Base Rate Fallacy

πŸ‘οΈβ€πŸ—¨οΈ Today I thought it might be helpful to discuss base rate fallacy. This is something I’ve touched on several times in my Covid updates. It’s formed part of the statistical misrepresentation that’s become commonplace on Covid-conspiracy social media since the start of the pandemic.

It’s more than likely that you’ll have witnessed someone say something along the lines of: “Covid-19 vaccines don’t work. The majority of hospitalisations/fatalities are occurring in the fully vaccinated!” Whilst the latter part of the statement is true, the first part is not. Let’s look at why…

What is base rate fallacy and how does it apply here?

Base rate fallacy refers to times where we ignore statistical information (base rates) in favour of specific information related to it.

πŸš— Let’s use the analogy of seatbelts. In 2019, the European Transport Safety Council reported that 27% of car occupants killed on UK roads were not wearing a seatbelt. This means 73% of those killed on the UK roads were wearing seatbelts. Adopting base rate fallacy mindset, we might falsely assume that the 73% figure means you’re more likely to die in a road accident if you’re wearing a seatbelt.

Of course, to adopt that conclusion would be false because it would be ignoring the base rates - the fact that 98.6% of car occupants wear seatbelts. The conclusion would also fail to incorporate a key missing piece of data - the number of people whose lives have been saved by wearing seatbelts (so, did not die, but would have done so without the seatbelt).

Bringing this back to Covid-19, then, and social media posts mentioning that the majority of hospitalisations/fatalities are occurring in the fully vaccinated and linking it to the idea that vaccines don’t work (or, worse, making the false suggestion that you’re more likely to go to hospital if you’re vaccinated). Yes, there are more hospitalisations and fatalities now occurring in the vaccinated than the unvaccinated. But, this is not a cause for concern. Allow me to explain why…

According to the last UKHSA Vaccine Surveillance report, around 82% of adults (over 18s) in hospital with Covid-19 had received at least two doses of a vaccine.

πŸ“Š Much like the seatbelt analogy, we need to consider the base rate. There are FAR MORE vaccinated people in England than unvaccinated. So, the number of hospitalisations/fatalities is a small percentage of a far higher base, and the figure doesn’t include an unknown statistic - how many people have NOT been hospitalised or died because they’ve been protected by their vaccine shot(s).

Age ranges also need to be factored into the equation. In older age groups, a larger percentage of the population has been vaccinated. But, these people are also amongst the most vulnerable in our society because of their age and underlying conditions. Vaccines increase protection, but these people remain more vulnerable than most.


Let’s look at the data mathematically. Around 90% of people in England aged 18+ have received two doses of a vaccine. That’s 40 million (source: NHS England) out of a population of 44.5 million (ONS estimate). Conversely, 4.5m have not received two doses of a vaccine.

If 1,500 people are entering hospital each day with Covid-19, and 82% of those have been fully vaccinated (at least two doses), that would mean 1,230 fully vaccinated and 270 non-vaccinated. This may seem bad at first, but when you refer back to the original base, the picture is different…

1,230 out of 40 million is 0.003%. However, 270 out of 4.5 million is 0.006%. So, as a percentage of the base, the rate of hospitalisations amongst the unvaccinated is higher - twice that of vaccinated individuals, in this case.

This figure, of course, gives an overall view of all age groups aggregated together. To get a more accurate picture of the impact of vaccines, you need to look at age-standardised statistics, because older age groups are both more likely to be vaccinated and more likely to be hospitalised. But, you get the point.

And so you now see why base rate fallacy can result in data being misrepresented to form an agenda that simply isn’t there. The next time you see posts suggesting that Covid-19 vaccines aren’t working, consider whether there is base rate fallacy involved.

For more reading, I recommend this excellent article on FullFact:…

Thanks to David Paton, Professor of Industrial Economics at Nottingham University Business School. Graphic from Marc Rummy. Seatbelt stats: . UKHSA surveillance report July 2022: .