Interlude: the math of dudes kissing

So I was having a NaNoWriMo-related discussion involving characters and perceptions of sexual orientation, and someone said ‘Unless you’ve got about fifteen characters, it’s statistically unlikely that any of them will be gay anyway’.

Statistics are funny about what’s likely and what’s not.  People have an intuitive tendency to think that if there’s a 10% chance of something happening, then it will happen exactly once out of every ten iterations.  (I see a lot of this in World of Warcraft; if a particular giant fire snake has a 10% chance to be carrying a particular fantastical treasure, some players tend to assume that either A) if they don’t have one after killing ten giant fire snakes then the percentage is obviously wrong, or B) if they get one from the first giant fire snake the probability is obviously much higher than everyone says it is.)

Statistics aren’t like that, of course – they laugh at our feeble attempts to predict the future (or the past, or the present).  I am not a masterful statistician, but I’m confident with my basics, so I drew a few Hermetic circles on the table, performed the somatic invocation according to the Vancian tomes of arcane lore and the much more user-friendly Jack Vance’s Big Book of Interplanar Summoning, and called upon mathematics to assist me.

Assume a 10% chance (P = 0.1) for any random person to be lesbian or gay.  (I have no idea if this is accurate, but it seems to be the popular statistic.  Because this is rhetorical math, I’m not calculating numbers for trans or bi or asexual people at the moment.)  That means that, ceteris paribus, there’s a 10% chance that the first character in a story will be L/G.  One we add a second character with their own 10% chance, we have a (0.1)*(0.1) = 1% chance that both characters are L/G, and a (0.1)+(0.1)-(0.1*0.1) = (0.2 – 0.01) = 19% chance that at least one of them is L/G.

Ignoring multiples at the moment, I’m interested in the probably that at least one character will be L/G, which means I can instead calculate the decreasing probability that every character will be straight.  That’s (1 – P) = (0.9), or 90% for any single character, so (0.9)^N where N is the number of characters involved.

0.9^1 = 90%

0.9^2 = 81%

0.9^3 = 72.9%

0.9^4 = 65.61%

0.9^5 = 59.049%

0.9^6 = 53.1441%

0.9^7 = 47.82969%

Interpreting ‘statistically likely’ as meaning ‘the thing that is more likely to happen than the other thing’*, then we have just passed the 50-50 threshold – with seven characters, there is only around a 48% chance that they will all be straight, and it is statistically more likely that at least one of them will be lesbian or gay.

This doesn’t control for cultures and subcultures, social institutions, shared interests, the diverse ranges of human sexualities – basically, this doesn’t control for reality, but I found it was an interesting couple minutes of calculation.  It suggests that (again, not accounting for any complexities whatsoever) we might expect at least half of all stories with at least seven characters to feature at least one QUILTBAG person.  Like the Bechdel-Wallace test, this is no way to judge how good a story is, but it might be illuminating to think about how frequently the books and math match, and why it is when they don’t.

*I probably shouldn’t try to write anything for Simple Wikipedia, because I would go entirely overboard.  ‘Null hypothesis’ = the thing that means the thing we were looking to see happen didn’t happen.  ‘Confidence interval’ = the area where it is most likely that things actually happen most of the time.  ‘Error term’ = the thing that happened where we didn’t expect something to happen and we don’t know why.

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12 comments on “Interlude: the math of dudes kissing

  1. Oh my god. There’s math … and Latin. An ablative fracking absolute. You, sir, are awesome.

    I tried to explain the reverse of this statistical thingy to someone when talking about Mythbusters: if something is one in a million and you give it a million chances to happen there’s still a 36.78% chance* that it won’t happen. You can’t just say, “I did it a million times, it should have happened once, it didn’t, thus it is disproven.”

    It suggests that (again, not accounting for any complexities whatsoever) we might expect at least half of all stories with at least seven characters to feature at least one QUILTBAG person.

    Ten percent is the figure I usually hear for LG. If that’s right then your figure is low because you’re leaving out everyone who is QUITBA. Though the B numbers might be contained in the LG numbers depending on how they are collected, in which case you’re still leaving out the Quita, of course some of them might be blg, and I must confess that I’ve forgotten what the U stands for.

