is quite good. I know I had to find out what ways ?guaranteed? I could grow my list.

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