Probabilities and the Math of Travel in Avalanche Terrain

I am a longtime backcountry skier and lately I have been thinking about the math of skiing in avalanche terrain. On some basic level are we ultimately just playing a game of chance/probabilities if we ski in avalanche terrain? Of course those of us who have made a practice of backcountry travel do our best to minimize exposure through terrain management, snow analysis/knowledge, travel protocol, rescue equipment and skills, but if you travel in avalanche terrain ultimately it seems to me that your risk gets down to a game of probabilities that the above practices can mitigate but perhaps not as much as we'd like to think. The odds really start to stack the longer that you are in the game. The recent rash of high profile pro deaths who supposedly knew their stuff have made me think more about this.

I dusted off my rarely used math probabilities knowledge and played with some numbers to illustrate.
See here for the math theory applied to dice: http://hyperphysics.phy-astr.gsu.edu...math/dice.html Feel free to correct me where I'm wrong as I don't claim to be a probabilities expert.

To start lets say that you're ignorant and/or crazy. You ski on high danger days in known repeat offender slide paths. You're odds of triggering a slide are say 30%. It doesn't take a rocket scientist to figure out that you're probably going to trigger an avalanche, if not on the 1st run, then probably on the 2nd, 3rd, 4th, 5th or the 10th. You'll probably learn one way or another pretty fast.

But lets compare with a different situation and say that you're a seasoned traveller in the backcountry. You have taken classes, read books, practiced in the BC for years, etc. You're even so good that you can make the call to a 99.5% good accuracy rate. 995 times out of a thousand, when you chose to ski avalanche terrain, you will not trigger a slide because of your decisions. But lets say that you do that over the course of 20 years, 25 times a year, so 500 times.

Then you're chances of never in those 500 times of avalanche terrain travel of triggering a slide are:
(995/1000)^500 = 0.0816 or 8% or conversely you have a 92% chance of at some point triggering a slide. Basically the math of repeatedly probabilities means that you are highly likely to trigger a slide and at those kind of probabilities, you're most likely going to trigger more than one or two.

Once you've triggered slides then the math of survival comes into play. The math will of course vary, where if you're skiing mellow bowls with several skilled partners you're odds are better versus if you are skiing solo or skiing big couloirs over glaciers, trees, cliffs, or terrain traps. But the math still works against you if you are getting into slides. Lets say that the survivability is 70% and you are in 5 slides in your life. We run the same math as above and you have a 83% chance of dying in an avalanche. Survival odds = (7/10)^5 = 17% or 83% chance of dying.

So what? Well I guess maybe it might make you quit BC(or at least Avy terrain) skiing, as some friends of mine have. Or maybe you shrug it off and accept the odds as the price for the joy of glisse in steep terrain. But for me the lesson is that the math is always at work and that my imperative is to minimize my exposure whenever possible in both when/where/if I choose to ski in avalanche terrain. 99.5% isn't good enough over many years of repeated exposure. You've got to basically be perfect.

What do you think?

Tremper has an actuarial table in his 2nd edition of Staying Alive in Avalanche Terrain. It's been too long since my one and only statistics class to validate his logic, but you might want to check it out.

Cheers,
Thom

What do I think?

That if you ski enough steep, snow covered mountainsides you will encounter avalanches.

if ya go outside in storms you'll probably encounter lighting
if ya party to hearty overdosages can happen
if ya surf in shark infested waters.....
perfections a myth
as is mastery of mother nature

Risks can be mitigated but life is not riskless.

A careful BC skier is probably more likely to die from his weakness for marlboro's or his appetite for Big Macs.

All figures below are for U.S. residents.

Cause of Death	Lifetime Odds
Heart Disease	1-in-5
Cancer	1-in-7
Stroke	1-in-23
Accidental Injury	1-in-36
Motor Vehicle Accident*	1-in-100
Intentional Self-harm (suicide)	1-in-121
Falling Down	1-in-246
Assault by Firearm	1-in-325
Fire or Smoke	1-in-1,116
Natural Forces (heat, cold, storms, quakes, etc.)	1-in-3,357
Electrocution*	1-in-5,000
Drowning	1-in-8,942
Air Travel Accident*	1-in-20,000

http://www.livescience.com/3780-odds-dying.html

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A careful BC skier is probably more likely to die from his weakness for marlboro's or his appetite for Big Macs.

