For a reminder that complex systems are hard to predict with much precision, it's hard to beat a good winter snowstorm.
Here's a tweet from the National Weather Service's Boston issued at 9:07 p.m. on January 2, 2018.
It shows the "snow amount potential" for the storm that wound up hitting on January 4. For Boston, it listed a "low end snowfall" of 4 inches, an "expected snowfall" of 11 inches, and a "high end snowfall" of 14 inches.
For Worcester, it listed a "low end snowfall" of 2 inches, an "expected snowfall" of 7 inches, and a "high end snowfall" of 11 inches. It gave Worcester only a 6% chance of snowfall in the 12 to 18 inch range.
A map of predicted snowfall the weather service issued at 4:55 a.m. on January 4 included a range of eight to twelve inches for Boston.
In fact Worcester wound up with 16.6 inches of snow, according to the Weather Service's official measurement. And the weather service folks reported that their own cars in Boston were "buried" under "nearly 17"" of snow.
These are the government's veteran professional New England weather forecasters.
With weather, as with elections and markets and sports, sometimes low-probability events wind up happening. There may have indeed been a 6% chance of snowfall in Worcester in the 12 to 18 inch range. But for the people in Worcester digging out from 16.6 inches, there was a 100% chance that they had that much snow, because it was on their sidewalks and driveways and cars. The fact that there was a 94% chance that it wasn't going to happen is not much consolation.