The conditional probability of shark attacks

“I like my odds. It’s more likely I’ll get struck by lighting, so I’m not really worried”.  This is what a San Francisco swimmer said in a TV interview after a white shark was captured on video attacking a sea lion right next to Alcatraz.

We’ve all seen the stats claiming that the risk of dying from a shark attack is only 1 in 3.75 million. And how much more likely it is to die getting a snack  from a vending machine (1 in 100.000), being struck by lighting (1 in 79.000), being killed by falling icicles (1 in 250.000), dying from falling out of your bed (1 in 8.300), being attacked by a hippo (1 in 830), killed by a champagne cork ( 1 in 150.000), etc… By the way, the 1 in 3.75 million risk is using USA data.  I recalculated this data using a  longer timeframe and taking into account worldwide data, and the global risk comes to 1 in 15 million of dying from a shark attack (Note 1).

The problem is that these reassuring claims are misleading, since they are calculated by averaging out among the entire population instead of taking into account conditional probability.  The death by shark attack risk is fully concentrated on those individuals that swim/surf/dive in waters where Great Whites, Tiger and Bull sharks live: California, Hawaii, Florida, South Africa, Australia, New Zealand, Brazil, Mexico, etc…  If you don’t swim in the ocean, you have 0 risk.  If you swim in the Mediterranean, you also have pretty much 0 risk of dying from a shark attack.

So, what’s the risk of dying from a shark attack if you are a San Francisco ocean swimmer?

– Over a 75 year lifetime, there will be 232 shark attacks in California, 23 of them fatal (Note 2)
– Over a 75 year lifetime, there will be 10 shark attacks in San Francisco, 2.3 of them fatal (Note 3)
– Over a 75 year lifetime, there will be 4.3 shark attacks to SF swimmers, 1 of them fatal (Note 4).
– There are 1750 ocean swimmers in SF (Note 5), so these individuals have a 1 in 1750 chance of dying from a shark attack over their 75 year lifetime (or, put it another way, 1 SF swimmer would die every 75 years from a shark attack).

The numbers will vary depending on many other factors and assumptions, but the main point is that the odds of dying from a shark attack are closer to 1 in 1750 rather than the 1 in 3.75 million being mentioned out there. So, the San Francisco swimmer interviewed on TV was wrong.  He is actually more likely to die from a shark attack (one in a handful of thousands) than from being struck by lighting (1 in 79.000).  That said, the 1 in 1750 are very favourable odds, which is why I continue to swim regularly in the SF Bay, just like I still sleep in a bed every night (risk of 1 in 8300) and open bottles of champagne every now and then despite the killer corks.

Note 1:
– 70 shark attacks per year worldwide, or 5250 over a 75 year lifetime. With a worldwide population of 7 billion, the odds of being attacked by a shark is 1 in 1.3 million.
– 5.9 fatal shark attacks per year worldwide (ISAF), or 442 over a 75 year lifetime. With a worldwide population of 7 billion, there is the odds of dying from a shark attack is 1 in 15 million.
Source: https://www.flmnh.ufl.edu/fish/sharks/statistics/statsw.htm

Note 2: In the 10 years between 2005 and 2014, 702 worldwide shark attacks, of which 31 were in CA (4.4%). 59 fatal WW attacks, of which 3 were in CA (5%).
Source: https://www.flmnh.ufl.edu/fish/sharks/statistics/statsw.htm

Note 3: Between 1926 and 2014 4.3% of shark attacks in CA and 10% of fatal attacks in CA took place in SF.
Source: http://www.flmnh.ufl.edu/fish/sharks/statistics/gattack/mapca.htm

Note 4: Between 1900 and 2009, 43% of shark attacks were to swimmers and bathers.
Source: https://www.flmnh.ufl.edu/fish/sharks/statistics/Act.htm

Note 5: Assuming that there are 1750 regular ocean swimmers in SF… assuming that 80% of the 1100 Dolphin Club members and 80% of the 1100 (?) SERC members are regular swimmers

Categories: Swim4Good