Crater lake morons

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Bosterson
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Re: Crater lake morons

Post by Bosterson » June 7th, 2016, 9:40 am

Chip Down wrote:But the thing is, we need to think about cumulative risk. Sure, my chances of getting lost/injured on any particular hike might decrease as my level of expertise increases, but my chances of needing help at some time will still increase with every trip. As an analogy, consider a guy playing Russian Roulette with a six-chamber revolver. If he survives, he moves on to a seven chamber revolver, then eight, etc. On any single round, his odds of survival are better than ever before...but ultimately, he's going to lose.
That's not actually how the statistics work for something like hiking. As an analogy, consider flipping a coin. Every time you flip a coin, you have a 50% chance of getting heads. So if you flip a coin 2 million times, on time 2 million and 1 the odds of getting heads are still 50%. Even if the first 2 million flips were all tails, the odds of each new flip being heads are always the same.

So if the odds of an inexperienced person getting in trouble outdoors are small (like, smaller than getting in a car accident), and the odds of an experienced person getting in trouble are either smaller (due to increased knowledge) or the same (due to balancing increased knowledge with increased level of difficulty), then those odds are the same each and every time that person goes outdoors, regardless of the number of times they went outdoors previously. Thus, unlike, say, radiation exposure, "cumulative risk" doesn't really apply to hiking.

Sorry for the thread drift, but maths. ;)
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Guy
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Re: Crater lake morons

Post by Guy » June 7th, 2016, 9:59 am

Bosterson wrote: That's actually not how statistics work. As an analogy, consider flipping a coin. Every time you flip a coin, you have a 50% chance of getting heads. So if you flip a coin 2 million times, on time 2 million and 1 the odds of getting heads are.... 50%. Even if the first 2 million flips were all tails, the odds of each new flip being heads are always the same.

So if the odds of an inexperienced person getting in trouble outdoors are small (like, smaller than getting in a car accident), and the odds of an experienced person getting in trouble are either smaller (due to increased knowledge) or the same (due to balancing knowledge with increased level of difficulty), then those odds are the same each and every time that person goes outdoors, regardless of the number of times they went outdoors previously.

Sorry for the thread drift, but maths. :idea:
Hmmm, well we are into the weeds now :)

So as I understand it while the odds of you having an accident to not increase with each time the probability does!

To use the coin toss analogy:

You have equal odds of flipping heads each time you flip the coin regardless of how many times you flip it. However the probability that you would flip heads 10 times in a row is only 1 chance in 1024. (1/2)^10 = 1/1024

So while the odds of having an accident do not increase each time you hike (all other things being equal) I'd argue that over time the probability does.
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Koda
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Re: Crater lake morons

Post by Koda » June 7th, 2016, 10:54 am

In studies done on avalanche accidents statistics show the most likely person to get caught in an avalanche is an experienced backcountry skier, unlike novices
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Bosterson
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Re: Crater lake morons

Post by Bosterson » June 7th, 2016, 11:14 am

Guy wrote: So as I understand it while the odds of you having an accident to not increase with each time the probability does!

To use the coin toss analogy:

You have equal odds of flipping heads each time you flip the coin regardless of how many times you flip it. However the probability that you would flip heads 10 times in a row is only 1 chance in 1024. (1/2)^10 = 1/1024

So while the odds of having an accident do not increase each time you hike (all other things being equal) I'd argue that over time the probability does.
I really wasn't trying to start thread drift on this! :lol:

But per above, "odds" and "probability" are the same thing.

Again with coin tosses:

As you note, the "odds" (ie, probability) of getting 10 heads in a row is 1/1024. (This is much smaller than 50%!) But the chance of just the 10th flip being heads is still just 1/2 (50%).

Put it another way: if the probability of a hiker getting in trouble on a single hike is p, and the hiker goes on n hikes, then the chance of them getting in n accidents (ie, on every hike) is p^n, but the chance of them getting in an accident on just the nth hike (ie, on a random hike at any point in time) is still just p, and n can be any number you want for this to be true.