    Anyway, there definitely should be more.

    * Technically much closer to 37.79% but I’m rounding down.

  2. anamardoll says:

    Will, this is just so wonderful. I can’t speak to the maths (I was dreadful at probability in school), but this has been bookmarked forever, thank you.

    One thing I’m having trouble with as a new author is that when I write someone “atypical” (as far as literary tropes go), I’m finding it hard to point out that they are atypical without being all HAVE I MENTIONED TODAY I AM GAY.

    I finished my novel and realized that one of my characters was a lesbian and another was asexual, but I didn’t explicitly call it out in text, which made me worry that it didn’t “count” somehow. (“Count” in what way, I do not know. My brain is weird.) And yet, their sexuality wasn’t core to the story, so I don’t know what to do. If I leave it un-explicitly stated, most readers won’t pick up on it, and leaving the characters silent on the issue doesn’t seem right. It’s a pickle.

    Another of my characters is fat, which has its own problems. Most of our culture’s words for “fat” are considered very ugly, unpleasant words and I’m torn between “no, she’s fat and it’s fine” and “dear god, please don’t let me accidentally trigger someone”.

    I don’t know the answer, but I’m glad that I’m not the only author thinking about these things. Thank you for this. :)

  3. Gelliebean says:

    I am having a hard time explaining why in words, but I really really like this…. Statistics like “One in ten people do X” encourage the thought that for every ten people you line up, one does X, in a consistent pattern, boom boom X boom boom X.

    It’s nice to see it laid out, with care, that “chance of” and “probability” are not actually interchangeable. With every flip of a coin, there is a 50% chance of heads, and a 50% chance of tails…. But for every flip in a row that comes up heads, the probability of the next being tails increases. Or at least, that’s what I think I remember from my statistics class…. :-p

  4. Will Wildman says:

    It depends on when you do the calculation relative to the flipping – the chance of getting seven heads in a row is (0.5)^7, so 1 in 128, but if you get six heads in a row, the chance of the next one being heads is still 50-50, because the probabilities are independent and P(b|a) = P(b) oh look I’ve gone crosseyed.

    Or there is my favourite commercial ever, in which two insurance guys are watching improbable things happening and giving the probabilities of each progressively more improbable thing, and then someone rides past on an ostrich. “What are the chances of that?” “Well, 100%, now.” Because P(x|x) = 1, always! MY BRAIN.

  5. anamardoll says:

    This is why the superstition that “dice have memory” is fallacious, yes?

    Like the D&D player in Darths & Droids that “pre-rolls” his dice? He rolls 100 dice, picks out the 1s (crit fail), and then rolls those again, and picks out THOSE 1s, and then carries them in special cases to games to pull out when he *REALLY* doesn’t want to crit-fail. Because the odds of the die rolling 1 THREE TIMES IN A ROW is astronomical!!

    Only it’s not, because the odds are still what they always would have been for that however-many-sided die to come up 1. Statistics hurt my head.

  6. People fail to understand randomness, independence and … and I’m sure I was going to say something else. Conditional probability maybe.

    That last one is what really blows everyone’s mind. Why is it always a good idea to switch doors when they show you which one of the other doors doesn’t contain a prize. People’s minds break down, even if you walk them through every possible case they’re left in a state of, “No, it can’t be.”

    Of course, that’s why we have entire branches of mathematics dealing with probability. If everything worked out the way you expected it to, there would be no need for them. You’d intuit the right stuff on your own.

  7. Will Wildman says:

    The door thing irritated me for years, but as usual wikipedia has soothing explanations.

    For those unfamiliar with the Monty Hall problem, you say you’re on a game show or something and have to pick one of three doors (A, B, C) that has a prize. So assuming it’s fair, you have a 1/3 chance of getting the right door. But then before the door you picked (say A) gets opened, the host opens one of the other two doors that does not have a prize behind it. Now there’s one open door (B), one closed door that you picked (A), and one closed door that you didn’t pick (C), and you are given the choice to stick with your current door (A) or switch to the other unopened one (C). The math says that you had a 1/3 chance of getting the right door the first time, but now that wrong door B has been opened, there are only two doors, there’s a 1/2 chance of the remaining door having the prize, and therefore your chances are better. Instead of choosing between A, B, and C, you’re now just choosing between A and C and your chances of winning go up if you change from A to C.

