The title should be "Why are the people who love endurance sports rich?"
There's no evidence presented that a majority or even a significant percentage of people who are rich love endurance sports, only that most of the people who love endurance sports are rich. Is there a name for this sort of statistical error? Because it's everywhere.
Let's pretend there's 10,000,000 "rich people" and 100,000 "people who love endurance sports". Easily 100% of the people who love endurance sports could be rich while it's still an insignificant percentage of rich people as a whole.
I'm going to guess that the majority of people who are competitive at any hobby are pretty well off, simply because people who are poor do not have the time or resources to practice enough to become competitive at leisure activities.
Media carries with it a credibility that is totally undeserved. You have all experienced this, in what I call the Murray Gell-Mann Amnesia effect. (I refer to it by this name because I once discussed it with Murray Gell-Mann, and by dropping a famous name I imply greater importance to myself, and to the effect, than it would otherwise have.)
Briefly stated, the Gell-Mann Amnesia effect is as follows. You open the newspaper to an article on some subject you know well. In Murray’s case, physics. In mine, show business. You read the article and see the journalist has absolutely no understanding of either the facts or the issues. Often, the article is so wrong it actually presents the story backward—reversing cause and effect. I call these the “wet streets cause rain” stories. Paper’s full of them.
In any case, you read with exasperation or amusement the multiple errors in a story, and then turn the page to national or international affairs, and read as if the rest of the newspaper was somehow more accurate about Palestine than the baloney you just read. You turn the page, and forget what you know.
I remember when I started noticing that the occasional time a newspaper wrote about something I knew something about, they usually got some vital details wrong, that really undermined my trust in that newspaper. I've got a better newspaper now, but that first one is generally regarded as a pretty decent one. But when they always get the details about stuff I know wrong, how well can I trust the articles about things I don't know?
Of course it's also possible I only remember the times they get it wrong, and I don't notice the many times they get it right when writing about something I know something about, leading me to underestimate the paper's accuracy.
I'm sure somebody somewhere is willing to make up a name for that effect too.
Perhaps Gell-Mann moved from a paper that was bad at writing about physics but good at writing about Palestine, to a paper that was good at writing about physics but bad at writing about Palestine. This kind of transition seems like it might help maintain a filter bubble.
This is certainly a risk, but unfortunately we can extend the argument to suggest that you can't ever trust any source. Say Gell-Mann wants to find a paper he can trust on Palestine. He's good at physics, and checks reporters covering both topics.
A reporter might be good or bad at covering each topic, which leaves us four cases to consider. If they're bad at physics, they could be a specialist in Palestine, but they could also be generally incompetent; Gell-Mann has no way to tell. If they're good at physics, they could just be talented reporters, but they could also be physics specialists who don't know Palestine any better than Gell-Mann does. And once again, he has no way to tell.
Even probabilistically, we could argue for either approach. Most people aren't experts in more than one thing, and it's easier for an expert than a random fool to garner attention for a baseless claim, so perhaps we should especially distrust good physics writers on Palestine. But incompetence is broadly correlated, and journalism skills apply to both topics, so perhaps we should view bad physics writing as a sign of weak fundamentals and distrust it everywhere.
(I'm talking about reporters instead of papers, but we can push the argument back a level easily; editors have to hire reporters for fields they don't know.)
Going alone, all I can see to do is to look for people who claim to specialize in a few things, one of which you know well, and trust them on their other specialties. As a society, we can perhaps do better by asking a bunch of experts who's competent in their domain and looking for alignment - provided we can all correctly agree on some experts in advance.
edit: a bit of searching suggests this is basically Berkson's Paradox. If we (boldly) assume that news sources which are bad on all topics don't circulate, then quality in one area lowers the expectation of quality in other areas.
Although there is another interpretation (especially in traditional newspapers): you aren’t just evaluating the the individual journalist, you’re evaluating the editorial staff. They are responsible for finding a physics expert to write about physics and a Palestine expert to write about Palestine.
