Quantifying and interpreting the risks of mountaineering

By Vasco Grilo🔸 @ 2023-06-03T08:25 (+19)

Context

I have done some mountaineering in the past, but understand it is a relatively risky undertaking. So I have estimated the risk of death for potential future activities I was considering. The relevance is that I cannot continue to have a good life, or (hopefully) help others if I am dead.

Risk of death

The calculations are here. The results are in the table below.

As a fun/deadly fact, “the main peak of the Annapurna massif is the most dangerous of the world's mountains, with a 29% fatality rate of everyone who tries to climb it”. Ouch!

I could not easily find information about the decrease in risk due to having a guide, or being roped in the relevant places^[10], but I guess these help. At least in the Alps, falls and rock falls apparently are the 2 most common causes of death^[11], and having a guide is arguably useful to avoid them.

Interpreting the risk

Based on the above, the risk of death for the activities I was considering is around 0.02 %, i.e. 1 in 5 k, or 200 micromorts (= 0.02*10^(-2+6)). This is equivalent to:

• Decreasing a life expectancy of 100 years^[12] by 7.30 days (= (0.02 %)*100*365.25).
• Going to a sold out football match in Estádio José Alvalade, whose capacity is 50 k people, knowing 10 randomly selected spectators would be killed. This is because 1 in 5 k equals 10 in 50 k.
• Increasing my chance of dying, excluding existential risk, by 55.1 % (= 0.02/0.0363) during 1 year.
• Correlationally smoking 683 cigarettes (= 7.30/0.0107). This assumes:
  • A reduction in life expectancy of 7.30 days, as calculated above.
  • Smoking one cigarette is associated with a reduction in life expectancy of 0.0107 days (= 0.513*0.5/24), given:
    • Smoking one cigarette is associated with a reduction in life expectancy of 0.513 microlives (= 10/((15 + 24)/2)), in agreement with 15 to 24 cigarettes correlationally reducing the life expectancy of men by 10 microlives.
    • 1 microlife corresponds to one half hour.
• Driving 29.3 k km (= 200*91*1.609) in the United States^[13], supposing 91 mile/micromort (and considering 1 mile equals 1.609 km).

Acknowledgements

Thanks to André Dias for prompting me to transform some notes I wrote into a post.

1. ^{^}

    Taken by me.

2. ^{^}

    This is supposed to be my baseline.

3. ^{^}

    This is part of Mont Blanc’s main climbing route.

4. ^{^}

    From Figure 6, falls accounted for 50 % of the deaths, rock falls for 29 %, being stranded for 7 %, illnesses for 4 %, and unknown or other causes for 10 %. “84% of accident victims were amateurs who were not under the supervision of a professional”, but I do not know the fraction of people under supervision. If half of the people were, having an accident under supervision is 20.5 % (= 1/0.83 - 1) as likely as having one without supervision.

5. ^{^}

    Climbing Mont Blanc requires at least 3 overnights, 2 in the Tête Rousse refuge (one on the way up, and another on the way down), and 1 in the Goûter refuge. So, assuming only half of the people use these huts, one can consider more than 1.5 overnight/climb (= 0.5*3), which suggests a risk of death higher than 0.0303 %/climb (= 1.5*0.0202 %). This is arguably an underestimate because not all deaths were included. “Operations conducted by rescue services downhill from the Tête Rousse refuge or uphill from the Goûter refuge, as well as those performed in the landing areas adjacent to these buildings, were not taken into consideration”.

6. ^{^}

    From Figure 1, deaths have been decreasing, but the correlation is poor (coefficient of determination of 14.1 %), and not statistically significant (p-value of 0.206). From Table 1, falls accounted for 80.9 % of the deaths, rock falls for 5.3 %, being stranded for 3.3 %, avalanches for 3 %, illnesses for 2 %, crevasse accidents for 1.3 %, material failure for 1 %, lightning for 0.7 %, being crushed for 0.3 %, and others for 2.3 %.

7. ^{^}

    Mean between the lower and upper bound. “It has been estimated that there are roughly 100,000–200,000 alpinists active per year in the highest parts of Switzerland”.

8. ^{^}

    Mean between the lower and upper bound. “The reported number of deaths is about 3 to 10 fatalities per year”. 6.50 fatalities per year is consistent with the 6 to 7 calculated here. “We estimate the number of people who die on Kili each year to be about six or seven”.

9. ^{^}

    Calculated based on data from the 1st figure of the section “Algunos datos de los rescatados en senderismo”.

10. ^{^}

     However, note one can only climb Kilimanjaro with a guide, so my estimates still apply in that case for having a guide.

11. ^{^}

     See footnotes 4 and 6.

12. ^{^}

     For context, Metaculus’ median community prediction for a country reaching longevity escape velocity is 2066. I suppose 100 years may well be quite short if transformative artificial intelligence timelines are only a few decades.

13. ^{^}

     Consequently, correlationally smoking one cigarette reduces life expectancy as much as driving 42.9 km (= 29.3*10^3/683) in the United States.