3 ms·

Yeah I thought about this and could find a news article that said they did around 5000 jumps a year since they started in 2001 (and they're located in Las Vegas

by amasad 10y ago

Yeah I thought about this and could find a news article that said they did around 5000 jumps a year since they started in 2001 (and they're located in Las Vegas so they I assume most of their customers are first timers). So that is 75000 jumps. In the news I could find two fatalities, and two serious injuries (but let's ignore those for now). Apparently, statisticians use the term "micromorts" which means a death per million activities when talking about risks from things like this. So for this business the track record is 26.7 micromorts. Compared to the base statistics in skydiving--which is 9--this means that this business has 3 times the likely risk. Am I getting this right?

function_seven 10y ago
Sounds like it. But like you said they're almost all probably first-timers, given the location. It's hard to tell if that completely explains the micromort difference or not. Also, it is possible that due to those fatalities, the business implemented better safety protocols as a response and may actually be safer now than it was then. It's my Jack in the Box theory. Back in the 90s there were a couple high profile food poisoning cases (salmonella I think) where customers had died after eating at Jack in the Box. It nearly ruined the company. But my feeling is that the safest time to eat there is a month or so after those events. When all the restaurants would be kicking their food-handling practices into high gear. So now I eat at Chipotle more often than I did before. Shorter lines and probably the cleanest food. I hope. My "theory" may be bullshit.
erroneousfunk 10y ago
You aren't applying Bayes correctly. As a general guide, you need to add the word "given" to your problem statement, assign two "situation A" and "situation B" variables, and then work the math. For example, assigning variables: A = You died B = You're skydiving at that particular dropzone Then: "What is the risk of mortality GIVEN that I am skydiving at this drop zone?" (P(A|B)) "What's the chance that I'm skydiving at this dropzone, given the fact that I died?" (P(B|A)) "What's the risk of my mortality while skydiving?" (P(A)) "What is my probability of skydiving at this dropzone?" (P(B)) P(A | B) = (P(B | A) * P(A)) / P(B) So you calculated P(A | B) in a non-Bayesian way, without finding out the other information to calculate it using Bayes, and then stopped there, like most people do. This is why Bayes is often difficult for people to understand and apply correctly, and, honestly, it's probably not the equation you want for the situation you're looking at. Another approach -- and this seems to be the one you want -- is to calculate a 95% confidence interval using a binomial distribution, to find out if their statistics are really anomalous. Death is a relatively rare event, and, even if they're distributed perfectly randomly, you'll find odd-looking clusters here and there. To figure out if it's anomalous, many people would use the normal approximation to the binomial confidence interval, which would be wrong -- the probabilities of death are so relatively tiny, that they can't be approximated normally (rule of thumb is P(A) x P(not A)x sample size > 5 to use the normal distribution, which this fails), so we need to do an exact calculation. I've done this by hand before, but it's a pain in the butt. That's why we have calculators! http://epitools.ausvet.com.au/content.php?page=CIProportion http://epitools.ausvet.com.au/content.php?page=CIProportion (If you don't trust it, you can use another one) You enter your numbers: sample size = 75000 number of deaths = 2 This gives the exact binomial confidence interval as: [3.23e-06, 9.633e-05] This means that their actual death rate could be anything from .00000323 (that's 3 deaths per million) to .000096 (that's nearly 100 deaths per million) Clearly, you cannot say with any meaningful level of confidence whether or not this drop zone is safer, or less safe, than average. Sorry! Edit: In my Bayes example earlier, I realized that you could actually use it in an interesting-ish way (I guess?) to find out an unknown: "What are the odds that I was skydiving at this particular dropzone, given that I died skydiving?" So: A = You're skydiving at that particular dropzone B = You died :( P(A | B) = (P(B | A) * P(A)) / P(B) We know that: P(B | A) = 2/75000 = .0000267 P(A) = their skydives / all skydives = (75000 / 3,300,000 x 15) = 0.0015 Note: I found out that there were 3.3 million skydives in the US in 2012, so, let's extrapolate that out 15 years as a rough approximation, and limit us to just the US. P(B) = .000009 Then: P(A | B) = (.0000267 * .0015) / .000009 = 0.00445 So, if you died, then the probability that you were skydiving at that dropzone is 0.4%! Note though, that there's some uncertainty in the calculation of P(B | A) (the probability of dying while skydiving at that dropzone) which you need to use confidence intervals, above, to actually figure out. Anyway, I certainly clarified some of my thoughts while writing this, and I hope that it helps you too, figuring out when to use confidence intervals, and when to use Bayes, and why it matters!
- amasad 10y ago
  This is great. Thank you

