To ask you to do some Corona related maths

[mathdoc]

I've been following some of the (many) corona threads here and I've realised that I've been doing a virtual eye-roll everyone says that they have been doing their own risk assessments, because I think assessing risk is incredibly hard. However, on reflection this might just be me being very arrogant (it has been known!) so I thought I'd get some actual evidence by asking you to try this little maths question. (See the disclaimers at the bottom for people who are even more pedantic than me). I'm not claiming that I'm right, because I'm just as liable as everyone else to make mistakes with this, so I'd be very happy to be corrected. I'm not expecting people to do calculations for this (although feel free if you like that sort of thing) - it's more about checking people's intuition.

The question is this. Suppose that 3 people meet up and you are one of them. Let's suppose that there is a particular probability of you getting the virus in this situation, and there's also a particular probability of the virus being transmitted between two people attending.

Now suppose that instead 6 people meet up.

1. By approximately how much has your risk of catching the virus increased?

A. Basically no change B. Doubled C. Increased by a factor of 2.5 D. Increased by a factor of 12 E. Increased by a factor of 20 F. Increased by a factor of 80

1. By how much has the risk to society of a "virus transmission event"increased.

A. Basically no change B. Doubled C. Increased by a factor of 2.5 D. Increased by a factor of 12 E. Increased by a factor of 20 F. Increased by a factor of 80

Disclaimers for those interested in the fine print.
I'm assuming:

• that these people are all chosen at random (e.g. not already in the same bubble)
• that everyone in the meeting spends roughly the same time with everyone else and in the same way, so that the probability of transmission for each interaction is approximately the same.
• that the probability of transmission in any individual interaction is very low, and independent of any other interaction

Obviously some of these assumptions are dubious, but as long as the probability of transmission is low I don't think that they have a large impact on the comparison I'm looking at.

The numbers 3 and 6 have been chosen to be illustrative. I'm not suggesting this is anything to do with the current rules - in particular whether or not they are sensible. This is just to see how good people are at assessing risk.

Depends

You assume that the others have self isolated, wear masks, don’t use public transport, aren’t NHS front line workers, haven’t been diagnose with the disease. Stick to the guidelines on hand washing etc

Because some people are selfish - in fact I am seeing an awful lot of selfish acts on here recently because they have ‘rights’

I think you are being a bit arrogant sorry. I don't claim to know stats but I do know enclosed space equals more risk. More people equals more risk.
Therefore my risk assessment is 'is the increased risk of illness worth it for the potential benefit to me?'. Pub? No chance. I hate them. Gym class? (Which is hypothetical at the moment) worth it in my own assessment of risk.

I'm rubbish at maths, but when people say they have risk assessed, I would consider that they have assessed their personal circumstances. Weighed up the likelihood of getting very unwell/passing covid on vs keeping life on hold.
I don't think they literally sit down and do statistics on the likelihood of that happening.
Eg, for me, I am young, reasonably healthy and not in contact with anybody vulnerable. My own risk assessment for what I feel comfortable doing based on that is going to be different to someone who has underlying conditions, is elderly or otherwise higher risk.

Sorry - I should have checked before posting. The options were for a different variant. The options for both should be:

A. Basically no change
B. Doubled
C. Increased by a factor of 2.5
D. Increased by a factor of 5
E. Increased by a factor of 10
F. Increased by a factor of 100

but as long as the probability of transmission is low I don't think that they have a large impact on the comparison I'm looking at

But it's completely relevant, if the risk is of transmission is high a doubling or an eighty fold increase in risk really, really matters.

When the risk is extremely a low, both of those even are completely irrelevant - 1 in million or 80 in a million are similarly as irrelevant, and will be for many both lower than the risk of not meeting up, and certainly lower than the risk from travelling to meet up in car.

This is not the kind of thing people mean when they refer to risk assessments in the current situation. It’s usually about choosing between two options that are (currently) considered risky - eg going into a medical setting to have something non-Covid related assessed, but risking transmission; or the risks associated with developing PND for an individual woman (and her household) if she doesn’t have external family support vs risk of transmission of coronavirus between households.

It’s a nice idea, and I think you are right about how we are probably not all that good generally about assessing true risk, but you’re just testing people’s maths skills rather than finding out anything about people’s risk perceptions in a meaningful way.

At the moment, my chance of passing on the virus is extremely low as I'm really having so very little social contact (likewise the rest of the household) that I'm unlikely to have caught it in the first place.

If I meet up with friends outside who are also having little social contact then they are unlikely to have it too, and as long as we meet up whilst distancing even if one of us has it the chance of passing it on is tiny.

On the other hand, if I was commuting by public transport I might have very different views.

What your first question doesn't take into account is the effect of actually catching it. This plays quite a large part in people's calculation of personal risk. For example, I am relatively young, not obese and with no underlying medical conditions. If I catch it I am highly likely to recover. I am therefore more likely to take a risk with a higher probability of catching the virus than say, an overweight person in their 70s.

If it's any consolation I'm doing a huge eye roll at this post.

So, what are the answers? Am I being thick, I really dont get the question.

Bladeofgrass

I think you need to reread the post!

BlusteryLake it’s more complicated even than that because people do think about their risks of transmitting to others too - eg if they have a parent who is vulnerable and who they want to see over and above seeing a friend.

It depends who is meeting - eg me meeting my parents, retired staying at home, shopping once a week wearing masks (previously worked nhs so they know how to wear a mask). I am wfh, dh is wfh, ds is homeschooling and dh goes once a week to the shop, then that is a different risk to people meeting someone who work on a covid ward or customer facing role etc. So your maths is over simplyfied.