If they do a poor job of selecting a physics expert, then it seems likely that they will do a poor job of selecting other kinds of experts as well.
Hm, lots of options going - negativity bias (bad stuff is more memorable), conservatism bias (low-frequency events are overestimated), availability heuristic (memorable events like misrepresentations are overstated).
Honestly though, I'm not sure I'd call it a bias in your observation so much as a sensible assessment of sources. A source that's right about 90% of topics is still misleading you quite often. And even worse, a source that's 90% accurate about each topic can leave you almost totally ignorant; there are a lot of stories where the entire message can be destroyed by any one of numerous errors.
(And of course, there's a pithy name for that too. "O-ring theory", after the Challenger shuttle disaster, describes phenomena where everything has to go right, so the failure chance at each step is multiplicative.)
I think that's just confirmation bias working in tandem with the amnesia effect described, but certainly it is a valid point. To me, the hardest part about this problem is that trust tends to be stored (at least in my brain) as a binary yes or no, though possibly with a fuzzy border and some room in the middle. It's tough for me to read something and internally modify my trust of the source by a proportional amount for getting things "right" that I "know" when even what I know is uncertain because I could be wrong.
The end effect is that I tend to double check just about any source, but I still have a handful of sources that I have strong reason to believe their motives are compromised on various topics where I expect their motive to conflict with the motive to tell the truth. It's still not great though because sources rarely move up in this system and frequently move down, which leads in a general inability to find information considered trustworthy. This works fine on things where there is a general consensus because I'll be able to find a varied set of sources saying the same thing, but not so great on hotly debated topics with lots of nuance. Also sometimes my brain is lazy and I don't do any of this processing because I'm an imperfect human.
Confusion of the inverse is the assumption that the probability of A given B is equal to the probability of B given A. In symbols, the fallacy is falsely assuming P(A|B) = P(B|A). You have to use Bayes' Theorem to convert from a conditional probability to its inverse:
It happens often when people have a limited consideration set of possible causes, often due to a natural degree of ignorance or lack of experience relating to the subject matter area, e.g., a small child sees a wet sidewalk and assumes it rained, because they aren't yet aware of sprinklers (or garden hoses, etc.)
Thank you! I knew it had to do with Bayes' theorem. So much confusion in the world seems to come from the fact that people don't understand conditional probability.
My favorite professor used to describe this statistical error as a major cause behind racism.
E.g. it may be true that most criminals in an area are of a certain race; that says nothing about the probability of a single person of that race being a criminal. Same with Islamaphobia–even if most acts of terrorism were performed by Muslims (which isn’t even true!), that’d say nothing about the likelihood that a randomly chosen Muslim person you meet is a terrorist.
I am interested in the stats error here. If there are 100 balls in a bag, 10 of each rainbow color and 30 blank, and I tell you 3 of the green balls have property X, while 10 total of the balls in the bag have property X.
You blindly draw a ball from the bag; do you know anything about the likelihood of that ball having property X? You now inspect it and find it’s green. Do you now know anything different about that likelihood? If I offered you “pay $100 to win $900 if you drew a property X ball, with the option to double your wager after seeing the color”, you would be happy indeed to see that you’d drawn a green ball and would double your wager.
Regardless of the colors, ratios, and desirability of property X, it seems to me like you do know something new about the likelihood after learning the color.
It also seems to hold if there are 300 million balls, 10 balls with property X, and 3 of those are green, just at a strong cause to believe “this specific ball does not have property X” overall (such as the case in the people examples you gave).
I'm sure there is a better term for it, but its a kind of unwarranted generalization, with respect to population sizes, e.g.:
- Nearly all murderers are men.
- Bob is a man.
- Therefore Bob is probably a murderer.
There's obviously a problem there. The population of murderers is an infinitesimal fraction of the male population. While you can say its more likely that any given male is a murderer, than any given female, its not really useful for making judgements about individuals.
Sure, but that's just a logic error. If you switch it around so we know that Bob is a murderer, then we can say that he's probably a man (and that's actually right).
