- Oct 2, 2017
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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