> In fact, Ranter says it is more common for an accident to happen just one day after another crash than two, three or more days later.

As written, a poisson distribution wouldn't explain this. If you have a crash on day 0, then a crash on day 1 is no more likely than a crash on days 2, 3, etc.

Day 1 is the day most likely to have the next crash, but it's no more likely to have any crash.

(It could easily be the case that Ranter actually found "...just one day after the previous crash than two, three or more days later", and this subtlety got lost somewhere down the line.)