The world is split right now between those who are very sure the vaccine is safe, effective, and anyone who disbelieves that is crazy, and those who believe it is obviously dangerous and harmful, and anyone who disbelieves that is crazy.

Both sides have an abundance of science and experts attesting to their particular side. Or, at least, stuff that sounds scientific and people being held up as experts.

How can you tell which is correct? Especially if you are, as almost everybody is, not really in a position to analyze the scientific claims or claims to expertise directly?

In this post, I am going to give you an objective mechanism that, if honestly applied, will allow you to a high degree of confidence to resolve that question. It does not require any special degree of trust in either side’s science, nor does it even require any particular trust in me. It doesn’t require a particular familiarity with mathematics, although if you can follow the high-school level math in this post it won’t hurt. But even if you can’t, I can give guidelines on how to estimate the probabilities enough for your purposes.

To start with, I need to explain a bit of terminology. Fortunately, social networking, for all its negative impacts, has introduced people to these concepts already, I mostly just need to name them.

Your Friend-of-a-Friend network (FoaF)

Your friend network is the set of people you are directly “friends” with. For the purposes of this post I use the term much as the social networks do; anyone you are in direct communication with, be they family, coworker, etc. is a friend. An estranged parent whom you have completely cut off communication with is not a friend for this purpose.

Your “friend of a friend” network is that network, expanded out to the people your friends are in communication with. This is your college roommate’s uncle (remember, assuming you’re still in communication with your college roommate), your pastor’s brother, your nephew’s girlfriend, etc.

The exact size of this network will of course vary from person to person, but in general it’ll be in at least the low thousands. You can’t just multiply the number of friends you have by the average number of friends they have because of overlap, but it’ll still be in the low thousands by the time it’s all said and done. I’m personally not that social and I could still get into that range no problem.

Base Rate of Early to Middle Age Cardiac Events

Now, let’s talk about what I think is the clearest signal: The number of deaths due to cardiac events or “unspecified natural causes” in the early to middle age category. Call it from 0 years of age to 40-50 years or so. Ask yourself: In a normal year (2019 and before), how many of these events do you see per year in your FoaF network?

You may also want to include people developing serious cardiac trouble or strokes, even if they don’t die, especially if they’re younger than 40 years. I’d also include people who die, and the family is coy about their death for no obvious reason. That is, I’ve certainly had people in my FoaF network die of what was almost certainly a drug overdose or drug-related complications, or what was obviously suicide, and the family was coy for obvious reasons. But that is not a mysterious death that fits this pattern.

Let me emphasize we are only considering cardiac trouble or strokes. Sadly, teenagers die in car accidents in my FoaF network every couple of years or so, but that’s effectively never because of cardiac trouble or strokes.

You may think you never see those, but that is also untrue. There are a number of conditions that can cause those issues in young people, and I had certainly heard of this before 2021. However, I can personally say that it was less than one per year. People simply dropping dead of a heart attack at 33 was not unheard of, but it was an event of note. A 22 year old developing serious heart problems, yeah, it happens, but it’s not common.

There is, unfortunately, some cognitive bias in trying to remember back this far, but since in this post I’m trying to limit myself to just things you have direct experience with and don’t have to depend on anyone else for, we have to take what we can get. Do your best with this number. Yours may be different than mine, due to several reasons.

We’ll want this converted into a “number per year”, so if you estimate “one every two years”, that’s 0.5 per year. That’s my rough estimate.

How Many In The Past Year?

Now, my question to you is, how many such events have you seen in the last year? How many heart attacks below 40-50? How many in teenagers? How many people have had strokes? How many sudden deaths, “please don’t ask questions and respect the family” that aren’t suicides or ODs?

If you are serious about this, I would encourage you to get a third party, a spouse or a family member you’ve had similar social circles with for a while, to help you go over your numbers. Don’t forget to consider the base rate as well; your mileage may vary and I’m not trying to pull a fast one. By all means be sure to be as accurate as you can with both numbers. If for some reason your personal base rate is not around one half per year, please use the correct one you work out.

My personal number is 6 of these as of this writing.

Calculating A Probability For Your Outcome

I say “a” probability because statistics is often as much art as science. But we can discuss some things.

