Lightning vs Lotteries

Here is an interesting question for both Michael Shackleford, the Wizard of Odds (posted to his forum at www.wizardofvegas.com) and the Freakeconomists Steven Levitt and Stephen Dubner (emailed to them at levittdubner@freakonomics.com). I have never seen this question asked just this way before, anywhere. Feel free to edit for printing, so long as the main gist of my question is not lost.

We have all heard that there are better odds of being hit by lightning than of winning the lottery. In fact, we can see this by reviewing and accepting lightning hit odds data presented by NOAA @ www.lightningsafety.noaa.gov/medical.html. A figure of 1 in 750,000 is arrived at based on the US Population and lightning hit data. This web site states that about 600 people have been hit and injured or killed by lightning in 2008. I have no data to prove otherwise.

We can also make a generalization about lottery winning odds based an "average" lottery odds being 1 in 8,000,000, or perhaps even greater. Of course, every lottery has different odds, but accepting these figures for the moment and comparing lightning odds to lottery odds, the math would result in about 10% of the number of people getting struck by lighting as winning the lottery. 1 in 750,000 compared to 1 in 8,000,000 -- 750,000 / 8,000,000 = ~10%. 10% of 600 = 60.

I would argue that winning $1M or more in any lottery drawing would be a win. Wouldn't you agree? We can be sure that there are way more than 60 $1M+ Lottery wins per year in the US, however. In fact, in my state of MA alone, I would guess that there are at least 50 $1M lottery wins per year with all of the traditional lotteries and scratch tickets we have. Not all states have lotteries in them, but even if only 10 states had lotteries with 50 wins per year, we are already at 500 wins per year which is about equal to the number of lightning strikes per year. Do you have data that tells how many lotteries there are in the US per year and how many $1M winnings there are per year?

What am I doing wrong, besides not buying enough lottery tickets? What is this called when the view of the data set is an incomplete or incorrect view and does not take into account the overall data set?

Thank you and best regards!
...Larry Levine

I'm not sure if precision is required here or not. The comparison with lightening strikes is meant to convey emotions and in all actuality your analysis of lightening strikes is greatly flawed.

Lightening strikes are skewed. Taking the entire US population and dividing it by the number of known lightening deaths is meaningless, since the people in Manhattan are rather unlikely to be struck by lightening whereas people in rural areas or on golf courses holding metal clubs are rather more likely to be struck.

I don't know what threshold value constitutes a lottery "win" but one million is fine to use as a working estimate.

Very few people will consider the purchase of a lottery ticket as competing with the seeking out of lightening strikes. The analogy is presented in relation to the purchase of a lottery ticket. No one goes out and purchases a lightening strike. Our views of risks are generally absurdly incorrect. That is why politicians and salesmen get rich.

Nor is there a lottery-rod to ward off wins ;)

Seriously, location does matter. Florida gets lots of rain and lightning, so it gives you a much better chance of being struck than Nevada. Besides which there are means of warding off lightning. Therefore the chances of being struck by lighting are as small as possible.

I think a better comparison would be some other form of random event, catastrophic or not, which tends to be rare and unusual, and for which you can do nothing about. Chances of being hit by a meteorite, say, or even the odds you'll see a meteorite. Or something downright weird, like the odds you'll be right at the edge of a rain cloud, so you're dry but it's raining accross the street (I've seen this a few times).

Quote: lml130

What am I doing wrong, besides not buying enough lottery tickets? What is this called when the view of the data set is an incomplete or incorrect view and does not take into account the overall data set?

Thank you and best regards!
...Larry Levine

Sample bias?

Risk of this kind is not very well understood. There's a big difference between your chance of getting hit by lightning in a year vs a lifetime. As already discussed, your chance of getting hit over any given period is based on your location and activities. We might also want to count (or not want to) non-fatal strikes. What about when you get hit, but not seriously injured?

All the being said, let's say you could estimate what the risk of being hit by lightning was to an average person over the course of a year. How do you compare that to a lottery player? The chance of winning the lottery once is very small, but so is the risk of getting hit by lightning this week! So, so we compare to the chance of winning the lottery if you play every week for a year?

The comparison is just to draw attention to the long-shot odds involved, but the actual claim is probably bogus.

As an aside, I have seen the following claim which should illustrate how tough it is to measure & compare these risks: your chances of dying in a car accident (or killing someone) today are very very slim, but over the course of a 50 year driving career, the average American has about a 1-100 chance of being involved in a fatal accident.

We need to frame what the question is better. How about, the chances of winning a 6/49 lottery, with a single ticket, are about the same as a single person getting hit my lightning over some unknown period of time.

The probability of winning a 6/49 lottery is 1 in 13,983,816. Let's just say in 1 in 14 million, to keep it simple.