The related mistake here is to jump from "not really useful for making judgements about individuals" to "not useful for making judgements about averages". Sometimes you are trying to predict about an individual. Sometimes you are trying to predict a population average.
Sticking with medical examples, the first matters for "does this guy have this disease?" The second matters for "how many doses should we order?"
Or, more controversially, "how many of the doctors we train today will still be working in 30 years?" Which came up as a question regarding the increasing proportion of women in medical school. And many people were loudly offended that this might be something to take into consideration. Because they read it as the first kind of question, "will this individual...". But that's different.
That error can creep in to diagnostics though. You can be at a 5 times increased risk for a very rare disease and it’s still overwhelmingly unlikely you have the disease.
Sometimes testing positive on a fairly accurate test for a very rare condition means you are still more likely to not have the condition, and even Doctors sometimes screw that logic up.
No, that's the first error. The usual base rate problem. I agree that it's a common mistake, but it's not the one I was trying to point out.
Knowing that this very rare disease affects 1 in 10_000 men, and 1 in 100_000 women, doesn't tell you that much about how to perform diagnosis on any one individual. But it does tell you accurately that the male ward probably needs 10x as many beds as the female ward.
No. Not what I was saying ... in my example the male ward needs no more beds than the female ward because the disease is ridiculously rare. I think we are inadvertently talking past each other.
Statistics are hard. At least for me.
Edit: also I wasn’t trying to respond directly/refute your comment. Just chiming in with a related concept.
OK maybe the beds is a bad example (maybe most of their occupants would be under observation... or there would be less than 1 per hospital). Let's say it's 90% fatal, and an outbreak occurs in a country where men are always buried in black coffins, and women in white.
Then we know what mix of coffins to load on the UN plane. But as a doctor on the ground, after your 99% accurate test comes back, you certainly need more information, and knowing the sex of the patient is not much help. The doctor, and the guy loading the plane, are asking very different questions.
Yeah it certainly still tells you something, but most people's intuitions about probability mislead them about the amount of information contained. Its like how people can be lead to believe they have a very rare disease if they test positive for it. Just because most people who have the disease test positive for it doesn't mean you can just ignore the prior probability that the disease is extremely rare in the first place, so you still likely don't have it. https://en.wikipedia.org/wiki/Base_rate_fallacy
>Regardless of the colors, ratios, and desirability of property X, it seems to me like you do know something new about the likelihood after learning the color.
Only if you're given the marginal probability ahead of time ;-). Marginals are usually intractable to compute, and people tend to vastly underestimate them. Priors have a similar issue: base rates for a lot of "interesting" conclusions are often really, really low (which is, in a way, why we'd be interested in estimating the posterior!).
Let's estimate the most controversial thing possible: P(criminal | black guy) = p(black guy | criminal) * p(criminal) / p(black guy).
Problem is, the prior (in all the cases I've checked) is lot smaller than the marginal (there's usually at least two orders of magnitude difference!), so even a seemingly high likelihood "washes out" in the posterior.
In your examples, the probability of a random green ball having property X is always higher than that of a random ball. If the incidence of X in the green population is higher than the base rate, then if a random ball is green, it means it is more likely to be X.
I think you meant probability instead of likelihood. That is: it may be true that most criminals in an area are of a certain race; that says nothing about the probability of a single person of that race being a criminal because you'd need to know about the prevalence of crime.
(In statistics, the likelihood is the probability of the data conditional on the hypothesis, so in this case the probability of being of a certain race given that one is a criminal.)
Let's say we have a group of 1000 animals:
900 rabbits and 100 foxes.
We also know that there are about 10 crimes happening every year and for every crime there's 50% chance of it being committed by a fox.
Then according to Bayes' formula:
P(fox is a criminal) = P(criminal is a fox) * P(animal is a criminal) / P(animal is a fox) = 0.5 * 0.01/0.1 = 0.05 = 5% chance for every given fox to be a criminal.
For every given rabbit the same formula gives 0.5 * 0.01/0.9 which is roughly 0.6%.
