Imagine that your friend comes up to you one day and proclaims that they are abnormally lucky. Intrigued, you ask them how they could be so lucky. “I’ll prove it to you,” they say. They ask you to flip a coin three times. You get 2 heads out of three flips. They respond “Oh yea, well I got 4000 heads.” “You only got 2 heads and I got 4000 heads, that’s how much luckier I am than you.”

Reading this, you may realize that this is a silly comparison for your friend to make. It certainly doesn’t mean they are any luckier than you are. Instead, the only reason they got more heads than you is because they flipped a coin more times. Now imagine your friend admits to you that they flipped a coin 8000 times. If they got 4000 heads out of 8000 coin-flips, then that means your friend had the standard 50/50 (or 50%) chance of getting a heads – not all that lucky.  The more times you flip a coin the more opportunities you get to get more heads. This difference in the number of heads between you and your friend doesn’t actually mean anything. It would only mean something if you each flipped the same number of coins and saw a difference in the proportion of heads you got.

The trick your friend pulled in this scenario is what is known as a false equivalence (1). In science, a false equivalence is when you take numbers from two different populations but treat them as if they were from the same population. Its like comparing apples to oranges. If one population is much larger and more inclusive than another, there are probably going to be higher numbers of every type of event than in the smaller population. This doesn’t mean that the event you’re trying to count is actually more common in the larger population, it just means there are more people. For example, there are more ice cream sales in cities than in suburbs, but that doesn’t mean that people in cities like ice cream more than people in suburbs; there are just more people to buy ice cream in cities.

Recently, some people on the internet have been using a false equivalence in an argument about the COVID-19 vaccines. They claim that incidents of sudden cardiac arrest in athletes are more common than before, and then claim, without evidence, that the COVID-19 vaccines are causing this. The people making this argument usually mention a certain blog (2). This blog shares data that seems to show an increase in cardiac arrest in athletes. However, this data involves the statistical trickery discussed above. In reality, there is no increase in cardiac arrest in athletes, as I’ll discuss below.

The blog first mentions a study that documents the counts of sudden cardiac arrest that happened on the playing field in athletes that were 35 or younger (3). This study shows that there are about 29 of these incidents per year worldwide. The blog authors then list hundreds of news reports from around the world of sudden deaths or collapses in people involved in sports. Notice the differences between the two populations they are comparing. The first study they cite has a very specific population: athletes that are 35 years-old or younger who experienced sudden cardiac arrest on the field and died. The collection of news reports mentioned in the blog is from a much larger population: people of all ages who were involved in some sport at some point in their life who experienced a sudden death or just a collapse from any cause, anywhere. They weren’t just comparing the rates of young athletes experiencing cardiac arrest mid-game. These news reports include people in their 70’s and people who were sports commentators but not involved with sports. Most suspiciously, they also included people who died in car crashes and athletes who just experienced cramps on the field. Most of the reports did not involve cardiac arrest at all. Many of the people in these reports did not die. In other words, this blog is making a false equivalence.

The only reason these recent news reports show higher counts than the study is because the news reports are counting pretty much anybody and everybody with any sudden severe health condition. It’s also important to note that these news reports include many older individuals. Many health conditions, heart related or otherwise, are much more common in older populations than younger ones. So it shouldn’t be surprising that a much larger, broader, and older population shows more counts of sudden severe health conditions than a smaller, more specific, and younger population. Just like how your friend flipped more coins to get a higher number of heads, the blog authors gathered more types of people to get a higher count of sudden severe health conditions. But just as seeing a higher number of heads doesn’t mean your friend is any luckier than you, seeing more counts of severe health conditions in this false equivalence doesn’t prove that the rate of cardiac arrest in athletes is any higher than it was before. Therefore, it makes no sense to say that COVID-19 vaccines are causing an increase in these incidents when there is no increase to begin with.

Most of the news reports also don’t mention anything about whether people got a COVID-19 vaccine, so there is no way to link their injuries to the vaccines. These were just random unrelated cases (like car crashes) that the blog authors were grouping together to create a false narrative. Instead, over 40 studies over the past three years have tested the COVID-19 vaccines and have found them to be safe in people of all ages (4).

Proportion – a proportion is a part of a whole. A proportion shows us how much of a whole amount a smaller amount is. For example, if you have a large pizza with 8 slices total, and your friend takes 2 slices, your friend took 2/8 of the whole pizza. 2/8 = 1/4 = 25%. So if your friend takes two slices of pizza, the proportion of the pizza they took is 25%. 

False Equivalence – a false equivalence is when people compare two things as if they were the same when they are not. In science, a false equivalence is when you compare two different populations as if they were the same. In this article, the blog authors are comparing the counts of sudden cardiac arrest in young athletes in past years to the recent counts of all types of sudden injuries in people of all ages. These things are not the same, so comparing them as if they were counts of the same thing is a false equivalence.

1. Bennett, B. (2012). Logically fallacious: the ultimate collection of over 300 logical fallacies (Academic Edition). eBookIt. com.
2. 1700 athlete cardiac arrests or serious issues, 1197 of them dead, since Covid Injection. Real Science Blog. Retrieved January 30, 2023, from https://goodsciencing.com/covid/athletes-suffer-cardiac-arrest-die-after-covid-shot/
3. Bille, K., Figueiras, D., Schamasch, P., Kappenberger, L., Brenner, J. I., Meijboom, F. J., & Meijboom, E. J. (2006). Sudden cardiac death in athletes: the Lausanne Recommendations. European Journal of Preventive Cardiology, 13(6), 859-875.
4. Graña, C., Ghosn, L., Evrenoglou, T., Jarde, A., Minozzi, S., Bergman, H., ... & Boutron, I. (2022). Efficacy and safety of COVID-19 vaccines. Cochrane Database of Systematic Reviews, (12). CDO15477.