I recently “finished” my journey across the Pyrenees, most of it with Javier. I say “finished” because I missed the first week or so, and we missed a good bit of Andorra after a snow-storm chased us into a bus. But we did most of the best parts of the most sadistic version of the Pyrenean High Route (HRP/ARP), and after about 50 cumulative nights in the Pyrenees over the last 7 years,[1] we made it to the sea.

As usual, I spent a lot of time thinking about risk. Generally in the evenings, lying on my back, because in the day, clinging onto a rock, the mind tends to sharpen, and abstract musings on risk don’t make the cut. I spend time thinking about risk in the mountains because people sometimes die in the mountains.

These are the kinds of things I think about when I think about dying in the mountains, with varying levels of self-conscious silliness: A woman, who we’d made friends with on the way up, died coming down Mt Kazbek (Georgia) the day before we summited. Around 10 people died in an avalanche in Ala Archa (Kyrgyzstan) while I was in the next valley over. A hiker died in the Pyrenees a few years ago while traversing a grassy slope near Benasque. Some people died in a type of Soviet helicopter that I once almost went in. A few people die every year on Table Mountain. Roughly 1-3% of Mt Everest summits/attempts are deadly. People die all the time from from exposure, dehydration, falls, gear issues etc.

I find it hard to distinguish between avoidable tragedy, bad luck, downright stupidity, and pure statistical necessity. And so it’s not easy to know how much to update my priors each time I hear a story like these. And overwhelmingly, I think many “extreme sports” types are incapable of properly interpreting and internalising the statistics.

# Micromorts and you

A micromort is a one-in-a-million chance of death. Wikipedia (just linked) lists the micromorts for common activities, such as: existing (about 1 micromort per hour), walking (1 micromort per 30km[2] ), and skydiving, at 8 per jump.

It’s a fantastic statistical concept, which is mostly used to understand comparative risks in a population. For example, you get 0.1 micromort per km while riding a motorbike, or 10 per Scuba dive. But what if you’re a pro motorcyclist, or drunk, or riding in a storm, or riding the Isle of Mann TT in a storm while drunk? Then clearly you’ll get a lot more, probably about a million.

So if we want to abuse the concept of micromorts and use them for personal decisions (rather than their intended use as a statistical concept), we must make these doses a function of three things:

$dose = hazard \times f(exposure, vulnerability)$

Where[3] hazard is the baseline statistical micromort dose, exposure could be conditions that aggravate the hazard, such as weather, readiness of hospitals, and vulnerability is your personal characteristics, such as age, health, fitness.

For a given loosely-defined hazard (let’s say, climbing Mont Blanc), there’s a 3D surface representing this function that looks something like the colourful skateboard ramp below. In this case (according to a suck of my thumb), your dose ramps very quickly with vulnerability (personal), more slowly with exposure (conditions), and peaks when both of these are maximum. If you’re slower, or less experienced, or if the Grand Couloir is misbehaving, or there’s high wind, or a cold snap… you’ll end up closer to that red pointy pointy bit at the top.

But let’s say we pin it down to a specific day on Mont Blanc, on a single route. Then we can hold the exposure axis more or less constant (everyone’s getting the same weather, sun etc). And we get a simpler line function relating vulnerability to dose. As you get more vulnerable, you get more dead. And the question for every summit hopeful is, where on this line do you fall?

Around 100 people die on Mont Blanc every year (every source I found for this dead-ended, but it’s probably order-of-magnitude correct) out of around 30,000 attempts. That’s an average rate of about 0.3%, or an average dose of 3000 micromorts. But of course these are not evenly distributed, and there’s a whole bunch of people (experienced climbers) whose dose is close to 0, while those further to the right get much more than they bargained for.

And this gets to the core of what I’m interested in: how do you know where on this line you fall? Most people either completely misunderstand (or ignore) the statistics, or assume they’re a low-doser. What the above charts above don’t convey (if they convey anything) is the distribution of these doses: what proportion of people are getting each dose? Is it a power-law distribution, with the majority of people having next to no risk, and a long-tail of less and less experienced people accounting for the bulk of the injuries and rescues and deaths? (This is the Pareto principle, or 80-20 rule.) Or is it more normally distributed, with the bulk of people somewhere in the middle, also accounting for the bulk of the deaths, and shorter tails on either side of experienced people and silly people.

For Mont Blanc, it’s most likely a power-law distribution. For wingsuit proximity flying? I wouldn’t be surprised if it were more normally distributed, and the median flyer is getting a hefty, deadly dose, while a few lucky experts remain unscathed.

# Personal caveats

Everyone is special, and everyone thinks they’re special. And no one thinks they’re the one that’s going to die doing the thing. But ~100 do every year on Mont Blanc, and 100s on other mountains around the world, and thousands and thousands doing all sorts of other things around the world, who also assumed they were in the low-dose regime.

So how do we improve our ability to understand the base stats, reduce our exposure, and properly assess personal vulnerability? And how do we communicate this to more would-be dead people.

In most cases the numbers are low enough that it’s easy to assume you won’t be the unlucky one. Even Everest “only” has a death rate of 1-3%. A 3% chance of death (equivalent to 30,000 micromorts) is not something I’d take lately, but it’s just low enough for hubris to kick in. And so every year, a 57-year old accounts exec (who has climbed Kilimanjaro, so of course he’s ready) heads up into the cold and the wind and dies, along with a few others like him. So you need to understand that not only is 3% actually really, really high, but also: that’s not your number! You’re somewhere else on those charts above, most likely (if you’re an accounts exec) in one of the high-dose areas, getting 100,000 or more micromorts!

