# The Probability of Three Category 4 U.S. Hurricanes in One Season

The 2017 hurricane season saw three Category 4 (Cat 4) hurricanes making landfall on the U.S. mainland. What does the data say about the likelihood of this season’s experience?

To begin, the overall annual probability of a U.S. hurricane (all five categories) is 80%.

Based upon the last 166 years of experiences, the distribution by U.S. hurricane size is as follows.

*Table 1: Category distribution of a hurricane hitting the U.S. (1851-2017).*

`Table 2 sets forth those sixteen years in the past 166 (excluding 2017) where more than one strong hurricane (Category 3, 4, 5 or Cat 3+) has hit the U.S. mainland.`

*Table 2: Years of multiple hurricanes (Cat 3, 4 or 5); 1851-2016.*

*Multiple Cat 3+ hurricanes in a single season occur about once every ten years. *

Note that there were three years (1935, 1969 and 1992) where a Category 5 hit the U.S., but in these three years no other large (Cat 3 or 4) hurricanes occurred.

Ignoring 2017 for the moment, what does the prior data say about the predicated probability of three Cat 4 hurricanes hitting the U.S. in the same year?

One can take the annual probability of one Cat 4+ hurricane (7%) and then calculate the joint probability of three Cat 4+ hurricanes (i.e. 7% x 7% x 7%). This produces a probability of 0.034% (once every 2,950 years).

Or one can take the observed probability of two Cat 4+ hurricanes (0.6%) and multiply by the probability of a third (7%). This produces a probability of 0.42% (or once every 2,400 years), roughly the same as the first method.

*The data prior to this year implies that a season with three Cat 4 hurricanes has a return period in the range of 2,500 years, a very rare hurricane season indeed.*

If we now consider the 2017 season, a Bayesian update of this probability is required. Given that it has now happened (once in 167 years), the probability of three Cat 4+ hurricanes can now be said to be 0.6%.

*This is at least 15 times more probable than would have been predicted previously. This is a really big Bayesian update. *

There you have it. The 2017 season is either a really remote (2,500 year return period) or not so remote (150 year return period).

Coming on the tail of 12 years free of any large Cat 3+ U.S. hurricane at all, it seems black swan-like, not necessarily any indication of change.

That said, the calculated probability from prior data of 12 years of no Cat 3+ U.S. hurricanes at all is (71%) to the12th power, or less than 2%.

Maybe this season is just catch-up by Mother Nature, who from 2005 up until this year seems to have been more focused on earthquakes, floods and tsunamis. No question, she can be fickle.

By: Danelle Bishoff and Jack Gordon