# Punk Rock Operations Research

## what is the conditional probability of being struck by lightning?

Posted by Laura McLay on February 9, 2012

There is not nearly enough information available on the Internet on the conditional probability of being struck by lightning.

I think of the odds of being struck by lightning and conditional probability every time I am in a thunderstorm. The conditional probability of being struck by lightning is probably not 1 in 6. NOAA estimates that the (unconditional) probability of being struck by lightning is ~1 in 1,000,000 per year and ~1 in 10,000 over a lifetime. That’s of little solace when I’m out running a few miles from home when a thunderstorm rolls in.

Jeffrey Seth Rosenthal’s book Struck by Lightning does not exactly answer this question. He does, however, report the annual probability of being struck by lightning conditioned on where on lives. Below are the figures from his book on the most dangerous states, the safest states, and the most dangerous countries (at least in terms of being struck by lightning). The “Annual Rates” report the expected number of people struck by lightning per year per 100,000. This could be due to differences in the prior probabilities (some areas have more thunderstorms than others) or in attitudes toward risk in thunderstorms.

Any idea of what the conditional probability of being struck by lightning would be given that one is outside in a thunderstorm? I need to know how much to panic the next time a thunderstorm rolls in when I am running.

1. ### matforddavidsaid

Come to the UK! Our fatality rate is lower than in the US. Also the statistics show that about five times as many men die as women. See http://www.torro.org.uk/site/lightning_info.php
But, as for:
Prob(Laura is hit by lightning before she reaches home | Laura is running miles from home AND there is a thunderstorm)
all I can say is it is in the range 0 < p < 1 without equality.

2. ### S. Phil Kim (@ksphil)said

The answer is all about how often people is outside when there is a thunderstorm. Of cause, I am assuming that all the event lightening strike happen outside.

If we can get the data from survey “how many times have you been outside in a thunderstorm a year?”(xi for i th person).
Then 45 / Sum(xi) i \in population of American will be the Conditional probability of being stuck by lightening.
Let’s say, an average American have been outside in a thunderstorm 0.5 times per year. then, 90/7million is the answer. But, how long should one be outside to be considered as been outside ?

If we consider the time expose to the thunderstorm, it would be more precise. Assuming the event happen as poisson process, we will need to estimate the rate and then we can calculate the probability if one is outside in a thunderstorm for an hour, for example. This case we need to know an average hour people spend outside in a thunderstorm.

Anyway, the portability will go up significantly, because I think most of people will not stay outside when there is a thunderstorm.

3. ### Paul A. Rubinsaid

First, the death rate its higher for men because men will continue to play golf (raising metal clubs) during a t-storm.
Second, I’ve actually heard of indoor”lightning”, but the story its too long to fit here.
Third, in addition to time of exposure, Laura would need to factor in terrain (trees, presence of metal above our below the surface) and the fact that she has above average height. (A lazy lightning bolt will take her before it takes me … unless I’m swinging a golf club.)

4. ### Michael C. Grantsaid

I wonder if the metal in my leg reduces my resistance to ground.

5. ### Laura McLaysaid

Thoughts from my husband:

why not ask the question this way: what is the probability that a given thunderstorm will injure or kill someone? I googled some stats, and found that the NWS estimates 100000 thunderstorms in the U.S. per year:

The same source quotes about 100 deaths per year, and 257 lightning related injuries per year. More recent data indicates that the fatalities have been declining to 55 per year averaged 1980-2009:

http://www.lightningsafety.noaa.gov/fatalities.htm

Assume that most incidents are individuals and not groups (seems valid given the tabular data from 2011), for any given storm P(death) = 55/100000 and P(injury) = 257/100000. Of course this is just a rough estimate, and perhaps with better data you could make estimates for geographic regions or specific time of year. Note that the NOAA link indicates that 73% (40/55) of deaths occur in the summer months, but then I’d expect that the majority of thunderstorms also occur in those months.

6. ### Jeffrey W. Herrmannsaid

I agree that the rates based on where one lives are not relevant to the conditional probability that we’re discussing; the rates above reflect the differences in thunderstorm frequency, the number of people who work and play outside, and other factors.

7. ### Assorted links — Marginal Revolutionsaid

[...] 3. What is the conditional probability of being struck by lightning? [...]

8. ### HSmithsaid

How come you attribute your statistics to Rothenthal’s book, but you don’t give credit to Randall Munroe for using his comic from xkcd.com?

9. ### Laura McLaysaid

@Hsmith: I provide a link to the comic, so I would argue that I give credit where credit is due. But you are right, I should have explicitly given credit to Munroe for his wonderful comic. When I use this comic in my classes, I always give credit.

10. ### Laura McLaysaid

@Jeffrey: I completely agree about the locations not being particularly relevant. But they were interesting in their own right, so I included them. I wonder if they *do* shed light on the conditional probability of interest. Perhaps in some locations, lightning tends to hit the ground more frequently? Not all lightning storms may be equally dangerous.

@Paul: I completely agree. Central Illinois was flat and had few trees. I felt like I had a target on me during every thunderstorm. I tried to modify my habits, but when I was a student, I got around by foot. Some risk was unavoidable. Luckily, I survived!

11. ### Jeffrey W. Herrmannsaid

Laura,

I didn’t intend to criticize your including the table of location-specific lightning mortality rates in your post; the fault lies with the author who intended such a table as a way to communicate a quite-controllable risk. Mortality rates are often used as estimates of risk, so this is an interesting example of when it is not appropriate.

12. ### Conditional Lightning Strike Probabilities | Floating Pathsaid

[...] information if you spend a lot of time outside, some locations have it much worse than others. Laura McLay at Punk Rock Operations Research  brings us some tables on the conditional probabilities.Most dangerous and safest states:Countries [...]

13. ### Weekly links – February 12 « God plays dicesaid

[...] Laura McLay, what is the conditional probability of being struck by lightning? [...]

14. ### Chris Borthwicksaid

So far all correspondents seem to have assumed that all people struck by lightning die, which isn’t the case; a percentage live through it. The advice (and I am not making this up) is to stand on one leg, to minimise the effect of electricity transmitted across the stance.

15. ### Laura McLaysaid

Chris: Thank you! I think that the vast majority of people who are struck by lightning survive. I went to high school with someone who was struck by lightning and lived, so I am well aware of this. Your advice to stand on one leg is consistent with other advice I have heard about how to position the arms. I think that these poses do not encourage the lightning to cross the chest, which would cause the heart to stop beating. But I’m not a real doctor.

16. ### Laura McLaysaid

Jeffrey: no offense taken! Thanks for your clarification. The tables do not display exactly what I would like them to, but they are the best that I have. They are, I think, useful for starting to unpack the impact of the frequency of lightning, the odds that people are outside in storms, and the impact of infrastructure in lowering the conditional probability. For example, the high rate in Cuba could reflect more manual laborers who remain outside in a storm? Or are the different building codes in different countries indirectly factoring into different conditional probabilities? I’m relying on the collective wisdom of my readers here.

17. ### Weekly links for March 18 « God plays dicesaid

[...] McLay, The conditional probability of being struck by lightning, parts one and [...]