# Detailed Calculation Of The Odds Of Death From A Mountain Lion Attack On A Person

On the page Mountain Lion Attacks On People in the U.S. and Canada, I give this simple estimate of the relative odds of a mountain lion-caused death versus an automobile-caused death:

In California, from 1986 through 1998, exactly two people died from mountain lion attacks, whereas in one year alone, over 4,000 people died in traffic accidents, including 800 pedestrians. This means that your car or someone else's car is ~2,000 times more likely to kill you than is a mountain lion.

This page reports the detailed calculation to arrive at the factor of ~2,000. (Note that this factor of 2,000 does not come from the ratio of 4,000 people died in traffic accidents to the two mountain lion deaths! It is just a coincidence that those numbers are the same.)

The probability of death from a car per year is simple: 40,000 deaths / 300 million Americans = 1.3e-4 = 1 / 7500.

To get a hiker's probability of death from a mountain lion, we need the number of hikers in California:

Number of hikers in U.S.: 50 million people over the age of 12
Number of hikers in U.S. hiking 10 or more days in 1992: 13.4 million people over the age of 12
Source: 1992 pilot of the National Survey On Recreation And The Environment, by the USDA Forest Service, reported in Wildlife and Recreationists, R.L. Knight and K.J. Gutzwiller, 1995, Island Press, p.9.

I assume that California has at least 10% of the hikers, since California has 10% of the population of the U.S. California probably has a higher ratio of hikers, so using this number will give an upper limit to the probability of death per hiker.

The number of deaths per year from a mountain lion in California is 2 deaths in 13 years.

Thus the probability of death per year per hiker in California, for all hikers, is (2/13) / (5 million) = 3.1e-8 = 1 / 32 million.

The ratio of these two numbers, 32 million / 7500, is 4300. Hence a person in California is 4300 times more likely to die from a car than from a mountain lion if that person is a hiker.

Now suppose that mountain lions never bother the infrequent hikers, and only the serious hikers who hike more than 10 days per year are at risk. That increases the odds of death from a mountain lion by a factor of 50 / 13.4, making the ratio 1150.

Hence the detailed calculation gives the calculated odds of being killed by a car as 1150 - 4300 times more than the odds of a hiker being killed by a mountain lion, a value of 2000 within a factor of two.

The biggest uncertainty in the above calculation is not the number of hikers or the number of miles they hike, but instead comes from the very small number of deaths caused by a lion. At the 95% confidence level, the maximum true rate consistent with observing only two deaths in 13 years is 7.4 deaths in 13 years, a factor of 3.6 times higher. The 95% confidence minimum true rate is 0.7 deaths in 13 years, a factor of 2.9 times lower. Hence one can state at the 95% confidence level that you are 320 - 3,300 times more likely to die from your own or someone else's car than from a mountain lion, even if you are a very active hiker and hike at least ten days per year.

Taking into account the 95% confidence uncertainties, and the range in estimates for the calculation using just hikers or just frequent hikers, the true ratio is between 320 and 12,500.

Bottom Line: You expect on average to be killed by a car at the very minimum 320 times before you expect to be killed by a mountain lion. So you really shouldn't start worrying about a mountain lion killing you until at least 160 of your hiking companions have been killed by automobiles.