I am a statistician and I buy lottery tickets
simplexify.net
simplexify.net
https://plus.google.com/107814003053721091970/posts/6sPpxMo6...
Some choice quotes from his Google+ post: "The lottery is not a tax on people who are bad at math. It's trading a little bit of expected-value for a lot of variance."
"There are many other cases in real life where mean/variance tradeoffs arise, and there are perfectly plausible objective functions under which it makes sense to follow a policy that doesn't maximize expected value.
The obvious example is insurance, where you pay a small bit of money each year to reduce the chance that you end up suddenly needing to pay a lot of money. Same with forming or joining a startup; on average you'll make less money than if you take a "normal" job, but there's some small chance that you'll have just joined the next Apple or Google and you'll end up rich.... "
Getting into an accident is far more likely. And everyone has health issues sooner or later, so the probability of that is 1.
But I can't see how that could be: I've seen lottery winners, and on average they don't look toasted at all!
True, but I didn't say anything about the constants involved, just the shape of the problem.
> And everyone has health issues sooner or later, so the probability of that is 1.
That may be, but health insurance premiums only cover a certain window of time, during which you may or may not have health issues.
http://www.wjh.harvard.edu/~dtg/DUNN%20GILBERT%20&%20WIL... (page 6 for remarks on insurance)
Obviously, certain kinds of disaster pose a greater threat to happiness than others. For example, health insurance may be a worthwhile investment for some, while property insurance may not.
I disagree. If he's using "average" in the sense of "mean" (not median), then he's saying that starting a startup has a lower expected return and is higher risk than working a normal job, meaning it's inferior in both regards (assuming diminishing marginal utility). Entrepreneurship is a classic "high risk, high return" venture. It has a higher expected return than a conventional job; that's what makes it financially attractive to founders and VCs in the first place. The astronomical success of the minority offsets the lack of success of the majority.
In a similar vein I disagree with his assertion that joining a startup (taking a risk) is like buying insurance (avoiding a risk). They are opposites.
In the exact same sense than a lottery has a "higher expected return that a conventional job", just with slightly better odds.
>The astronomical success of the minority offsets the lack of success of the majority.
That doesn't make sense. Except in the light of something lke the Dunning-Krueger effect, where most people involved in startups expect they will be that "minority".
A lottery has negative expected return, so I disagree that it's "higher expected return that a conventional job".
Well, doesn't a startup also have the same "negative expected return"? Or, actually, much worse?
(Considering that the majority of them fail and the money you could make just working for some company in the same time).
If anything, starting a startup is an investment.
My argument is founded not on experimental data but rather on the axioms of utility theory. If startups had higher risk AND lower expected payoff, it would make no financial sense to found or invest in one, since that would be a textbook example of a bad investment:
http://en.wikipedia.org/wiki/Security_market_line
Yet there are lots of (otherwise) smart/rational people founding and investing in startups.
Looking at all of the people who applied to YCombinator and seeing how many of them have successful businesses a couple of years later would be fascinating.
Professional investors (VCs, Angels, Incubators) choose the best startups (most efficient choices) and do not fund the rest which eliminates a huge number of founders who simply fail and get zero return for their work. On top of that, there are a number of VCs and angels who are completely unsuccessful picking startups and end up out of the business unable to raise additional institutional money or who lose their additional investment capital.
The expected return of investing in startups is very likely negative if you add all the smart and non-smart investors together. (I don't have data, and can't even imagine where to get it, so I'm saying "likely".)
Using the security market line to prove your point isn’t really fair since not much research has been done on applying it to startups. One of the major issues with applying the SML is the fact that it is very hard to calculate beta of startup investments since they have very long term time horizons. SML has more to do with portfolio construction and how you can get a portfolio which doesn’t deviate from the benchmark too far while still producing Alpha. (Alpha is active return). The Tryenor ratio is more about making sure public equity managers are not doing really crazy stuff.
Overall my point is that there is no evidence that suggests the expected return from investing is startups in net positive. Whether founding or working for a startup produces positive expected returns or not is also very hard to know, but I would estimate that working for early stage startups for lower than market pay has a negative expected value even after considering the possibility of huge exits (a lot of companies fail that you have never heard of).
Where I think startups have a much higher expected return comes with the experience and growing up you can do while working in a small company. When you calculate total earnings over a lifetime for people who join even failed startups early on, I would not be surprised if they made more and had more enjoyable lives, even if they ended up at big stable companies later. When you add the possibility of a big exit to the higher future earnings I think the expected value goes net positive.
And most of that money doesn't actually go to the founders - YC owns a chunk of them, and so do other investors (as PG says, 94% of them get funding from elsewhere too).
Interesting stats though, thanks!