    What bothered me about this is that it seems to treat your initial choice as having altered the door, Heisenberg-style. If we threw that out, then in round one you would choose between A, B, and C (1/3 each) and in round two you would choose between A and C (1/2 each). Why should door A keep its 1/3 chance if door C is getting recalculated based on information about C? But we can imagine it backwards – say that after choosing door A, you had the option of switching to both of B and C, but no doors were opened. We know that only one door has a prize, so at minimum one of B or C is wrong, but there’s still a 2/3 chance that one of them is right. Obviously between choosing A or B+C, the latter is the better choice – opening wrong door B just distracts us from that, even though it’s logically obvious that if we got to pick two doors, one would always be wrong.

    I categorise this in the same part of science as orbital velocities, also known as ‘travelling so fast that you try to fall to the ground and you miss‘. It’s like we’re hacking the programming of the universe. Any sufficiently advanced science is indistinguishable from cheat codes.

  8. Will Wildman says:

    I loved Pete’s pre-rolled dice on Darths & Droids. Also his one-shot die in the latest episodes, which is haphazardly cut but has all twenty values assigned to sides by random dice rolls, thus making it acceptably random for a single dramatic use.

  9. Something that only now occurs to me about the Monty Hall problem is that people do assume that picking the door changed the odds. That’s what messes them up. They assume that picking door A made it more likely to be a winner. They just don’t realize that’s what they’re doing.

    After all, you picked door A, which had a one third chance of winning, you’re told something that doesn’t give you any more information about door A at all, yet now you think it has a 1/2 chance of winning. Where did the extra 1/6th come from? What stunning magic could accomplish such a task?

    People almost universally assume that by picking door A, door A’s probability changes.

    Maybe that would be a better direction for explanation: choosing a door does not magically make it more likely to win. Instead of trying to explain conditional probability to someone, ask them to explain to you how door A suddenly became more likely.

  10. Brin says:

    Ana: Because the odds of the die rolling 1 THREE TIMES IN A ROW is astronomical!!

    Shouldn’t it go the other way ’round? Take the ones that roll 20s several times in a row, since that might be because they’re made wrong in such a way that they favour 20s?

  11. It should be the other way around. You’re right.

    The only way that knowing what it came up in the past would give you information on what it might come up in the future is if the die is less than fair, and in that case it’s more likely to come up as the thing it’s already come up as a bunch of times than the thing it’s come up as less often.

  12. Will Wildman says:

    I finished my novel and realized that one of my characters was a lesbian and another was asexual, but I didn’t explicitly call it out in text, which made me worry that it didn’t “count” somehow. (“Count” in what way, I do not know. My brain is weird.) And yet, their sexuality wasn’t core to the story, so I don’t know what to do. If I leave it un-explicitly stated, most readers won’t pick up on it, and leaving the characters silent on the issue doesn’t seem right. It’s a pickle.

    I meant to reply to this bit too – hope you’re still checking this thread dutifully, Ana! – but I’ve been puzzling over the same thing with a secondary character in my NaNo novel. He’s single and he’s not coupling up with anyone in this book (he might have better luck in the sequel, if he gets promoted to main character), but if I don’t say anything then I expect readers will assume he’s straight. I’m thinking that he and the youngest female character are good friends, so while they’re hanging out from time to time it might come up in normal conversation (“Oh, yes, I feel so sorry for you being pressured by the queen to spend more time in public with your hot boyfriend. I can’t get the baker’s apprentice to look at me twice and I’m starting to think he has a thing for that new blacksmith”). I’m still worried that it will be clunky, but those thoughts get put in a box until the January Editing Festival commences.

    I don’t think you’re just being odd about things ‘counting’, though – the absence of QUILTBAG characters is a legitimate problem, and if readers aren’t picking up on them where they do exist, then no progress is made toward normalising the presence of QUILTBAG people in fantasy. Given statistics, most people are probably always going to assume that characters are straight until told otherwise, but at the absolute minimum we should be able to get to the point where “No, she’s lesbian” is not at all jarring or surprising, but merely an “Ah, okay”.

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