Let's use your figure of 600 people being hit by lightning in the US per year. The population of the US is about 300 million. So the expected number of hits per year per person is 600/300 million = 1/500,000. So the odds of getting hit in 1/28th of a year, or 13 days, would be about 1 in 14 million.

So, assuming these assumptions are right, it could be said that if you buy a single 6/49 lottery ticket, then your odds of winning are about the same as getting his by lightning in the next 13 days.

Of course that doesn't consider location, and time of year, which play a big effect in your lightning odds. Living in Baltimore, I was genuinely worried sometimes making the long walk from my office door to my car in midst of a rainstorm. It was also not unusual for the community pool to be closed due to fear of lightning. Meanwhile, my kids probably have never seen lightning, growing up in Vegas.

Quote: lml130

What am I doing wrong, besides not buying enough lottery tickets?

Strange as it may seem, that is part of the problem.

You're comparing the number of people hit by lightning to the number of people that win the lottery.

That apples and oranges.


No person has ever won a lottery. EVER!

However, there have been lots of people who held the winning TICKET.


I.E. You need to compare the number of people struck by lightning vs the population count, to the number of wining tickets vs the tickets purchased.

Do you know anyone who has been struck by lightning? The son of one of my work acquaintances was. It burned him and his wife and killed his dog. I was almost hit once, back in the '70s; I was on the porch watching it rain, then I felt my hair stand up all over, and then it hit a tree about 50 yards from the house. I'll never forget that, though. I was living in Indiana at the time, and I'd watched that storm walk across the plain, getting closer and closer, and then that... scary stuff. Big blast of light and sound and the air ripped apart. In the '60s, the house next to ours was hit by lightning during the middle of the night. It went halfway down the lightning rod then burned through a brick in the side of the house, then followed the plumbing and burned up the bathroom and some other stuff; that was maybe '64.

I also have met several people who have won million+ lotto jackpots. Some of them were sensible with the money, some were not; I know two of whom it drove to bankruptcy. The best one was the 23 year old guy who won 8M and started a marina business; he was pretty cool, a good businessman. The worst was a trucker who blew it all within a year. Second worst was a guy I knew in high school, who worked menial jobs and lived with his mom into his 30s. They won the lotto together for about 5M, then bought a bunch of stuff with no way to sustain the lifestyle. Lost the home, cars, etc. I can't say I cared, I never liked him anyway.

Recommended is Money for Nothing: One Man’s Journey Through the Dark Side of Lottery Millions, by Edward Ugel. Ugel worked as a salesman for an annuity company; they bought out lottery winners who needed the cash right away. Coincidentally, he was also a heavy gambler... good stuff, from the intersection of life and money and risk and reward.

Quote: lml130

Here is an interesting question for both Michael Shackleford, the Wizard of Odds (posted to his forum at www.wizardofvegas.com) and the Freakeconomists Steven Levitt and Stephen Dubner (emailed to them at levittdubner@freakonomics.com). I have never seen this question asked just this way before, anywhere. Feel free to edit for printing, so long as the main gist of my question is not lost.

We have all heard that there are better odds of being hit by lightning than of winning the lottery. In fact, we can see this by reviewing and accepting lightning hit odds data presented by NOAA @ www.lightningsafety.noaa.gov/medical.html. A figure of 1 in 750,000 is arrived at based on the US Population and lightning hit data. This web site states that about 600 people have been hit and injured or killed by lightning in 2008. I have no data to prove otherwise.

We can also make a generalization about lottery winning odds based an "average" lottery odds being 1 in 8,000,000, or perhaps even greater. Of course, every lottery has different odds, but accepting these figures for the moment and comparing lightning odds to lottery odds, the math would result in about 10% of the number of people getting struck by lighting as winning the lottery. 1 in 750,000 compared to 1 in 8,000,000 -- 750,000 / 8,000,000 = ~10%. 10% of 600 = 60.

I would argue that winning $1M or more in any lottery drawing would be a win. Wouldn't you agree? We can be sure that there are way more than 60 $1M+ Lottery wins per year in the US, however. In fact, in my state of MA alone, I would guess that there are at least 50 $1M lottery wins per year with all of the traditional lotteries and scratch tickets we have. Not all states have lotteries in them, but even if only 10 states had lotteries with 50 wins per year, we are already at 500 wins per year which is about equal to the number of lightning strikes per year. Do you have data that tells how many lotteries there are in the US per year and how many $1M winnings there are per year?

What am I doing wrong, besides not buying enough lottery tickets? What is this called when the view of the data set is an incomplete or incorrect view and does not take into account the overall data set?

Thank you and best regards!
...Larry Levine

I think the Wizard said it best.

If you buy one ticket for the lottery, your odds of winning are roughly the same as an "average" US resident person getting struck by lightning in a year. The fact that there are many many more lottery winners than people being hit by lightning is of course that the average US resident buy far more than one lottery ticket in a year.