The rate of unrelated deaths of the nature we’re talking about will be a Poisson process. Confounding factors against that distribution will be fairly minimal, since we’re staying below the age where “natural causes” is indeed quite normal, and also most of the “confounding factors” a hasty critic might come up with are actually things that are outside of the relevant statistical universe in the first place. e.g., “But we’re in a pandemic and people are dying of COVID!” is irrelevant, because COVID deaths are neither in the base rate, nor in the population being counted. They’re not in the statistical universe in question at all. The same will be true for most of the “standard objections” internet critics could be expected to roll out.

(Had COVID killed a lot more people than it has, even taking the statistics at face value, we might have to account for the change in the size of your FoaF network, but unless your FoaF network has hundreds of COVID deaths you don’t need to worry about this.)

The Poisson distribution allows us to take a base rate, and a whole number of occurrences, and compute the probability that particular number can occur given that base rate. That’s not quite the probability that “this number is suspicious”, though. We usually do that by taking the probability of a number that extreme or more in the distribution. The formula for that, given the normal rate and the occurrence being checked for oddness, is:

You can go ahead and check that now:

Normal number of incidents in a year:

Your incidents in the last year:

Probability of your incidents or greater: (not computable)

One over probability, or “1 in” chance: (not computable)

(This calculator cuts off at 25 incidents in the last year because this uses a naive calculation method with simple floating point numbers. It is accurate, it just isn’t written to be stable above that. Anything below 10^-16 or so will round to zero, but that’s already well below what you need.)

At a base rate of .5, 6 or more incidents in a year comes out to 0.0000142, or if you prefer that in percent, 0.00141%.

Anklebiting Objections

Should this post end up getting passed around, there are various objections that will be made by people who know less about statistics than they think they do.

One of the greatest statistical errors is to simply assume that citing some source of bias immediately and fully overwhelms the statistical analysis. So, for instance, by citing the fact that it may be legitimately hard to count exactly how many instances of mysterious death you’ve experienced, tada, you’ve completely wrecked the argument!

This is false. What errors will do is, well, just that. Cause errors. However, at least for my personal numbers, the error can’t overwhelm the strength of the signal.

My challenge to anyone who wants to run this argument is this: Do the math. Whatever math you think is correct, do it. Be as open as I have. Show all your work. Show the assumptions you’re tossing in.

Ignore anyone who doesn’t do that and just argues by appeal to incredulity or anything similar.

The second is to think that just tossing out “it could be…“s means anything. Analysis must be done. Moreover, again, the signal is very large. If nothing else, these people deserve better than dismissing them with “it could be…”

Finally… questions of bias and errors in analysis can swing both ways. In fact, I knowingly gave you a biased analysis above. I deliberately neglected:

1. The fact that vaccination rates are much less than 100%. If suspicious vaccination events are occurring, you’d need to factor in the fact that the sample population the events can occur in is lower.
2. When I said I have 6 incidents I’d count, that was within a 6 month time frame. The base rate I cited was annual. To be a fair comparison I’d have to annualize my incident count as well.
3. I don’t think my base rate of these events was .5 a year. I think it was closer to .25, honestly. 25 year olds just don’t drop dead of heart attacks every year.
4. The number of events that I’m still pretty sure was vaccine-related, but wasn’t a “death”, cardiac event, or stroke. There’s still a bizarre uptick in other things as well, like paralysis and sudden autoimmune disorders within my FoaF.
5. I’m deeply unconvinced I’ve heard about all incidents in my FoaF network. It would be very easy for some others to have slipped by.
6. Given that the time frame I’ve been counting in is shorter than the timeframe I used for my base rate… alas, the number of events can still go up from here.

Guess what including all those does to the final probability?

Well, you don’t have to guess. There’s a calculator right up there. Pick your set of confounding factors and run the math. I strongly encourage experimentation, to grow some intuition around how Poisson processes work.

The Poisson distribution turns out to be probably a lot sharper than you think. If the base rate of something is 2 within some time period, you might intuitively think that the odds of seeing a 15 aren’t that surprising, but in fact it’s almost inconceivably unlikely: .000000387%. The probabilities of things that tend to happen .5 times in a given time period happening 6 times in that time period is already pretty small, and if it’s actually something that ought to be multiplied by 2 to account for the time scale and multiplied by another 2-ish to account for incomplete vaccination, and we cut the base rate back down to .25, the probability starts wandering pretty deeply into “ten to the negative” land.

That also disposes of another potential objection from people searching for a way to discredit this analysis without doing the math. I’m not too worried about the possibility of a statistical effect caused by selecting a time frame where there may have happened to be a lot of events, because the probability of there even being such a time frame to choose is so tiny, it can’t be used to explain the problem away.

