Why Unlikely Events Are Not Unlikely

A recent FaceBook post starts:

Is it really a coincidence that so many unprecedented weather events are happening this year

with a link to a news story about a "once in 50 years" rain in Japan. It is an argument I frequently see made, explicitly or implicitly. Lots of unlikely things are happening and there must be a reason. When the subject is climate change the unlikely things are mostly about climate.

It looks convincing until you think about it. The world is large. There are lots of different places in it where, if an unusual weather event happens, it is likely to show up in the news. There are at least four categories of unusual weather events that could happen—unusually hot, unusually cold, unusually large amount of rain, unusually small amount of rain—and probably a few others I haven't thought of. A year contains four seasons and twelve months and a record in any of them is newsworthy—a recent news story, for example, claimed that this August was the hottest August in the tropics on the record.

For a very rough estimate of how many chances there are each year for an unlikely event to happen and make the news, I calculate:

100 countries prominent enough + 100 cities prominent enough +10 geographic regions (tropics, poles, North America, ...) + 50 U.S. states = 260

x

12 months + 4 seasons=16
x 

4 kinds of events that would qualify 

=16,640 opportunities each year for an unlikely weather event to occur and be reported.

So we would expect more than 300 once in 50 years events to happen each year and about sixteen one in a thousand events.

My guess is that those number are too low—the story about floods in Japan does not make it clear whether the one in fifty years record is for the whole country or only one region. But they at least show why we should expect lots of unlikely things to happen each year.

If you flip a coin ten times and get ten heads, you should be surprised. If you flip sixteen thousand coins ten times each, you can expect to get ten heads about sixteen times—and should not be surprised when you do.