And then we have things like Mont Blanc, which is a tenth as dangerous, which makes it far easier to gloss over the 0.3% death rate (3000 micromorts) and so far more people die. But again, if you look at the power-law distribution, there are a bunch of people getting a far higher dose. And they need this message! It’s more dangerous than you think, especially if the conditions are bad (most of the time in the Alps, these days), and especially if you’re Joe-average.

# Judgement

And then we get to me. I have no desire to stand in a queue on Everest, or play ten-pin bowling with Latobius, God of the Alps. But I’ve climbed some reasonably sized mountains, done some rock climbing, and spent many days and nights in the outdoors somewhere. And many times I’ve turned around, or not even started: about 99% of the way up Pigeon Spire, Valter and I looked at our watches and decided it was turn-around time. I flew to Kyrgyzstan (with Javier) to climb Khan Tengri, and climbed Korona Peak as a warmup. Except we didn’t quite get to the top, and turned around when we realised what getting to the top would involve. Then I turned around and left the country altogether, without climbing Khan Tengri, when I decided I wasn’t experienced enough and it wasn’t worth the risk.

I like to think I’ve built up a certain respect for unfinished objectives. I’m proud that we never summited Pigeon Spire (and it was convenient, as coming down Snowpatch Col in the dusk rather than pitch black was a relief). I love giving up! It tells me that I’m pushing myself to my limit, but following the rules. I’ve nearly climbed Pic Carlit twice so far, and I look forward to adding a third failed attempt.

So there’s an additional dimension to the charts above. Let’s call it Judgement. Do you put on your seat-belt when you drive, do you avoid motorcycles altogether, do you turn around when things get sketchy, and do you understand your limits and stay well within them. As this hang gliding article put it in 1998 (HN comments here):

You see, here’s how I think it works. The overriding determinant of pilot safety in hang gliding is the quality of pilot decision making. Skill level, experience, quality of equipment; all those things are not determinants. What those things do is determine one’s upper limits. More skill gives you a higher limit, as does more experience or better equipment. But safety is not a function of how high your limits are, but rather of how well you stay within those limits. And that, is determined by one thing; the quality of the decisions you make.

Picture this as shifting the all the previous risk curves upwards. If your judgement is perfect you get the default curve; anything else and you shoot up. Except as the quote above suggests, you start to get wonky interactions between skill and judgement. It’s not hard to imagine a judgement regime where increased vulnerability (lower skill) actually makes you safer - you’re less able, and less likely, to do something so unforgivably stupid as wing suit through a rock formation.

# Faulty priors

But perhaps I’ve overthought it past the point of usefulness.[4] Sometimes people (my dad) ask how I can scramble along a rock ledge without using a rope. And the answer is that I trust my feet. The same way you can walk along a sidewalk without worrying that you’ll jump into traffic (except sometimes you do, don’t you), with a certain level of rock experience, you can pick your way around certain-death falls with a modicum of calmness. And at a micro-level, it doesn’t matter what the stats say, or your vulnerability, or exposure. You know you can take that next step and be fine.

So that’s what brings us, finally, to Mr Thomas Bayes.

$P(A|B) = \dfrac{P(B|A)P(A)}{P(B)}$

How should I update my priors when I, for example, learn that a helicopter crashed in Kamchatka? I know that helicopters are dangerous. Especially Soviet ones. Especially in Kamchatka! So I should already expect a certain percentage of them to crash, and shouldn’t need to update my priors at all when I learn that one of them does.

Similarly, learning that someone died slipping off a grassy slope in the Pyrenees caused me to be completed freaked out, when the following year I spent three days sliding around on precarious, wet grassy slopes (Ctrl-F “grass”) in the Pyrenees. I’ve never been so relieved as when we crossed back onto dry Spanish rock - I just wanted to get back the feeling of knowing I can take the next step, and be fine. And again, mountains are dangerous, and slippery when wet. This story shouldn’t have changed my feelings about being amongst them. But it did, and even though I over-reacted, it was a useful reminder that even innocuous-seeming things quickly become dangerous if the exposure or vulnerability changes.

So, to get better at this: I should correctly understand the baseline risk of an activity, consider the factors that increase the exposure, and sensibly assess how my personal vulnerability plays into it. I should use that information to build useful priors on how dangerous that activity is. Those priors should be considered enough that most new things I learn are not surprising enough to update them. Remote helicopter crashes probably don’t make the cut. But when something does surprise me, I should update those priors based on that new information. For example, news of melting glaciers and increased rockfalls[5] have changed my priors enough that I’m now deeply suspicious of Alpine rocks, and don’t plan to linger underneath them in the future.

And finally, I should accept that stats and Bayes will only get you so far. At the end of the day, the only thing that makes a slanted slope dangerous, covered in slick, wet grass, vanishing steeply downhill into the foggy distance, is that a cliff I see there, who knows, but the sun is setting, and the wind’s picking up, I’m lost, and my toes are waterlogged, and as I was saying, the only thing that makes the slope dangerous, or not, is whether my grip is good and I trust my feet.

[1] go back Some of these before explicitly starting the ARP.

[2] go back So, unless walking compounds with existing, and unless you can walk 30km in under an hour, walking is actually net negative micromorts. Relative to merely existing.

[3] go back Note that along with abusing micromorts, I’m deliberately abusing the standard hazard, exposure, vulnerability framework.

[4] go back That’s what blogs are for, after all.

[5] go back Not surprising in themselves given what we know about climate change, but creating surprising and prior-altering conditions.