How to Play Softball During a Pandemic

[clemenslee1]

Just for fun, let us do some back of the envelope math here to quantify the probability that at least one person will be infected with COVID at a softball tournament. Let us just pick my state, OK to do the calculations e.g. we are just assuming everyone at the tournament is from Oklahoma and differences between different counties within the state are ignored.

As of today there are 3618 reported cases in OK and the population of the state is 3.957 million. So the ratio of infected is 3618/3957000=0.000914 hence the ratio of uninfected is 1.0-0.000914=0.9991. To determine the probability that at least one person in a tournament with 500 people attending is infected you raise 0.9991 to the power 500 which gives 0.6329. Subtracting this number from 1 gives 0.3671 e.g there is a 36.71 % chance that a person attending the tournament is infected. If instead that tournament has 250 attendees that number goes to 20.44 % while if that number is 1000 that number goes up to 60%.

Now if you attend 3 such tournaments with 500 people the expected likelihood that at least 1 infected person will attend one of those tournaments is then (1.0-0.6329^3)=0.7465, e.g. about 75%.

Not making any conclusions here, just putting out some actual numbers for people to chew on.


Note:
a) These calculations assume that there is equal likelihood that infected and uninfected people will attend. In reality it is likely that symptomatic infected people will stay home which would mean the probabilities are overestimated. For example, at the moment in OK, especially in my county, a large percent of the cases are in nursing homes. However

b) on the otherhand, the calculations are done based upon the number of confirmed cases which is likely much lower than the actual number of infections.

c) The calculations don't actually give a likelihood of being exposed and infected at a tournament.

I think you could add D) the numbers in OK are for A overall majortiy of people who really haven't been social distancing as much as perceived.. Not saying none have, but a large portion, no. IMO

 

[_MIA_]

I think you could add D) the numbers in OK are for A overall majortiy of people who really haven't been social distancing as much as perceived.. Not saying none have, but a large portion, no. IMO

That wouldn't change the calculations given, my notes were for things that would modify the calculation results or for clarification about what I wasn't calculating. What you are proposing would mean that certain people might have immunity already which would mean for them the risk of infection (which I wasn't calculating) would go down.

 

[clemenslee1]

That wouldn't change the calculations given, my notes were for things that would modify the calculation results or for clarification about what I wasn't calculating. What you are proposing would mean that certain people might have immunity already which would mean for them the risk of infection (which I wasn't calculating) would go down.

Correct. Also scientists have found that the virus dies quickly whenexposed to heat and sunlight and humidity. Which while difficult to assume, weather forcasters are already expecting a overly hot month of may into summer.

 

[_MIA_]

Correct. Also scientists have found that the virus dies quickly whenexposed to heat and sunlight and humidity. Which while difficult to assume, weather forcasters are already expecting a overly hot month of may into summer.

Which again would change risk of infection...which I wasn't calculating

 

[clemenslee1]

Which again would change risk of infection...which I wasn't calculating
Risk of infection would depend on a lot of things and would be almost impossible to quantify.

Sorry man lol

 

[_MIA_]

Risk of infection would depend on a lot of things and would be almost impossible to quantify. However we do know that it would go down when the number I calculated goes down. For example some recommendations are saying that social distancing only be stopped when you have 1 case per million people (not saying that is right or wrong). In that case the probability of somebody being infected attending a tournament with 500 people attending would be 0.05%...

 

[_MIA_]

Now with that said, those probabilities I calculated are probably higher for the flu every March and April in most states. How much higher would determine how similar the risk of infection at a softball tournament is for the flu and COVID since COVID by all indications is (much?) more infectious. You combine that with case fatality rates for the people you are making decisions for and this will give you an indication of how much additional risk you are taking on by attending a softball tournament compared to what you do every flu season.

 

[radness]

Seriously this thread infected by math also....

 

[_MIA_]

Seriously this thread infected by math also....

Math is like spinach, it is good for you.

 

[clemenslee1]

Math is like spinach, it is good for you.

Not If I'm doing the math I finally figured out what I was doing wrong in our math discussion of the other thread, I was leaving off one 0.