Sure, but if you're looking for kangaroos because of an incorrect belief that they're mostly responsible for something, and it's actually perpetrated more by mountain lions, you might actually be on the wrong continent.
Incels have killed more people than Islamic extremists in the US in the last decade.
Re the systematic racist bias in 4. - since you postulate a world in which 100% of terrorists are muslims, why would anyone non-muslim ever be investigated for terrorism? (whether with 'gusto' or not)
Because point 4 is about non-terrorist charges. Pretty much what we find with the black population being biased with charges of drug possession. If searches are applied to blacks 10x as often relative to whites, then if neither is more likely to possess marijuana you'll come up with statistics which say 10x as many blacks illegally possess marijuana than whites. When instead one needs to say what percentage of those searched are in possession
No, point 4 was about the fact that somehow it is racist to prosecute people of type X for crimes they commit if those crimes are discovered because of an investigation into a different type of crime (which only type X people commit) - the alternative being to give them a free pass, I assume? The premise doesn't hold water anyway, since even in this hypothetical world where only type X are terrorists, I assume terrorism is still a rare event? So, the extra crimes discovered in the course of terrorism investigations into type X suspects will be dwarfed by the investigations into normal crimes in the whole population during the course of normal every day police work.
// Assuming the police are not incompetent, of course, which may not hold in your hypothetical world where they investigate non type X people for terrorism even though they commit zero percent of terrorist attacks - probably out of some misguided diversity quota or affirmative action policy, I assume? ;)
> it may be true that most criminals in an area are of a certain race; that says nothing about the likelihood of a single person of that race being a criminal
Huh? If 10% of purple people in an area have been incarcerated, and you select one individual from the purple people population of that area at random, the odds are 10% the individual you selected will have been incarcerated. That's fundamental to how sampling works.
The situation isn’t that 10% of purple have been incarcerated; if it was, you’d be correct.
Instead, the situation is that 90% of those incarcerated are purple. You can’t draw any meaningful conclusions from that without knowing the number that you were referring to: what percentage of purple people that makes up.
You are flipping around the percentages. Parent says "10% of incarcerated people are purple". This does not imply that "10% of purple people are incarcerated".
That's funny, because the URL slug (why-are-most-endurance-athletes-rich) for the article literally is that headline. I think the authors probably intentionally chose that headline because it's more clickbaity. Given the less clickbaity title is in the URL, mods, how about updating the headline to "Why Are Most Endurance Athletes Rich"?
Authors generally don't choose the final headline for online articles. It's the editor who does that. Sites can show multiple headlines for the same article and settle for the one that gets most clicks. The url of the article can sometimes reveal the original headline authors gave.
It's basic modern media literacy to ignore the headline of the article.
Endurance sports, by its very definition, implies the availability of time. You can't be an Ironman competitor if you don't have hours to train every day.
David Goggins and Scott Jurek were definitly not rich when then won their first important ultras. And according to their bio (didn't fact check it though), they trained AND had a job, which means either waking up very early, or going to bed very late.
I'd rather think that if you can run a 100K, you have the mind to overcome amazingly hard situations, and to keep trying, again and again, being in the game for a long time. Which increases your odds of success, so bigger probability to get rich in the end.
I'd agree with this, but I don't even think it has to be that extreme. An endurance sport requires patience and overcoming a certain level of discomfort in pursuit of a goal.
I know people who stop pursuing whatever it is they want at the first signs of discomfort or adversity. They want the good things to just happen them, and they rarely do.
That's funny, I know people who pursue the path of least resistance and are quite well off actually, and good things do just happen to them (by virtue of their talent lets say, or other innate qualities). But that's just my own anecdata.
I do know some people like what you're talking about too, but then again I know some people who are big into endurance sports but aren't really go-getters in other spheres either ...
> I know some people who are big into endurance sports but aren't really go-getters in other spheres
Same. Although I suspect for a lot of them it's because go-getting in other spheres would impact on their ability to do the running and they're happy in their situations as they are.
