How many victims before we all know someone?

The Quarantine Zone
21

I’m not a statistician but my husband (who happens to be the OP :D) and I were discussing this topic a few days back. The closest analogy would be the birthday question: How many people would you need to have in a group to have a better than 50% chance that two people have the same birthday.

https://betterexplained.com/articles/understanding-the-birthday-paradox/

You’re looking not at the odds of any given person having your birthday, but the odds of every person not having your birthday.

In a room of 23 people, there’s a 50% chance that there are two people with the same birthday. (23*22) / 2 = the number of possible pairs overall in the room - because person 1 has to check himself against 22 people, person 2 has to check himself against 21 and so on.

Then you take the odds of someone’s birthday NOT matching yours: 364 / 365 (let’s ignore leap years). So everyone in the room has to not match you. Then everyone else in the room has to not match person 2, and so on. Basically, (364/365) raised to some power - in this case 253 - gives you 50%.

If you have a room of 100 people. it’s (100*99) / 2 comparisons. Excel gives me a 0.0001% chance of not having a match.

I would think we could extrapolate that logic, making some out-of-thin-air assumptions about:

  1. How many people are in the room with you = how many people you are at least on speaking acquaintance with. That would include your family, friends, co-workers, the cashier at the grocery store whom you know by name, and so on. No clue what that would be - but let’s say it’s 100 people.

  2. What the death rate is per million of population. New York’s right now per worldometers.info is 478. So the odds of any one person having died is .000478 (right now - that is changing daily). And the odds of that person NOT having died is 0.999522.

So, using the birthday logic: if you know 1 person, you have less than 1% chance of knowing someone who died.

If you know 10 people, you have a 2% chance of knowing someone who died.

If you know 100 people, you have a 90% chance of knowing someone who died.

This all assumes that you and everyone you know are in New York. By comparison, California has 17 deaths per million population. At that rate, in a circle of 100 people you have about a 9% chance of knowing someone who died. In a circle of 200, you have a 31% chance of knowing someone who died.

So - you have to do some further extrapolation to get to the point where more than 50% of the people in the US know someone who died of COVID. I used Excel and just bumped up the deaths per million until the calculation said about 50%. At 140 deaths per million, and 100 people in your circle, you’re at the 50/50 mark.

22

I’m defining “know” as someone I would have greeted by name if I had met them in the street, at any point in my life. Such as a former classmate or work colleague, even if I wouldn’t have recognized them decades later. No doubt there are one-time friends whose subsequent death has not been reported to me.

23

I’m revisiting my own math.

The birthday scenario deals with “in a group of people, what are the odds that there is a pair of people with the same birthday as each other”, NOT “with the same birthday as you”.

“Same birthday as you” would be (364 / 365) to the 22nd power:
0) you

  1. 364/365 has a different birthday from yours
  2. 364/365 has a different birthday from yours
    So for neither to share your birthday, it’s ( 364*365) squared.
    Taking that out to 22 people, there’s about a 6 percent chance that one of them has the same birthday as you.

I calculated it out - and to find someone with the same birthday as you with 50% probability, you have to be in a room full of about 250 people (which violates some social distancing laws, I’m quite sure, unless you’ve got a really big Zoom call going on).

Using the same logic:
(1 - 140/1,000,000) to the power of # of people in your group

You’d have to know about 750 people to have a 10% chance of knowing someone who has died from it. You only hit 50% around 4800 people.

If the death rate is 552/1,000,000 (NY’s most recent) then at about 180 people you have a 10% chance of knowing someone has died. You hit 50% around 1238 people.

I think I must be doing something wrong here, however. It doesn’t make sense that to quintuple your chances of knowing someone who has died, you have to MORE than quintuple the number of people you know. I’d love to hear from someone who knows what they’re doing, to see what I’ve done wrong :).

24

Since I last posted a man I’ve known for over 20 years has died (Just noticed I had posted about him before) along with my best friends uncle. 2% of my town has tested positive and it’s very hard to get tested here so I’m sure the infection rate is much higher.

I had a very good friend die from a “flu” that wasn’t responding to treatment a few weeks before all hell broke out here and I now believe this is what killed her.

25

Consider a small town in the middle of nowhere, where everyone knows each other, but outsiders have little contact with the town. Sure, there’s some contact, like the guy that drives the truck that brings stuff to the store in town, but not very much. It’s possible that the virus never comes to that town at all. And while some folks in the town might know someone outside the town, some folks won’t. So you’re never going to get literally everyone: Even in the US, there are some places that, while not completely isolated, are isolated enough.

26

On the other hand I still don’t know anyone who’s even got the disease including friend of friend situations. I think the suffering in NY and NJ is skewing the national numbers. We’d need about 1,800 deaths here in Colorado before we reached my projection above and we’re at about 700.

27

I think you’re right. It makes sense that the chance increases more slowly than linearly, because as the number increases, the chance approaches 100%, but never actually reach it. Even if you know 3600 New Yorkers, the chance is “only” 86%. (If it were linear, it would be 200%.)

28

…on the other hand, this study says an average person recognizes 5000 faces. Of course that includes people you’ve only seen on TV, or seen pictures in history textbooks, etc. But we’re not far off from the point where most people know of someone who has died.

29

LurkerInNJ, I’m sorry for your losses.

30

I’m afraid the states that haven’t been affected are just behind NY and NJ, and that few if any states are doing things to effectively prevent corona virus infections.