Please note that improbable doesn’t mean impossible. Who would watch sports or buy lottery tickets if very improbable things could not happen?
Still, the probability of five deaths (of rioters, bystanders or police) happening within a day of the Capitol Riot might be 2.6%, and perhaps be as low 0.16%. It depends very heavily on how many people were caught up in the riot. [UPDATE: In fact, four of the deaths appear to have taken place within several hours of each other on January 6, so much sooner than within a full day. Taking that into account would drive the probability much lower for those deaths, but I conservatively used a full day in this analysis.]
What death rate to use for people at riot?
The probabilities above assume a death rate of 3.29 per day per 100,000 people
In 2018, the crude death rate in the United States averaged about 2.4 deaths per day per 100,000 people. That means that if you selected 100,000 people from the entire US population in a scientifically random way (i.e. so that every person in the country had an equal chance of being selected) then 2.4 is how many you would expect to die on a given day in 2018. The COVID-19 pandemic increased that by about 21 percent throughout 2020, and by 40% in January of 2021. So I bumped up the 2018 death rate by 40%. Please note that this must overestimate the “normal” mortality risk of people who were at the Capitol building on January 6. People who showed up to work at the Capitol on January 6, or to participate in a protest, are probably heathier than a random sample of the entire US population. This analysis suggests something dramatically increased their mortality risk – something like getting caught up in a riot that dispersed the US Congress. The much bigger uncertainty in the analysis is how many people were there as protesters, bystanders or Capitol Building workers.
How many were actually at the riot?
If there were 50,000 people in or just outside the Capitol as it was being stormed (not the same as the number of people at Trump’s rally beforehand) then the odds of 5 of more them dying within a day of the event is 2.6%. If there were only 25,000 people at the breach and in the building, then the probability is only 0.16%. David Rosnick of CEPR kindly did the probability calculations for me.
Crowd size estimates are notoriously partisan. One journalism professor, Stephen Doig, doubts there were more than 10,000 protesters who actually stormed the Capitol. A New Yorker piece claimed 8,000 protesters left Trump’s rally to march on the Capitol. On the other side of the ledger, 10,000 seems like a high estimate of number of people working in or visiting the Capitol building that day. If these numbers are reasonable (and I fully accept that it’s the weak point in the analysis) then 25-50,000 people were caught up in the riot. It is statistically very improbable that five of them would end up dead within a day unless something drove their mortality risk way above normal on January 6.