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Those 2 words speak volumes.

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Originally Posted by galibier_numero_un

Tremper has an actuarial table in his 2nd edition of Staying Alive in Avalanche Terrain. It's been too long since my one and only statistics class to validate his logic, but you might want to check it out.

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Found it on Google Books https://books.google.com/books?id=xM...0table&f=false

Temper seems to come to a very similar conclusion as my ciphering, although he uses a lower fatality rate once caught. I think that there is more than a 10% fatality rate from trauma alone. I'd chalk that up as a lesson from recent years - although more people are getting dug out quickly by their friends a lot of them are dying from trauma inflicted.

I see your points about risk elsewhere. In the end the odds of dying somehow are 100%

There is a paper on this by the usual euro people:

http://arc.lib.montana.edu/snow-scie...12-501-505.pdf

http://mt1.powderguide.com/fileadmin...statistik1.jpg

Same thought experiment here fyi

http://www.tetongravity.com/forums/s...509-Competence

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Originally Posted by Coño Frío

Risks can be mitigated but life is not riskless.

A careful BC skier is probably more likely to die from his weakness for marlboro's or his appetite for Big Macs.

All figures below are for U.S. residents.

Cause of Death	Lifetime Odds
Heart Disease	1-in-5
Cancer	1-in-7
Stroke	1-in-23
Accidental Injury	1-in-36
Motor Vehicle Accident*	1-in-100
Intentional Self-harm (suicide)	1-in-121
Falling Down	1-in-246
Assault by Firearm	1-in-325
Fire or Smoke	1-in-1,116
Natural Forces (heat, cold, storms, quakes, etc.)	1-in-3,357
Electrocution*	1-in-5,000
Drowning	1-in-8,942
Air Travel Accident*	1-in-20,000

http://www.livescience.com/3780-odds-dying.html

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Except that is an incomplete argument, and basically false as a result. Everyone dies eventually, no shit.

The number one cause of death for males 18-40 is (usually) trauma, the same age as *most* people who get buried and die in avalanches. Almost nobody 18-40 dies of heart disease, very few of cancer.

Compare death rates of backcountry skiers during their prime years (work, mortgage, family) and see what you come up with. It ain't going to be pretty.

(Not taking a position on the thread, just this argument).

the world is a car and youre a crash test dummy.

Wow. So those odds at my rate don't win me powerball. Fack! But I should be dead by now.

Fuck me. But seriously:

I'm still not against giving up on taking a few months off and revisiting terrain evaluation after a recent 15 year track record of getting lucky I suppose. It's not luck. SFB or BobAthy or Klaus might agree.

Knock on wood, but sometimes you just feel, with science and math as your friend, that a brief respite is worth it.

The bank needs to be refilled. Your eyes need to focus on the new normal. I know that is a crappy corporate term, but shit is changing.

I'm not the IMF or the world bank, but I have narrowed avi fatality risk down to a few major categories that are totally ignored.

The first is acknowledging that terrain is not familiar given what is coming to be unusual weather cycles. This is why the Euro's are dying.

The second is that, given the above, the locals, refuse to adapt. You cannot get blood from a stone.

A bonus third is that folks just don't know when to cool off, and ratchet down to suss shit out. That might actually take a season to not ski all those familiar lines. Big, or small. The planet doesn't discriminate. But skiing that one line that you always ski when you think it's good to go may not be. Heed. Use that time to explore new lines until you are proven mostly kinda right, or not;

It's pandemonium.

I'm more of a round the edges kinda guy. Knock on wood, it works. I still throw lines, am not super scared, but it's a calculus. Daily. I don't post about it, I don't share. I do the work. It's come to be a micro science thing for me.

Knowledge, depth with the environment, experience. That's my start. Just a start.

Then comes the hard part with gut, science, and a dearth of feeling for "human factors".

That is the fuck up. That is what kills. Other people. I'm not immune, but I try to isolate as much as possible.

That's what I count on.

Haven't had a single pull over in my life driving, and have met the avi dragon a couple times, but from the right POV.

I think it works.