While it is legitimately a danger to go hypothesis shopping, that danger is in the context of p values so small, like p = 0.05, that you are statistically certain that if you start filtering through random hypotheses you’ll eventually find one that is “significant”. Unless you’ve filtered through 100,000 hypothesis, you’re not going to find one in the 0.0000142 probability range, and it gets worse as that probability shrinks. Plus, if I did find such a hypothesis through hypothesis shopping, others who run my hypothesis on their own data won’t get the same result unless there’s a real signal.

For similar reasons, I’m not worried about my choice of what I’m tracking.

Statistically speaking, there exists a set of people who can perform this analysis and legitimately come to the conclusion that the vaccine is safe and it is the other side that is crazy. However, based on what I’m seeing in the world, most people can run this analysis and determine that there is something out of the ordinary going on that merits investigation. Technically, we can’t completely pin this on the vaccine just because of this analysis, but a combination of other factors out of this analysis certainly leaves that cause as the most likely reason by a wide margin.

Incidentally, using this same analysis, I would agree that there is in fact some sort of COVID pandemic as well. There was an unusual number of deaths and hospitalizations. It’s not as strong a signal, though. The base rate for flu deaths every year in my FoaF is at least 2, probably, and my FoaF network didn’t have dozens of COVID deaths or anything. But there was something there, whatever it may be; we were noticeably above the base rate.

If The Signal Is This Strong, How Is It Being Hidden?

The mathematical intuitions of the general public are not tuned for an event like this. Usually, when there is news of a large number of deaths, there is some characteristic of them in common, most often where they are located. Sure, lots of people died in that natural disaster, or in that war, and so on, that makes sense to us. But we’re not used to dispersed disasters.

Consider a million deaths excess annual deaths, just to pick a round number to work with (that is, I’m not claiming that’s the current vaccine count, it’s just round). US population is around 350 million, which would mean 1 out of 350 dying. In a conveniently-round FoaF network of 3,500, that’s 10 deaths. Scattered across 365 days, that’s just under one a month. The vast majority of them will be in your FoaFs and not directly your friends, because your FoaF network is much larger than your direct friend network. You have a pretty decent chance that nobody in your direct friend network will be affected at all, even despite such odds.

It’s amazing how little of a finger on the scale it takes to hide that behind “natural causes” and “don’t speculate this could be caused by X or we’ll socially ostracize you”. Especially if, as appears to be the case with the vaccine, they aren’t all identical (that is, 10 heart attacks is harder to hide than 2 heart attacks, 3 strokes, 2 seizure deaths, 3 “unspecified natural causes”, etc). And if you’re mostly just scrolling by them on your Facebook feed once a month and not putting the pieces together.

This is the same effect that made it hard to tell that smoking was bad for you for so long. If you gathered all the people who died of lung cancer in one place, it might be obvious what they all had in common, but when dispersed among the general population, in a population that had a lot of smokers in it anyhow, it’s much easier to explain away “the two smokers I knew that died of lung cancer a few years apart from each other” as just the vicissitudes of life. As strong a signal as “smoking causes cancer” is… it was not above the threshold where people could just look around and see it for themselves. So people smoked for centuries, en masse and society didn’t get more than a vague idea it might be bad for you. ¹

FoaF networks are too small to make such things obvious, but also large enough that everyone experiences things that are simply coincidences. In my own network I know of two rather distant people who both have a genetic disease so rare that I should not have more than one of them in my network, yet, it happens. There’s enough such oddities that can happen that pretty much everybody has at least one somewhere in their FoaF network. So we’re already used to life just having some oddities to it. We have to compare notes if we want to notice that we all seem to have the same oddity.

So it is in fact surprisingly easy to potentially hide this with just a little bit of social pressure and just a dab of censorship making sure that nobody’s allowed to say what’s necessary for people to put the pieces together.

Objective Evidence

So there you go. There’s how you can gather some data from social media, even through the censorship, put your own numbers together, and come to your own conclusion.

Is everything just as media describes? Is the vaccine unquestionably safe and effective, and anyone who thinks otherwise is insane and crazy and without evidence?

Or is your own social media newsfeed over the past few months mathematically screaming at you that something bizarre is afoot?

Discuss on Social Galactic

Post your own base rate, incident rate, and resulting probability on Social Galactic.

(There’s no “like” button here, I have no metrics, no monetization, no ads, and so on. I’m legitimately interested in whether this test works for others.)