What people do is decide what they want to do, and work backwards from that to try and justify it to themselves (when they don't need to). So for example, there is a risk to hugging granny, but if someone wants to they will choose to do that and say well we probably won't get it anyway. Actual stats etc are pretty much rendered useless when people are able to do what they want anyway.

In fairness to the OP she has made it clear what the assumptions are and this kind of question is always going to be oversimplified. But the trouble is that the question doesn’t actually give the “evidence” she is seeking

Mathsdoc..you won't get a proper answer unless people are good at maths/ stats . I'd say you are right that wihtout this basic knowledge risk assessments ( even personal ones) are pretty much impossible.

What people generally mean by risk assessment in his context is ill take what I want to hear based on my anxiety levels and my personality and base my decision on that.
I'm not great at maths and I'd always say that people are as a rule terrible at assessing risk. 'I too roll my eyes a bit at I do my own risk assessment '

As to your question. In the first case I'd guess ( and it is a guess) that since the situation has changed that the risk is doubled. Catching from 6 people instead of 3.

In the second, the risk is maybe 12 times?.

If say the op has an excellent point actually in that even in this incredibly simplistic scenario that would never exist in real life, noone here has even tried to answer the question . I'd hazard a guess that for most it is because they don't know the maths I include myself in that ). If we don't know the answer to this simple question how the can we asses our risk in the much more complex real world?

I'm going to answer this with some maths.
Which is somewhat dangerous as probability & stats was always my weakest area.

Say I do have the virus.
Say my probability of passing it to someone in a social situation is 0.1
That means my probability of not passing it on is 0.9

So if I meet up with 2 others, my chances of not passing it to either of them is 0.9^2 = 0.81
So my chances of passing it to at least one of them is 1-0.81 = 0.19 ~0.2

If I meet up with 5 others under the same conditions, my chances of not passing it to any of the 5 is 0.9^5 = 0.59049~0.6
So my chances of passing it to at least one of them is now 1-0.6=0.4

So it has approximately doubled.

However, that is all assuming I do have the virus. Which I probably don't. So say my chance of having the virus is 0.0001 (1 in ten thousand).

So both those probabilities of passing it on need to be multiplied by that.

So I have gone from 0.1 in 1-1 contact to 0.00001
And from 0.2 in 1-2 contact to 0.00002
And 0.4 in 1-5 contact to 0.00004
So doubled but doubled from a tiny amount to still a tiny amount.

It’s not just about probability as other posters have said.
DS1 is 16 and went back to school for a week. We reasoned that he was at lower risk for transmission due to his age. Even if he did catch it and bring it home no one in the family is especially vulnerable. Additionally DH and I are both working from home so self isolation wouldn’t be a major issue etc.
It wasn’t about absolutely risk but contextualised risk.

absolute risk

My DD also attempted to go back to school as we took the view that risk&impact of her catching the virus was less than the known impact being at home has had on her mental health.

Years ago I was quite good at that kind of exercise but I’m out of practice and can’t be bothered these days. I also think people start from entirely different assumptions when they’re thinking about the current pandemic. I suspect most people who have been working from home, only going out for essentials, and not in contact with anyone diagnosed with CV19 assume they’re at low risk of encountering the virus, and also that anyone they now socialise with is also at low risk for similar reasons.

I’m reminded of those STI posters from the 1980s which suggested that if I had sex with one man I risked infection from any of his previous partners, and their previous partners etc. I don’t think they were effective at stopping me from shagging anyone because the inclination to have sex was considerably stronger than the fear of syphilis, especially as I’ve never met anyone with syphilis (not that they’d tell me, right?). And also, we want to believe that people we like are like us, and therefore careful (which we can’t be sure of).

That’s a long way of saying I think risk assessment is psychological rather than mathematical for me and probably most people I know. So I know the risks are much higher than I think because I don’t have all the information, but also I’m going to meet three friends outdoors on Tuesday because I’m slightly desperate. I’d be fairly unlucky if this led to infection with Covid 19 (or syphilis).

“ If say the op has an excellent point actually in that even in this incredibly simplistic scenario that would never exist in real life, noone here has even tried to answer the question . I'd hazard a guess that for most it is because they don't know the maths I include myself in that ). If we don't know the answer to this simple question how the can we asses our risk in the much more complex real world?”

I am sure this will be the OP’s “gotcha”

Some very interesting responses! Many thanks.

I totally agree that determining the risk of something happening is very different from looking at the expected impact (although that too is a minefield) and risk assessment should include both of these things. I've just focused on the first of these which I think is important, but certainly not the whole story.

Several people has pointed out that, no matter what the factor of increase is, when it is applied to a small number the answer will still be small. This is true for any individual meeting but when scaled up many millions of people each increasing their risk substantially can have massive population level effects.

This discussion reminds me of when I read "The 5 languages of love". Not about love obviously, but analogously when I'm debating something I work in numbers, even hypothetical ones (thankfully my partner is the same!) Just like the five language of love, I've come to understand that my way of communicating is neither better nor worse than others, but the problems come when I expect others to use the same language they use. I guess I wanted to understand more what people meant when they said "done a risk assessment" as in my mind that is really really hard, and I wanted to get a sense of whether they were doing what I understand as a risk assessment badly or rather (it seems based on this thread) they had a totally different understanding of what a risk assessment is.

I think your question is worded in an overcomplicated and confusing manner and it's a bit tricky to chose the numbers 3 and 6, as if you are trying to catch people out. The size of the gathering has doubled but if you are asking people to calculate the risk to them of catching the virus at a gathering of 3/6 people that includes them, what you are actually asking is if "they" meet 2 or 5 people.

I can read a scientific paper and interpret the data without thinking but reading your question made my head hurt