Come up with your own survival strategy. And just make it, for me, to survive and not get hurt, your first priority.

Given that sermon above, enjoy it after your coffee calculus, trust yourself, and enjoy the pow.

Namaste.

One of the subjects I enjoyed the most back when I was studying Industrial Engineering was statistics. I had an AWESOME teacher.

I have a very vivid memory of him defining what probability is on our very first class. He proceeded to give us numerous definitions on probability according to different people. And after that he said: "do you want to know what probability REALLY is? It is just a number between 0 and 100."

Did you guys understand it too? Or should I expand on that?

Oh, and there's one FACT on skiing and probability that I can give you: if you decide to quit BC skiing because you're scared of dying in an avalanche after reading a couple of statistics, there is a 100% probability that you will never have the same fun on skis again.... but there won't be a 0% chance of you dying while caught in an avalanche!

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Originally Posted by Nick Martinez

One of the subjects I enjoyed the most back when I was studying Industrial Engineering was statistics. I had an AWESOME teacher.

I have a very vivid memory of him defining what probability is on our very first class. He proceeded to give us numerous definitions on probability according to different people. And after that he said: "do you want to know what probability REALLY is? It is just a number between 0 and 100."

Did you guys understand it too? Or should I expand on that?

Oh, and there's one FACT on skiing and probability that I can give you: if you decide to quit BC skiing because you're scared of dying in an avalanche after reading a couple of statistics, there is a 100% probability that you will never have the same fun on skis again.... but there won't be a 0% chance of you dying while caught in an avalanche!

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i dig it when jongs post shit i like
gives hope for the future
i fear the aggro dipshit driver multi car power passing for inbounds pow fever and clueless miss texting/twitttertwatting social media whore drivers more than avvies
i really don't get peoples endless obsession w/ avvy deaths or shark attacks considering how low the #rs truely are.

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Originally Posted by powtario

Except that is an incomplete argument, and basically false as a result. Everyone dies eventually, no shit.

The number one cause of death for males 18-40 is (usually) trauma, the same age as *most* people who get buried and die in avalanches. Almost nobody 18-40 dies of heart disease, very few of cancer.

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Good point. I guess I was looking at it from my perspective, which is a few years into the kill zone for HD and the Big C. Perhaps the answer is that most skiers in their prime should focus on getting their thrills inside the ropes leaving the BC for those of us holding a half day life ticket.

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Originally Posted by klar

There is a paper on this by the usual euro people:

http://arc.lib.montana.edu/snow-scie...12-501-505.pdf

http://mt1.powderguide.com/fileadmin...statistik1.jpg

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Interesting paper, but utilizing massive assumptions on the fatality stats. I'm also wary of the relevance of their euro-centric model to other areas. From my limited experience (in Europe), and compared to my backyard, I saw a far more cavalier attitude to death, a complete disregard for safe protocols, a sense that rescue was just phone call away, and relatively few safe options in times of high hazard. I am one and know many "very active ski tourers" and the way we play, the lifetime risk of dying in an avalanche isn't anything close to 1 in 50.

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Originally Posted by skifishbum

... i fear the aggro dipshit driver multi car power passing for inbounds pow fever and clueless miss texting/twitttertwatting social media whore drivers more than avvies ...

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This. By a lot, and across all seasons too (road bike).

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Originally Posted by klar

There is a paper on this by the usual euro people:

http://arc.lib.montana.edu/snow-scie...12-501-505.pdf

http://mt1.powderguide.com/fileadmin...statistik1.jpg

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Interesting data. I'm surprised at how low the odds are for fatality -even if in the highest risk/highest frequency end. Only 1/10 chance of death after 2600 days of aggressive, high risk profile touring. Knowing how sweet the joys of backcountry glisse, I'd almost take those odds to enjoy those kind of runs so often.

My gut is that those numbers are somehow too low. That is the conclusion of my number play - that no matter how low the odds on any given encounter - the small odds will catch up to you with enough rolls of the dice. But I suppose these come from real world numbers of users to fatalities so maybe my numbers are overstating the odds.