Many, many years ago, I ran a fifty-miler. I was not, by US standards anything like rich, in fact I was in between two ill-paid jobs.
My running commitment amounted to something less than ten hours per week. Now according to Wikipedia, the American average for TV watching in 2017 was about 28 hours/week. I have no idea what it was in 1982, but at even half the rate, I spent less time running than my average fellow citizen spent in front of the tube.
>I spent less time running than my average fellow citizen spent in front of the tube
Time watching TV is not time spent sitting "in front of the tube". People cook, eat, clean the dishes, iron clothes, play with their kids, while the TV is on. If you are running, you can't be doing anything else.
Yes and no. People can cook, etc. while the TV is on. They certainly get in some time just plain watching.
Also, some of my running time amounted to commuting: knock 45 minutes off the 90 minute run. Running can be a social activity. Those who care to can run listening to their iPods (then, Walkmans). Etc.
Now imagine coming home from a day of hard physical labor on a roadwork crew when it's hot as hadeys outside and then consider how much you may feel like spending your free time running.
Not being rich isn't the same thing as being poor, or being blue collar. Most of us being knowledge workers, have advantages beyond earning power.
I don't know if its true that the median wealthy person has more leisure time available to them.
> According to the Census Bureau, the average wealthy household (defined by the IRS as the top 20% of income earners in the US) worked five times as many hours as the average poor household. The cause? Single-parent households and high unemployment among poor households. [0]
Although I imagine they may spend less time doing household chores or running errands
Counting work hours by household seems a bit weird.
I'm married, my wife and I work fairly typical 40-45 hour weeks. So, 80-90 for the household.
My son is single. He works the same 40-45 hours. But, by the metric above, my household works twice as much. Sure, we literally do, but we have twice the manpower and twice the income. And still have the same amount of leisure time per person.
In a sibling comment, somebody linked to an article [0] that describes the wealth/free-time paradox. Basically, poor people are extremely underemployed (particularly young white males) and frequently stuck in part-time jobs (or unemployed completely). If a poor person is only able to find 10 hours/week employment, I'm at 4x that. If the poor person is single, my household is 8x because there's two of us.
This.In ancient times rich people were pale and that suggested they didn't have to work. Poor people had tan. It's the same now - If you've got time you can train and have photos of you running marathons in different places in the world each month.
First, the article doesn't appear to talking about actual rich people (billionaires, etc) but upper-middle-class white-collar people (i.e., they still have a day job and can't live off savings & interest). But, we can call them rich to keep it easy.
In a literal sense, rich people have more time, as they tend to live longer than poor people.
In the sense of day-to-day free time, I'd argue rich people have more. Both in absolute terms - they rarely have to work two jobs, though they might do occasional OT. And in their ability to time-shift work obligations. Take a software dev - typically they have flexible work hours, might have some ability to schedule their own meetings, and nobody blinks if they duck out early once a week for a long run/ride/whatever.
I'd say they have the same amount of time, the difference is how they choose to use it. Going away for a weekend is great use of their time if they enjoy it and also get a benefit (both physically and mentally) out of it. Doing the sport is valuable to them.
Isn't that debatable? Actually, it's debatable what your statement means. What's value? How much you make per time unit? Or, if you live pay check to pay check, maybe time is more valuable than when you're rich, because if you don't invest that time unit, you won't be able to pay rent?
This article for me seemed to miss the obvious point of endurance sport as status display. This also highlights the limit of the research methodology, because very few people will acknowledge that they participate in these events to display evolutionary fitness, or are even aware of this compulsion. So what you may have in these results is some confounding of drivers: people more inclined to display status want both to earn more money, and look fitter to display evolutionary status. The phenomenon described in the article could be correlation not causation, and I’m a little surprised this was not investigated.
If being rich is simply a requirement to participate in the activity, but most people rich people don't engage in it then it really doesn't tell you anything about "rich people" as a group. If 99% of rich people don't participate in endurance sports, then it is not a characteristic of rich people in any meaningful sense.