Sure, for the ones investing capital. For the workers, I can't imagine startup's mean pay being anywhere near as high as a "normal" job. A mean will cut out the Zuckerbergs, Serg, Brin, etc. Also, remember you can't compare mean startup salary to mean "normal" job salary since the bulk of startups are in the valley. To get a closer estimate you'd need to give the same weight to "normal" jobs in a given area as number of starups they have there (e.g. lots in SV, some in NYC, etc.).
If you want high variance, wouldn't you then want to make high-risk investments in the stock market? I'm not very knowledgeable on the subject, but my understanding is that the expected value rises with increased variance on the stock market, rather than decreasing.
"So why do I still buy lottery tickets? <b>Definitely not for the expected monetary return on investment.</b> I think of it as a discretionary entertainment spend. I get literally hours of enjoyment from fantasizing what I’d do if I won."
funny, thats exactly what i do too!
It's entirely out of the realm of probability, although just slightly within that of possibility.
The realms of probability and possibility are the same.
Incidentally, it's amusing to note that $100 bills are actually more valuable than gold relative to their weight. The obvious next question would be, what's an even denser store of value. For one amusing example, Cristiano Ronaldo has a transfer value in excess of $130 million by last valuation, and weighs less than 200 pounds, making him more than ten times as valuable as $100 bills per unit weight, let alone gold. Judging from the transfer market, it would seem that many top-flight athletes are literally worth their weight in gold.
Interestingly, high-denomination casino chips, some professional players don't cash them out since it's much easier to transport them to their place of staying.
Suppose you have $100,000, and repeatedly bet .001% of your net worth on a single ticket in the lottery at 100,000,000:1 with a 2x EV (disregarding that you can’t bet more or less than the price of a ticket). You do it 2,000,000 times, and then you hit the jackpot – pretty lucky since the odds are 100,000,000 to 1, right? But by the time you hit the jackpot, your bankroll has been so depleted that winning 200m x your bet, you only get back to 41% of your original net worth – because you overbet!
A longer discussion (by me) of why only millionaires should play Powerball - http://blog.streeteye.com/blog/2011/11/why-only-millionaires...
For example, our fast brain does not really understand probability. It only knows three categories: either something is impossible, it is possible, or it is a certainty. A lot of human behaviour with regards to probability can be explained by this simple assumption.
Why do people buy lottery tickets? For their intuition, it moves an impossibility into a possibility. The fast brain system that fuels their intuition does not care what the actual probability is and does not understand anyway.
Looking at everything from the profit/cost point of view can lead to a very boring life, for most of the people.
I've been interested in the topic for a long time as I have a relative who spends most of his income on lottery tickets. Any time I can, I ask people who play the lottery why they do it. Most of them spend a tiny amount and it's something they have a little bit of fun with their workmates or family, these are the "normals". But about 20% of the players account for 80% of the ticket revenue, these are the people playing out of desperation because they are in a poverty trap and they have no other way out. They are foregoing essentials to pay for the lottery tickets, so if they didn't play, they wouldn't accrue the money they "saved". These people are often on the brink: depressed, panicked and alone. A lottery ticket is a temporary "self medication" with which they can temporarily quiet their anxieties, until of course, they need the next hit.
Then of course there's the simple point that less money comes out of lotto than goes in, simply to pay for overheads and profit of the gaming company (as with all gambling) plus a bit of tax on the ticket. The ticket sale simply can't be a zero-sum game; less has to make it back to the winners than was paid in the first place.
That being said, I also pay the idiot tax every month or two, and for the same reasons as the author - entertainment.
There is certainly some truth in the vision of the poor guy being a more vulnerable gambling victim but I would not generalize that to non-addicts. Gambling vs. other kinds of entertainment is a matter of personal preference.
Actually gambling is quite popular among rich people, in the form of financial speculation...
The argument is that gambling houses are taking advantage of people's poor education to bilk them out of money. In principle, everyone in developed nations should know that gambling is a poor investment, but it takes good financial sense to really understand that. People with good financial sense usually aren't very poor.
So when you look at how poor people spend money, the rational economist would never advocate spending the money on the lottery. The utility is low, and even if the expected value is positive, the variance makes it a bad idea. Poor people would be better off spending money on things with greater returns.
The problem is that poor people don't spend their money on things with greater returns. They spend far too much of their money on lottery, and it's probably combination of psychological factors and financial illiteracy. I could be off on this, but I remember a statistic showing that there isn't much deviation on how much money any random household spends on the lottery. So a household with $100,000 in incomes spends as much on the lotter as a household with $20,000 in income. The result is that the lottery has become a regressive tax.
