I've always had a bit of an interest in the quirks of probability, statistics and our regular inability to effectively assess risks in our lives.

I have an example of how we can have these logic missteps, you can try this and maybe make a few quid into the bargain.

Choose any FA cup final you like, doesn't matter which. Now consider the number of people on the pitch during live play. That would be twenty three. Eleven players on each team and the referee. Each of these people has a birthday and that day could be any one of three hundred and sixty five days. Ignore 29th February and leap years for now.

So we have 23 people and three hundred and sixty five different potential birthdays. What is the chance that two or more players share the same birthday? Not born on the same day but just share the same birthday?

We'll have a bet, say £10. But you get to decide which way you want to bet and I have to take the other choice. So you can say "I do not think any of the 23 players share a birthday." and if you are right you win the tenner. Or you can say "I think two or more people do share a birthday." and if you're right you again win the £10. I have to take the other option.

Statistically which choice seems the more likely. 23 people on the field with 365 possible birthdates to share. If you decide that it seems unlikely that two people share the exact same day and month you would not be alone. Almost everyone would choose that a birthday is not shared and almost everyone would be wrong! It's slightly more likely that two people on that football field do indeed share a birthday. 50.07% to be exact. So you're only a tiny bit wrong, but make that choice many times and you will end up loosing money. If you play the same game but include four substitutes, two linesmen and two team medics, choose right - then you're onto a winner as it's close to a 75% chance that a birthday is shared.

We make this bad choice due to coming at the problem backwards and looking at 365 days and 23 people and somehow comparing the big number of years to the small number of people and making an assumption. But the way to think about the problem is backwards.

- If you have two people on the pitch then there is one way they can share a birthday, it's just to share it with each other, there is no one else. So the chance is 1/365. Pretty clear.
- But if you have three people there are three ways they can share a birthday A & B, A & C and B & C. That's a 1/222 chance or about 0.8%.
- Four people get more likely, obviously. There are six ways four people can share a birthday - A & B, A & C, A & D, B & C, B & D, C & D. That's 1/61 or 1.63%
- Five people gives you 1/37
- Six people gives you 1/25
- and so on until 23 people which is just better than 1/2 or 50.729%

What we do subconsciously is think about the chance of two

I began thinking about this as it's quite worrying that this problem understanding probability and risk (and I am just as able to make these mistakes as anyone else) seems to be affecting our daily lives, Especially at the moment.

There is some good evidence that the Oxford Vaccine can very occasionally produce blood clots which can themselves sometimes prove fatal. However there is also mounting evidence that Covid 19 itself can cause blood clots. These blood clots can occur in the under 30 age group as well and seem to be higher in women aged under 60. So people are worried about whether they should take the jab and governments around the world are making some arbitrary decisions which they claim is to protect the public. But is this sound thinking or are politicians as easily confused by the statistics as the rest of us.

Currently the belief is that in the UK there is about a 1 in 250,000 chance of developing a blot clot after taking the Oxford Vaccine.

In the UK 36,000 people a year develop blood clots for any reason, which is about 1 in 1,833 people regardless of whether they had Covid 19 or a vaccine or neither.

UK Women seem to be far less "wave their arms around in blind panic". There is a 1 in 2,000 chance of developing clots when taking the contraceptive pill and there are zero restrictions on prescribing that to otherwise healthy women!

And most telling of all is that the chance of getting blood clots from actually catching Covid -19 itself is believed to be 39 in a million (more data coming in all the time), which is significantly higher than 4 in a million from the vaccine. 8 to 9 times higher. Add the fact that 30% of blood clotting seen in Covid 19 patients is in under 30's and the statistical chance of getting a clot from the disease is still a lot higher for young people than from the vaccine.

Now of course some people who have the vaccine were actually never going to catch the virus. So statistically it's possible someone who would have lived to a ripe old age actually died having a vaccine they in fact didn't need. But Covid 19 isn't a one time deal. If everyone decided not to get jabbed then eventually everyone would catch the disease or one of it's increasingly 'interesting' variants and far more people would die from clotting let alone all the other far more common ways Covid 19 can kill you -

Hypoxia

Sepsis

Multiple organ failure

Septic shock

Respiratory failure

cardiovascular failure

Pulmonary embolism (correct me if I'm wrong Dr Chaos :) )

I'm speculating now but I guess the reason the UK has shifted to not giving the Oxford vaccine to under 30's is more about pandering to the Me First Culture and less about actually saving lives. It's also very telling that all the medical experts and Health Boards and authorities (MHRA (UK), EMA (Europe), WHO (world)) are of one clear voice. listen to the science and follow the data "Get the jab whether it's Moderna, Pfizer, Oxford AstraZeneca, Johnson & Johnson etc. To do otherwise is idiotic"

While politicians, Governments etc seem not to be so clear and maybe a bit "How do I appear to be Ministerial, listen to the worries of the general public (moronic or not) and get re-elected next time?"

Oh half three already, time to walk the dog :D

https://www.ox.ac.uk/news/2021-04-15...id-19-vaccines ]]>