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Originally Posted by kootenayskier

Interesting paper, but utilizing massive assumptions on the fatality stats. I'm also wary of the relevance of their euro-centric model to other areas. From my limited experience (in Europe), and compared to my backyard, I saw a far more cavalier attitude to death, a complete disregard for safe protocols, a sense that rescue was just phone call away, and relatively few safe options in times of high hazard. I am one and know many "very active ski tourers" and the way we play, the lifetime risk of dying in an avalanche isn't anything close to 1 in 50.

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Are you skiing avalanche terrain or staying out?

Thats how I always have thought of myself, conservative enough that my exposure is less than even your average ski tourer. But even if you have a high confidence in your ability to make the call and manage risk on any given day/place - if you are skiing avalanche terrain you never really know and there is some chance of it sliding. A few weeks ago with low danger I was skiing down a run and, while we stayed out of the bulk of the path, at one point it was required to cross steeper and corniced terrain to get to the lower good skiing terrain. I thought - yes its low danger, but it could slide and so I wondered what the odds are - 1/500, 1/1000? and what is the cumulative effect?

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Originally Posted by Coño Frío

Risks can be mitigated but life is not riskless.

A careful BC skier is probably more likely to die from his weakness for marlboro's or his appetite for Big Macs.

All figures below are for U.S. residents.

Cause of Death	Lifetime Odds
Heart Disease	1-in-5
Cancer	1-in-7
Stroke	1-in-23
Accidental Injury	1-in-36
Motor Vehicle Accident*	1-in-100
Intentional Self-harm (suicide)	1-in-121
Falling Down	1-in-246
Assault by Firearm	1-in-325
Fire or Smoke	1-in-1,116
Natural Forces (heat, cold, storms, quakes, etc.)	1-in-3,357
Electrocution*	1-in-5,000
Drowning	1-in-8,942
Air Travel Accident*	1-in-20,000

http://www.livescience.com/3780-odds-dying.html

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Eh, these numbers are spread out across the entire population, so pretty misleading.

Nearly everyone is subject to cancer, strokes and vehicles. Avis aren’t exactly blowing out neighborhoods so when compared across the population, I expect one to have a greater chance of being mauled to death by prairie dogs then getting buried in a slide.

The second chart is more accurate since it’s focusing on people that actually go into avalanche terrain and their odds of survival over an extended time period.

http://www.ucalgary.ca/asarc/files/a...9_Jamieson.pdf

In the mountains where I ski there is always the opportunity to manage the risk through timing and terrain selection. The snowpack instabilities are knowable, there isn't any sense of competition for lines or glory, and I have all the time in the world. We ski the big lines when they're stable, and supported terrain and/or in the trees, or in bounds, when it's not. I have vivid recollections of the times when I've guessed/hoped that a slope would hold together, but relying on luck isn't a valid long term strategy, and I put constant time and effort into overcoming my bias towards optimism and enthusiasm, and cultivating a calculating and patient protocol. It seems obvious that most ski tourers don't have the experience or the discipline to manage risk in any meaningful way, and therefore statistics based on guesses about the full spectrum of ski tourers behaviour necessarily exaggerate the risk for some, while underplaying it for others. Any consideration of these stats to justify (or not) participation in ski touring just legitimizes hoping and guessing as a risk management strategy, when all that really matters is the extent to which an individual is prepared (in the broadest sense) to continually make sensible decisions. Know thyself.

Kootenay. Most other skiers are time constrained. We have luxury of time which IMO affords more clarity for decisions

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Originally Posted by LeeLau

Kootenay. Most other skiers are time constrained. We have luxury of time which IMO affords more clarity for decisions

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"Time constraint" in what manner? Everyone juggles numerous things in a day. You mean the flexibility to time a ski day and a location simultaneous with snow conditions? So if it's risky and you're a Type A++ doing 80 hr weeks at the white collar mill, you adjust your expectations. You don't insist nature comply with your "time constraint." Shouldn't busy life = more prudence, not less?

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Originally Posted by Cold_Smokin'

Eh, these numbers are spread out across the entire population, so pretty misleading.

Nearly everyone is subject to cancer, strokes and vehicles. Avis aren’t exactly blowing out neighborhoods so when compared across the population, I expect one to have a greater chance of being mauled to death by prairie dogs then getting buried in a slide.

The second chart is more accurate since it’s focusing on people that actually go into avalanche terrain and their odds of survival over an extended time period.