This misses the point of the article, which is that gambling should not be regarded as an investment, but as entertainement. But I agree that poor people are possibly more likely to see it the wrong way, i.e. as a good investment.
The result is that the lottery has become a regressive tax.
By the same argument you can conclude that potatoes are a regressive tax since they cost a higher fraction of the poors' revenues.
When you give money to the government with nothing in return (except as a member of the collectivity), that is a tax. Not when you give money to a private company in exchange for some kind of entertainment.
*The ticket sale simply can't be a zero-sum game*
PS: Powerball tickets also cost 2$ now which means you need a larger jackpot to break even.
But nevertheless. Yes, the lottery is a tax for the poor. And if you expect your life to change for the better by winning a big bag of money (that you will have taken to the other suckers who lost, minus the organiser's fee), then you just need to reconsider what makes a happy life. You should also consider how many people get isolated after they have won, not knowing how to deal with such a change, such a "responsibility", such a social pressure from family and friends after they have won.
I'd never play the lottery not because of the ridiculously low chances of winning (I also am a statistician), but because what I would win would change nothing to my human condition. I prefer reading Epictetus instead. It's cheaper and the effect lasts longer.
While I agree with you in philosophy, I wonder if that is the best example. I don't think I've ever seen a news report of someone getting hit by lightning and a bus at the same time, but people do seem to win the lottery on a fairly regular basis. This suggests that winning the lottery may be the more likely of the two.
If it was a tax on the poor and undereducated, the correlation should be negative, yet the first three articles I found on the matter said it's positive, and that income is the strongest determinant of gambling activity.
Secondly simply looking at the number of times person partakes in an activity or just how much they spend only gives a small and incomplete picture. The really important number is what proportion of their total income is spent on gambling. Most studies seem to find that the poor spend a higher proportion of their income on lottery tickets than richer people.
A couple of randomly chosen references: http://walkerd.people.cofc.edu/360/AcademicArticles/LotteryR... http://www.cfcg.org/articles/CPGI_report-Dec4.pdf
That's awful presumptuous. A big bag of money can buy food, and food can go a long way towards a happy life if you usually don't have any.
A big bag of money buys your more trouble than food, it buys you restlessness and an insecure future. A regular income from a stable job, for instance, provides food as well, without buying you the trouble of having to secure the money you've got by chance.
And no, that's not presumptuous. We know of plenty of people who were happy with little, nowhere needing the cash that big lotteries pretend you can have.
Not to mention all those stories of people who win the lottery and then lose all their friends out of jealousy. But that's harder to analyze.
The only weekend when casinos did not make a profit, in the entire history of Las Vegas, was when the annual U.S. statisticians conference was organized in Las Vegas :)
For what it's worth, neither does the American Statistical Association.
But hey, next year we get to go to the fascinating city of... Baltimore! Again. Then... Denver! Again.
I imagine the real problem would be crowding your casino with people who just showed up for the buffet but refused to gamble.
At any rate, if the expected return over long periods is $.58 for $1, I sure wouldn't expect it to even get close to $1 on the best weeks.
One could argue that spending money on a lottery ticket is actually better for you than spending the same amount of money on a soft drink. One gives you hope and entertainment and might have other positive "feel good" side-effects. The other fills you with sugar (high fructose corn syrup) and is not good for anything at all.
This advertising presumably motivates citizens who would not ordinarily buy tickets, to buy tickets.
They are not forcing you, of course, but they certainly are encouraging you.
You are not obligated by law to buy lottery tickets, therefore, it cannot, by any stretch of the imagination, be called a tax. Period. They can advertise all they want. You can still say "no".
In fact, you can stand in front of a government lottery official, extend your arm out, point a finger at them and laugh out hysterically while loudly proclaiming that you will not buy their tickets. Try telling the IRS that you will not pay taxes because, well, you don't want to.
I was just responding to your statement:
"No government agency was involved in making you spend the money."
and I was careful to make the distinction between "encouraging" and "forcing" people to spend.
I would rather the government get out of the lottery business, because it seems like a basically useless activity. If we need money, let's ask for money. But it's not a high priority for me. Living in CA, there are plenty of other, much bigger problems than lotto.
I tend not to think of an added 1/4th as "just over" but perhaps that's a difference in perception.
Not that the Government doesn't take their cut, it's just already been factored into the advertised prizes.
Beyond that your time is wasted, statistician or not.
Source: http://articles.nydailynews.com/2010-04-02/news/27060744_1_l...
sounds like college, s/entertainment/networking
There's not even a hint of irony.
It's all about the 'entertainment' value.
Am I seeing a remake of the book/movie 'Hunger Games'?
"Oh Nigel, do kindly pass me two of your Entertainment cards. You'll get a treat if you do..."