by amasad 10y ago

function_seven 10y ago

Sounds like it. But like you said they're almost all probably first-timers, given the location. It's hard to tell if that completely explains the micromort difference or not. Also, it is possible that due to those fatalities, the business implemented better safety protocols as a response and may actually be safer now than it was then. It's my Jack in the Box theory. Back in the 90s there were a couple high profile food poisoning cases (salmonella I think) where customers had died after eating at Jack in the Box. It nearly ruined the company. But my feeling is that the safest time to eat there is a month or so after those events. When all the restaurants would be kicking their food-handling practices into high gear. So now I eat at Chipotle more often than I did before. Shorter lines and probably the cleanest food. I hope. My "theory" may be bullshit.

erroneousfunk 10y ago

You aren't applying Bayes correctly. As a general guide, you need to add the word "given" to your problem statement, assign two "situation A" and "situation B" variables, and then work the math. For example, assigning variables: A = You died B = You're skydiving at that particular dropzone Then: "What is the risk of mortality GIVEN that I am skydiving at this drop zone?" (P(A|B)) "What's the chance that I'm skydiving at this dropzone, given the fact that I died?" (P(B|A)) "What's the risk of my mortality while skydiving?" (P(A)) "What is my probability of skydiving at this dropzone?" (P(B)) P(A | B) = (P(B | A) * P(A)) / P(B) So you calculated P(A | B) in a non-Bayesian way, without finding out the other information to calculate it using Bayes, and then stopped there, like most people do. This is why Bayes is often difficult for people to understand and apply correctly, and, honestly, it's probably not the equation you want for the situation you're looking at. Another approach -- and this seems to be the one you want -- is to calculate a 95% confidence interval using a binomial distribution, to find out if their statistics are really anomalous. Death is a relatively rare event, and, even if they're distributed perfectly randomly, you'll find odd-looking clusters here and there. To figure out if it's anomalous, many people would use the normal approximation to the binomial confidence interval, which would be wrong -- the probabilities of death are so relatively tiny, that they can't be approximated normally (rule of thumb is P(A) x P(not A)x sample size > 5 to use the normal distribution, which this fails), so we need to do an exact calculation. I've done this by hand before, but it's a pain in the butt. That's why we have calculators! http://epitools.ausvet.com.au/content.php?page=CIProportion http://epitools.ausvet.com.au/content.php?page=CIProportion (If you don't trust it, you can use another one) You enter your numbers: sample size = 75000 number of deaths = 2 This gives the exact binomial confidence interval as: [3.23e-06, 9.633e-05] This means that their actual death rate could be anything from .00000323 (that's 3 deaths per million) to .000096 (that's nearly 100 deaths per million) Clearly, you cannot say with any meaningful level of confidence whether or not this drop zone is safer, or less safe, than average. Sorry! Edit: In my Bayes example earlier, I realized that you could actually use it in an interesting-ish way (I guess?) to find out an unknown: "What are the odds that I was skydiving at this particular dropzone, given that I died skydiving?" So: A = You're skydiving at that particular dropzone B = You died :( P(A | B) = (P(B | A) * P(A)) / P(B) We know that: P(B | A) = 2/75000 = .0000267 P(A) = their skydives / all skydives = (75000 / 3,300,000 x 15) = 0.0015 Note: I found out that there were 3.3 million skydives in the US in 2012, so, let's extrapolate that out 15 years as a rough approximation, and limit us to just the US. P(B) = .000009 Then: P(A | B) = (.0000267 * .0015) / .000009 = 0.00445 So, if you died, then the probability that you were skydiving at that dropzone is 0.4%! Note though, that there's some uncertainty in the calculation of P(B | A) (the probability of dying while skydiving at that dropzone) which you need to use confidence intervals, above, to actually figure out. Anyway, I certainly clarified some of my thoughts while writing this, and I hope that it helps you too, figuring out when to use confidence intervals, and when to use Bayes, and why it matters!

amasad 10y ago
This is great. Thank you