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What I find interesting is comparing the two charts.

If the data given is to be believed, I have probably around a 1 in 100 chance of dying in an avalanche. Maybe slightly more, I might be slightly higher than RM 1 as far as risk level goes. Place that on the overall chart for all forms of death... I have about the same chance of dying in an avalanche as getting killed in a car accident, or offing myself, provided I take care to make intelligent decisions in the backcountry.

I'll take those odds.

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Originally Posted by creaky fossil

" You mean the flexibility to time a ski day and a location simultaneous with snow conditions? So if it's risky and you're a Type A++ doing 80 hr weeks at the white collar mill, you adjust your expectations.

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To the first sentence. Exactly.

To the second sentence. Hopefully the type A hypothetical has that patience/judgment

We're up to 4 or 5 inbounds non
Avalanche deaths in UT resorts
this season.
Why don't this odd morbid infatuations with
Avvy deaths extend to other aspects of
An inherently risky activity ?

Because we're all experts in our own minds, and think that we are too good, too cautious, know our limits, so we couldn't die in a crash.

We obsess over avalanche deaths because there's a delusion shared by a lot of b/c skiers that only people that don't know what they're doing, or are too agressive, or are too prone to risky behavior die in avalanches. And we don't want to be one of those people. We think that given the right skills, mindset, and attitude, avalanches are completely avoidable and you can remove yourself from the risk pool. Truth is avy victims range from your highly educated, risk-averse smelly tele meadowskipper that makes a bad call and strays onto a rollover in a touchy CO snowpack, to joe blow from philly that heads out the gate and has no idea what the fuck an avalanche even is, to extreme bro brahs pushing the limits in 55 degree chutes in cham after it dumps. Death doesn't discriminate. You only hear about the avalanche experts and sponsored athletes dying in slides because they're the ones people know, but go read a few years of the CAIC incident log and you'll see that it's all types.

nailed it
sadly i think fuckin up early in your bc career is one of the best things
being blessed w/ a solid snowpack and the ability to get after objectives and positively reinforce a expertise that may or may not be all that
the worst.

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Originally Posted by skifishbum

sadly i think fuckin up early in your bc career is one of the best things

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I was in a big avy when I was big into mountaineering. I quit climbing and took up skiing (inbounds). My risk profile took a 180 on that day.

So if I've skied out of 4 avalanches can I statistically let er rip for the next decade or so as I have satisfied the requirements the equation?

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Originally Posted by SkyIsland

http://www.ucalgary.ca/asarc/files/a...9_Jamieson.pdf

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Finally got around to reading this paper estimating the odds of dying. I like that it factors in the relative avalanche danger rating, number of avy trigger zones traveled, and not just odds of triggering something but something fatally large to give a probability of death rather than my hodge podge two step odds of triggering and then odds of death separately.

https://www.tetongravity.com/images/...aph__forum.jpg




I plugged in my same ballpark numbers for days out. At moderate or lower danger skiing for 500 days with the odds of dying in an avy and the 1/20000 odds one would have a 2% chance of dying in an avy.

At Considerable danger for 500 days and 5 or fewer trigger points skied @ 1/3000 chance of dying one in any day would have a 15% chance of dying in an avalanche

At High Danger for 500 days and 5 or fewer trigger points @ 1/1000 chance of dying in any day one would have a 39% chance of dying in an avy.

Actually paints a pretty rosy picture of a life of skiing at moderate or lower danger.

I'll take that as a go!

Um, so in looking at that graph I was wondering what "Ski 1 day (Munter)" meant?

Googled it and found this:
Munter. Most often used to describe an incredibly unattractive female who you wouldn't touch with a shitty stick.

So as long as I stick to my M.O., and avoid the munters on any given day I'm golden.

Munter was probably the name of the dude that made the graph

This is Werner Munter.

http://www.ortovox.it/xfiles_a6/1349876350_124b.jpg

http://en.wikipedia.org/wiki/Werner_Munter

He is the super popstar of probabilistic risk management and the reason nobody digs pits in europe ;) Without having read the paper, I am guessing "skiing one day (Munter)" refers to skiing one day at a risk level that is acceptable according to his reduction method, i.e. <1.