I won’t even try to wade into the math arguments but as someone who has been on 8000 meter mountains 10 times (4:Everest, 1:K2, 1: Lhotse, 1: Manaslu, 1: Broad Peak, 1: Cho Oyu 1: Shishapangma) with 3 summits, I can attest that the more popular the mountain (Everest, Manaslu, Cho Oyu) people have less experience.
On a personal note, my first 14er was Longs and after spending almost a year of my life on 8000 meter mountains, I am still alive … I think.
On K2, arguably one of the more dangerous 8000ers, my observation was that most everyone there has significant experience and more importantly, mountain sense.
For me the big picture of risk is that the less climbed 8000 meter mountains i.e. less than 400 summits, have the higher death rates primarily due to: less known routes, winter attempts, remote location with less medical/rescue resources, less understood weather patterns, climbers attempting new routes, fewer climbers thus lower potential of help and finally, less use of oxygen. On the use of oxygen, looking at Everest as a proxy, of the 7001 summits, both side, all routes; 282 people (169 westerners and 113 Sherpas) have died from 1924 to now. 2.7% summited without supplemental oxygen but 36% of the deaths were those who climbed without supplemental oxygen according to the Himalayan Database.
Since I’m pretty sure this thread will devolve into Everest bashing to wit: "And how many of Everest's summitters are New York high society types getting dragged up by Sherpa's? A lot.” let me give a first hand observation.
To be sure, as Everest becomes more popular and the local Nepali/Sherpa companies offer lower costs climbs ($30K vs $65K), less experienced people are attracted to the mountain. However, in my observation, the vast majority i.e. greater than 60% have sufficient experience to be there with climbs on Denali, Aconcagua and/or another 8000 meter mountain. That still leaves ~150 each season with climbs on Kilimanjaro, Mont Blanc or Rainier as their sole experience thus the death rates will increase on Everest due to climber/guide error in the future - imho.
I know this table reflects summits to death and not attempts to deaths but for discussion it might be useful. I compiled it in 2012 using the latest numbers from the Himalayan Database, 8000ers.com and my own research. I am positive it is not 100% accurate but is very close. The only significant change is on Everest (7001/282) and Manaslu (800/70) but the rank order didn’t change significantly.
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