The empirical changes are not very low. Assuming each plant has a uniform probability of failing once every 10,000 years, that comes out to an accident once every ~50 years in one of the ~500 nuclear power plants on Earth.
We had a major radiological incident in a Polish coal plant recently. That not counting a whole power plant block failing, contaminating water and emitting tons of fumes.
It still has not been fixed as the replacement block turned out to not meet new emission standards.