Large-scale, high-consequence, strongly systemic or correlated events are difficult to model and describe.

Death-by-asteroid is one of the more interesting cases. That would be a bad day for you (or your descendants), but also, quite likely, many others, when it happens. The days aren't frequent, but they're big.

http://blogs.discovermagazine.com/badastronomy/2008/10/13/de...

More generally, there's a lot summary statistics don't tell you.

https://www.autodeskresearch.com/publications/samestats