You might as well ask "Why do rich people love helicopter skiing?" I'm sure everyone that does that is pretty rich, but probably most rich people don't do it. I'm sure there's a ton of not-rich people who would also enjoy it, but they simply can't afford to do it.
>If 99% of rich people don't participate in endurance sports, then it is not a characteristic of rich people in any meaningful sense.
That doesn't follow. If 1% of rich people do X, and only 0.0001% of non-rich do it, then X is very much a trait of rich people. It's not of most/all rich people, but it is predominantly of rich people.
Personally, I wouldn't consider anything that only applies to a tiny percentage of a group to be a trait of that group. You could say that being rich is a trait of people who participate in endurance sports, but not vice versa.
It reminds me of a funny argument I had a while back. My then girlfriend old apartment had cast iron plumbing and a joint in one of the pipe had a very small leak that smelled pretty bad. One night, at a family gathering of her, someone said that "it leaks because it smells"; which made me laugh obviously. I thought it was a slip of the tongue and said "yeah, it smells 'cause it leaks" and they started arguing that "it means the same thing"... To this day, I still can't understand how someone can believe that "it smells because it leaks" means the same thing as "it leaks because it smells".
Generally you're using language "correctly" when the vast majority of people understand what you were trying to communicate.
In that way and in that context it's a "passable" statement.
Don't view everyday life and sentences through the narrow lens of mathematics/logic. If you're lucky that'll make for some dinner conversation, if you're unlucky you'll just be annoying.
"I know this must be leaking because it smells." is fine in an everyday context, even if not strictly and always true.
It wasn't meant in the sense of "I know it leaks because of the smell", it was literally said as "The leakage is caused by the smell". The conversation was in French so I have to translate here :D. I wasn't trying to be an ass at the time, I was just... surprised at their twisted understanding of basic logic.
I am terrible at formal statistics so maybe I’m wrong, but I think you are taking issue with the wording of the headline rather than a statistical fallacy.
If I wrote “why are wealthy people over represented in endurance sports” would you be ok with it?
If say ... 1% of the population is wealthy but 20% of participants in marathons are ... that would be potentially of statistical interest, no?
Also, people in sedentary (white collar) jobs have more need of exercise. If you work on the land all day, maybe you prefer to sit down after work, instead of getting more exercise.
Although farmers do seem to be overrepresented in marathon skating.
I think the title is fine as is. I know plenty of rich people, and I know plenty of people into endurance sports.
The % of rich people who enjoy endurance sports tends to be pretty high. The % of people in endurance sports that are rich tends to be pretty low, triathletes excluded because triathlons are #$#@$ expensive and so that population is cash-gated.
Agreed. And they don't even consider the other angle, which is do rich people love endurance sports more than other sports? That is, of the rich people who participate in sports, how many are in endurance sports versus those in other sports?
True. I used to race cars. The same logic applies there - you have to have money and free weekends to race cars. Even better if you have flexible work hours so you can practice on Fridays (before weekend events) and fix the car in the evenings (because they break, wear out, and get crashed).
> Is there a name for this sort of statistical error? Because it's everywhere.
Yes. It's called not understanding Bayes' theorem. Bayes' theorem is precisely about how the probability of "B, given A" (P[B|A]) relates to the probability of "A, given B" (P[A|B]). In our case, that would be "rich, given love for endurance sports" =/= "love for endurance sports, given rich". It is immediately obvious from Bayes' equation that the two are, in general, not the same.
There's no evidence presented that a majority or even a significant percentage of people who are rich love endurance sports, only that most of the people who love endurance sports are rich. Is there a name for this sort of statistical error? Because it's everywhere.
Let's pretend there's 10,000,000 "rich people" and 100,000 "people who love endurance sports". Easily 100% of the people who love endurance sports could be rich while it's still an insignificant percentage of rich people as a whole.
I'm going to guess that the majority of people who are competitive at any hobby are pretty well off, simply because people who are poor do not have the time or resources to practice enough to become competitive at leisure activities.