In other words, the probability of an accident happening on a single, random hike doesn't increase over time. So you could debate about whether novices or experts are more likely to need rescue (Lurch seems to have answered this: it's the novices), but the number of hikes itself isn't a factor. Hiking is as "dangerous" as the p probability, every single time you go out, and that doesn't change unless the circumstances themselves become more dangerous.

So if walking up the pavement to the Benson Bridge to look at Multnomah Falls isn't very "dangerous" (ie, p is extremely low), you could do it 1000 times and you're no more likely to get injured on the 1000th time than the first time. (In fact, if, say, p is 1 in a million, you'll probably not ever need to be rescued there.) But if you go when it's icy, maybe the objective "danger" (p) is higher. But this is a function of the conditions - it's a different p because the hike itself is different. The number of times you go still doesn't matter.
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Re: Crater lake morons

Post by Lurch » June 7th, 2016, 11:38 am

There's lots I could say here, but most of it I probably shouldn't say :lol:

A long time ago I learned that there are essentially 3 types of people out there (especially when it comes to hiking/wilderness skills)
  1. The people who know they don't know - These are your newbies to the woods, the ones who're green, sticking to well established trails and routes, relatively timid about venturing too far because they know they lack in skill and experience
  2. The people who know they know - These are the 'professionals', who clearly know their limits, understand their strengths and weaknesses, and like to toe the line for the rush of it, but know when to call it and come back another day.
  3. The people who don't know they don't know - These people are really in group 1, but think they're in group 2. They are the dangerous ones, who over-reach without realizing it. They usually succeed, but that's mostly on luck, not because of skill. They're overconfident, and don't have an full understanding of the consequences of the game they're playing
Take your time, and always be reviewing which category you may fall into at any given moment on any given topic, because being in #3 is the hardest to self-identify.

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Guy
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Re: Crater lake morons

Post by Guy » June 7th, 2016, 11:50 am

Lurch wrote:There's lots I could say here, but most of it I probably shouldn't say :lol:

A long time ago I learned that there are essentially 3 types of people out there (especially when it comes to hiking/wilderness skills)
  1. The people who know they don't know - These are your newbies to the woods, the ones who're green, sticking to well established trails and routes, relatively timid about venturing too far because they know they lack in skill and experience
  2. The people who know they know - These are the 'professionals', who clearly know their limits, understand their strengths and weaknesses, and like to toe the line for the rush of it, but know when to call it and come back another day.
  3. The people who don't know they don't know - These people are really in group 1, but think they're in group 2. They are the dangerous ones, who over-reach without realizing it. They usually succeed, but that's mostly on luck, not because of skill. They're overconfident, and don't have an full understanding of the consequences of the game they're playing
Take your time, and always be reviewing which category you may fall into at any given moment on any given topic, because being in #3 is the hardest to self-identify.
Yep, I think that says it all very succinctly!
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Re: Crater lake morons

Post by Aimless » June 7th, 2016, 2:26 pm

Just as a non-mathematical sidelight, from reading about experienced hikers who get into serious life-threatening trouble, their situation is quite often the result of multiple compounded errors, rather than a single error. For example, they take a hike on the spur of the moment without much planning and leave no itinerary with anyone, then they omit the ten essentials because they anticipate the hike will be brief or easy or both, then partway through they are tempted into an offtrail side trip, or they start too late and walk far past their intended turnaround time, then it gets dark, or they injure themselves, or it rains and they get hypothermic, etc.

At each step of the way they accept additional risks, seeing each one in isolation as a small risk, but in reality they have been compounding their risks until the aggregate risk is much higher than they recognize. Then something goes wrong and they find they are immediately deep in the soup. :shock: A novice can be so inexperienced that they do not even see a risk as risky, but experienced hikers who can recognize risks sometimes fail to notice when they've put a series of small risks together into something much larger and more dangerous.

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