Ahhh…summer. It’s that time of year where the number of outdoor activities seems endless. In any other year outside of 2020, folks are holding gatherings in their backyards, flocking to baseball games, enjoying parks, attending outdoor concerts, and, if they’re lucky, enjoying a swim in the ocean.
It’s also the time of year where, at least in some parts of the United States, we witness severe, but captivating, thunderstorms. I remember watching these storms on the front steps with my parents, hoping to catch the flash of lightning and the loud rumble of thunder. Even as an adult, I’m still in awe when I get to witness such storms. I’ve found myself turned into a willing spectator and peering out a window in the predawn hours after being awoken by the pop of an approaching storm system. I suppose the ability to witness something so primitive, so dangerous yet beautiful, up close but in a protected environment is what makes me enthralled by lightning. The assurance of safety is key here though. Step outside and you go from a willing spectator to an unwilling participant.
I recall going on a run a few years ago and 20 minutes into the run a storm began to approach. I made the comment that we should head back to one of my running buddies. He responded by spouting off a statistic that the chances of us getting struck by lightning were 1 in 1 million. In fact, I can see how he believed he wasn’t too far off with his risk assessment given what the National Weather Service suggests:
Source: https://www.weather.gov/safety/lightning-odds
He even jokingly suggested that if we were struck we should purchase a lottery ticket. Because I felt he wasn’t truly grasping how he failed to frame our risk, I thought I’d ask him what he knows about the likelihood* of another popular summertime statistic…shark attacks.
*Although commonly used interchangeably in lay conversations, there are distinctions between chance/likelihood/probably vs. odds in the statistical world that I don’t feel are worthwhile to discuss here. However, when probabilities are extremely low, they are very similar to the odds.
You see, another phenomenon that seems to occur during the summer is the uptick in stories regarding shark attacks. This isn’t totally surprising given that most beaches in the United States are more popular in the summer, thereby increasing the chance of human/shark interaction. Further, the fascination with sharks due to summer blockbusters and annual the Shark Week series makes shark related conversations all the more top of mind during the summer months. Thus, folks can become enamored for a short time with the likelihood of actually being attacked by a shark. But is the risk of the surfing champion the same as the sun bathing snoozer?
My friend responded that he didn’t know the likelihood of a shark attack and admitted that they are likely more infrequent than lightning strikes. But my point wasn’t concerning the relative likelihood (or even the odds ratio to my statistically minded friends). My point was to get him to think about an important concept when calculating probability – the difference between unconditional and conditional probability.
The conversation went something like this (an obvious paraphrasing):
- Me: What do you think is the likelihood of getting attacked by a shark?
- Him: I don’t know. I mean you are probably more likely to get struck by lightning than attacked by a shark. Why does that matter?
- Me: What do you think the likelihood of getting attacked by a shark is for people who live in and never leave North Dakota?
- Him: I’m not sure – I guess zero…
- Me: What is the likelihood of us getting attacked by a shark right now?
- Him: (Laughing) Given that we aren’t in water, zero.
Looking back at our table from the National Weather Service, we can see that the likelihood of getting struck by lightning in a given year (e.g. 2019) is 1 in 1,222,2000. To obtain this number, the authors of the table took the average number of known human lightning strikes in the U.S. per year between 2009 and 2018 (243 injuries and 27 deaths) and divided that by the approximate U.S. population for 2019 – 330,000,000. Using these two values, we can compute that the probability of getting struck by lightning in a given year (e.g. 2019) is 270/330,000,000. This number (the probability) isn’t too helpful because of the small size (0.0000008182) so we’ll flip the calculation by making the numerator (270) the denominator (330,000,000) to arrive at 330,000,000/270 = 1,222,222.22 OR 1 in 1.22 million. If you are curious, the calculation for a lifetime likelihood simply divides our given year likelihood (1,220,000) by the lifetime estimate of 80 years, yielding approximately 15,300 or a 1 in 15,300 chance you will be struck by lightning in your lifetime. But after my conversation with my friend regarding those dormant North Dakotans and shark attacks, something should strike you about these numbers and the common “1 in a million” chance of getting struck by lightning.
You may start asking yourself:
- Why use the population of the United States in the calculation?
- Are you more likely to get struck by lightning outside vs. inside?
- Are you more likely to get struck by lightning during a storm?
- Are you more likely to get struck by lightning when in an open area?
- Are you more likely to get struck by lightning when in a metropolitan area?
- Are you more likely to get struck by lightning when near or on a body of water?
- Are you more likely to get struck by lightning in some parts of the country versus others?
- What happens if you are in a DeLorean and need to harness the power of lightning to generate 1.21 gigawats?!
With the exception of that last question, all of these are great questions and essentially change the framing of the probability and, subsequently, our risk. Was the probability of us getting struck by lightning 1 in a million? I think it is safe to say, no. This statistic is an unconditional probability. The one in a million statistic assumes that every person has an equal chance of getting struck by lightning at any time, in any location, during any activity. Given that we were outside, in a storm, and in Virginia our denominator is different than that of our North Dakotan friends who are currently indoors enjoying Shark Week as they swear off the ocean for good. Thus, a conditional probability conceptualization is more appropriate.
The point here is that numbers and problem framing matter. For example, the likelihood of rolling any number on a fair, six sided die is 1 in 6. Now imagine if I rolled two six sided dice at once and wanted to know the likelihood that the sum of those dice would equal 8 or more.
What you should see here is that a total of 8 or more occurs 15 times out of 36 possible rolling combinations – or 15/36 = .41. Thus, you have just over a 40% probability of rolling a number of 8 or more when rolling two dice at once. But what if you rolled one die first and then wanted to know the probability that the sum of the dice would equal 8 or more. Now you know something you didn’t before – the conditions have changed! For example, given that the first die lands on a six, how likely is it that the sum of the dice is 8 or more?
In this new scenario, we now see that the probability of a total of 8 or more, given that the first role is a six, is 5/6 or 83%! Consider this our fishing on a boat off the coast of Florida during a storm while wearing a metal hat lightning scenario.
In essence, there are some conditions that obviously make your chances of being struck by lightning more likely than others – know what those are and avoid those conditions.
So how do we go about calculating the likelihood of getting struck by lightning? And what about shark attacks? The folks at the Florida Museum of Natural History sum it up well:
In an attempt to fine tune the divisor to calculate more accurate odds of being attacked and/or dying by a shark, we have used beach attendance data kindly supplied by the U.S. Lifesaving Association for a large number of United States beaches in the year 2000. These beaches were located on both the Atlantic and Pacific coasts and geographically and ecologically represent areas where sharks and humans routinely interact. Using ISAF data, we quantified the number of shark attacks that occurred on these specific beaches during that year.
In this analysis, we use the number of beach users as the divisor. While this is a huge step forward from using the population of the United States or of the states where the beaches were located as a divisor, there are still problems. For example, not all beach users went into the water and not all spent the same amount of time in the water. Bathers did each act the same in the water – some waded, others surfed, swam, etc. – and each wore uniquely colored/shaped/sized bathing suits and possessed varying base skin colors. Some were sweaty when they entered the water and some wore perfume, deodorant, or suntan lotion. Some women were menstruating and some bathers had open wounds or sores. So commonality was limited to the bathers being Homo sapiens! One can see how difficult it is to take the next step, determining which factors contribute to a shark attack.
https://www.floridamuseum.ufl.edu/shark-attacks/odds/more-people/. Retrieved on 08/10/2020
In other words…
