So I figured out recently that a certain event (call it X) is approximately 280 times more likely to happen to me than my chances of winning the lottery (assuming approximately 1 in 14 million chance). Yet my first instinct is NOT “wow, winning the lottery is really unlikely” or “wow, that is an interesting comparison between two very unlikely events,” but “wow, event X is more likely than I thought!”
I think I realize that this reaction is wrong, but it’s nothing new. I’ve never been of a mathematical bent at all.
What about y’all? How are you at concepts like this?
Why is the reaction wrong? If the lottery odds are 1 in 14 million, then the odds for event x are 280 in 14 million. which is 1 in 50 thousand.
So what did you THINK the odds are? BTW, I’m sure I could have struggled through reducing the fraction on paper, I ‘cheated’ and used a calculator. Are you suggesting this means that I don’t have a mathematical bent?
I think it is hard to grok big numbers, and that many of us are fooling ourselves when we think we do.
One time I made a mistake, getting a number wrong by a factor so big that its base ten log was more than 1e100. The vastly smaller incorrect value I reported is, itself, huge beyond comprehension. Its cube root is huge beyond comprehension. These numbers might as well be fairies in a dream, for all my mind can make of them.
I think that you misunderstand what being good at math is all about. It’s not necessary to have an intuitive feel for the probability of something or the comparative probability of two things. It’s just necessary to look up the statistics and calculate the probabilities. There are people who can quickly tell you the probabilities of various things and can quickly tell you how those things compare in probability, but those aren’t necessarily the people with the best mathematical skills. Those are people with good memories, and that has no necessary connection with mathematical ability.
There are lots of cases where people are far too much worried about things that happen quite rarely and far too little worried about things that happen quite frequently. It’s usually claimed that such people are bad at mathematical reasoning. I don’t think that that is the problem. Usually you can carefully explain to such people what the true probabilities of such things are and they will understand your reasoning, assuming that you can get them to sit down and think for a minute. The problem is getting them to sit down and think. These people aren’t stupid. The problem is that they are lousy at making nonemotional personal decisions and at making nonemotional public policy decisions. They don’t want to stop to think for even a minute about their choices. Something emotionally bothers them now and they don’t want to pause to think about it.
It’s easy to find somebody to work out the mathematical aspects of something. You might have to pay them some money for it, but it will be worth it. The real problem for people who make decisions too much based on immediate emotional reasoning and too little based on careful calculation is that they refuse to wait for any amount of time. The answer to making correct decisions is to slow down. Find an expert to figure out the technical details if that’s necessary. Just don’t rely on your immediate emotional reactions.
Well, this particular event is getting a disease that’s called “rare” in a certain way (base odds increased by another, common event - getting the flu), which is the only reason I thought of it that way. I thought that if my impression weren’t true, there’d be huge epidemics of this disease across the country/world.
Maybe I’m doing the math wrong. The baseline rate is 1/100K. Getting the flu, according to one study, increases its odds by an extra 1/100K. That seems like simple addition. So if it’s that common, why is it still called “rare”?
Could you explain this to us more carefully? What disease are you talking about? What do you mean by the baseline rate? What do you mean that its odds are increased? If you explain this carefully, we might be able to help you understand it better.
Part of the issue may be you’re comparing to events that aren’t the same.
Winning the lottery is pretty cut and dry. You buy tickets and sit back and wait. Unless you break in to the lottery office and fix every machine you have no control
But getting an illness isn’t the same. If it’s a communicable illness, like the flu, you are very much in control of increasing your chances, simply by hanging out with people who have the flu. If it’s about breaking a leg, you can easily do that to yourself to increase your odds.
Of course that wouldn’t apply to an inherited illness, but you get my point.
It’s something that actually came up around the time of that first thread, but then I found a flaw in my thinking and forgot about it. Then seeing a bus ad series (about H1N1, not GBS) brought it back to mind.
Plus, when I was a kid, I read a Reader’s Digest excerpt of a book written by a woman with GBS. It had bits so horrifying in it that it’s stuck in my mind ever since. (Example: she lost every bit of muscle during her paralysis. From what I can tell, this would never be allowed today, but this book was written something like 20(?) years ago.)
ETA: And that, incidentally, is why I didn’t even mention it in my OP.
If the odds of GBS are 1 in 100,000 among the general populace, then (if this 10x stat is correct) 10 times those odds are 10 in 100,000 (or 1/10,000), but only among those people who are ill with the flu. I looked at that Wiki page and don’t see that number anywhere. But for every million flu sufferers, that would mean 100 people develop GBS.
That does seem like a lot, and the page also notes:
Hmm. So it would be fair to say that becoming paralyzed for months is a not uncommon effect of the flu? :eek: If more people knew this, I’d think the vaccine would be a LOT more popular!
If that frightens you, don’t look up the odds for getting in a car accident or being bitten by a rabid animal. I don’t know if you could take the pressure.
I just thought it was remarkable, considering how much people know about the flu, yet how few get vaccinated against it. Why isn’t it recommended for everyone and anyone, not just the high risk groups, with that kind of odds?
(Plus, just interacting with people in an office can’t cause you to have a car accident or a rabid animal to show up. :D)
1 in ten thousand is pretty fuckin’ uncommon. Plus, I didn’t see anything on the page that says months.
Also, the cite for this 10x estimate is the paper Investigation of the temporal association of Guillain-Barré syndrome with influenza vaccine and influenza-like illness using the United Kingdom General Practice Research Database. It wasn’t a clinical study, and by the title it appears that there was no actual certainty that these patients actually had the flu. There being a “temporal relationship” is pretty far from a cause and effect relationship. It may, for example, be an indicator that someone whose immune system is vulnerable to the flu is also more vulnerable to GBS. Or perhaps there is something about the UK memdical system, or the UK population, that results in a higher number there than elsewhere.
But you said in your last post “that does seem like a lot.” Isn’t that directly contradictory to your line here?
If not, it just gets back to what I said in my OP: that I have no sense of mathematical proportion. What does 1/10,000 or 240/14 million or whatever mean? What’s it like? I have no idea. It’s just a bunch of 1’s and 0’s. I have no way to conceive of it in a way that puts it in perspective for me. It’s the same kind of thing that leads people to gamble: “how hard can it be?”
Exactly, it seems like a lot. It isn’t. And remember when you asked “why doesn’t EVERYONE get the vaccine?” Because most people won’t wind up sick to begin with. It’s like asking “why doesn’t EVERYONE get full health insurance?” Every choice you make is a gamble. Oh, and in case you’re thinking about getting the vaccine just to be on the safe side, that might not save you either.
It’s not just you. I learned this from the Bullshit! episode dealing with numbers. How many numbers can you imagine in your mind without grouping them? I can imagine five. Beyond that I have to imagine it as two sets of three, a set of four and a set of three, etc. But we’re expected to understand numbers like “1 in 1,000,000”?!
Basically, you’re fine.
There is absolutely no use worrying about the odds of each little thing happening. The only thing that’s probable is that SOMETHING bad to you will happen.
