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Humans are notoriously bad at estimating risk – especially for low probability events.

Intuition fails when trying to imagine the difference between 0.00000885 and 0.00043165 probability of death. This can lead to gross misapplication of statistics to justify risky behavior. (eg- driving is more dangerous than jumping, ha!)

There is a concept called a survival curve, which graphs the probability of living to a particular age. In normal human populations, that curve looks something like:



I think of this curve often when considering the risks of jumping. If I do a sketchy jump with a high risk of death, it’s like taking a chunk out of my life expectancy. If you know the probabilities, it is easy to compute your new survival curve.

As an example, imagine playing a game of russian roulette. If you play once at age 30 with a 1/6 chance of losing, your survival curve will look like:



Ok, what about jumping? It’s not easy to get accurate statistics, because there is huge variation in how risky certain types of jumps are. But taken in aggregate, we can get some approximate values for how risky parachuting is:

Skydiving: 371 fatalities / 41900000 jumps = 0.00088544% [1]
BASE: 9 fatalities / 20850 jumps = 0.04316547% [2]

Now we have the probability of dying per jump. If we know when and how many jumps we intend to make, we can estimate the probability of dying during a jump, and the impact that has on our survival curve.

I started skydiving at 27 years old, and average 100 skydives per year. The impact of skydiving on my survival curve is:



I started BASE jumping at 30 years old, and average 40 BASE jumps per year. Assuming I have a 10 year BASE career, my survival curve now looks like:



As with everything in BASE, draw your own conclusions. But for me:

Extreme risk is hard to understand intuitively

Skydiving is safe as fuck

420 BASE jumps is 16% chance of death… 1 round of russian roulette

BASE jumping reduces my chance of living to age 40 from 98% to 77%

No wonder we are uninsurable

BASE is still worth it for me, but as the season starts to ramp up, everyone should think carefully about how much life they have left to live, and the risks they are taking. Make good decisions out there, because this shit is seriously dangerous.

You can play with your survival curve interactively here: https://base-line.ws/survival

Rationalizations in 3, 2, 1...

This is totally awesome. I don't really like the way your survivability is in a constant state of decay though. Although you might see an incentive to stop BASE jumping in order to reduce your rate of descent, why wouldn't your survivability return to normal once you stopped BASE jumping? The model seems to draw too much on the "luck jar" concept, but is that realistic? If I stop jumping now, does my life expectancy not return to normal? I suppose if you have wear and tear on your body, it's going to take a toll that could kill you more quickly. I'm guessing this is an artifact of the Gompertz Law rather than your own analysis. Cool stuff though.

On a slightly related note, if you've ever seen Pirates of Silicon Valley, there's a really funny scene with Bill Gates talking about how exercise is bad for your health, because we only get "x" beats of our heart in a lifetime, and if you increase your pulse rate you're using up all your beats.

That's a fair point. The graph actually shows the probability of survival from birth until a given age. Since you have already survived to your current age, all the lines should be shifted up proportionally to 100% at your current age, and drop off from there.

So you are right, jumps in your past do not factor into your future odds. There is no such thing as a "luck jar".

I think what's interesting about the graph is seeing the impact on survival that a BASE career has, relative to all other causes of death in a human lifetime.

It made no difference to my chances of living to 40. I didn't start till 51 ;)

But a great way to visualise and understand it, thanks

Great Post!

I ask my students would they play Russian Roulette.
Most blanche at the idea, after they express their
thoughts I explain I might, depends on the gun,
the payoff, and mostly my current age/health.

RE: Gun

I own a 5 shot .38 special, 1/5 = 20%
I'd prefer a 6 shot .44, 1/6 = 16.6%
if I was going to point it at my head.

RE: Age & Health

A healthy 20 year old should not play
but person 103 with terminal cancer...

Nice work.

I think Ian's point is fair, but the graph still gives a good tool for decision making when deciding whether to get into (or continue with) BASE.

Basically, comparing the two life expectancy lines (with and without BASE) gives you a visual to help with decision making for the future. If you stop jumping (or choose never to start) you hop back up to the higher survival line.

I just noticed this, haha. I think it does a good job of illustrating how dangerous the sport is, and would probably act as a pretty good deterrent for skydivers, or other risk takers who think BASE jumping isn't THAT much more dangerous. Maybe it will make people already doing it reconsider their jumping and type of jumping as well. I wonder what the curve would look like for terrain flyers. I'm just not a huge fan of statistics (probably because I was never very good at it).

It actually boils down to the percentage of possibility of your demise on each individual jump.

Thanks for the statistics I agree that the chances are slim that a person will get hurt base jumping, but we often forget/underestimate that it will happen. It is important to remember not to get overconfident and always be safe!

hahaha it says i am more dead than alive!!!

BSBD

Actually, I think your original interpretation in the first post is correct. The line shouldn't shift back to 100% (or more correctly 98.xx% or 99.xx%, since there is some chance of death in the general population model even at younger ages), it should just revert to the non jumping decay model from that point onward (which is what your figures appear to show, can't confirm without the equations behind the model). The natural instinct to shift the line back to "100%" after the risk level returns to the general population model is a manifestation of survivorship bias. Because we have survived, we discount the effects that the increase in risk had on our probability of survival at the current time. We neglect the overall distribution of the population, which is what survival curves are meant to show.

To visualize this, it is easier to compare a group of 100 people. Two of these people are expected to be dead by age 30 under the general population model. Then remaining 98 say fuck it and become rad base jumpers. If we use your original parameters (jump from age 30 to 40, 40 jumps per year) the model says that we should expect 77 to be alive at age 40. These 77 jumpers then live out the rest of their boring lives subject to the normal dangers, diseases, and aging processes of the rest of the population. If you are one of the 77 standing at age 40, looking back you see your survival rate as 1.0 because you are still standing, without thinking of the population that your survival rate is describing. You are still a part of the "base jump, 30-40 @ 40 jumps per year" population, and the size of this population doesn't increase.

To better manage some of the assumptions implicit in the above explanation and make it cleaner (and more applicable to people playing with the model page), I prefer to look at the model as showing 100 iterations/lives/ "parallel universes" where you begin jumping at the same time under the same exact conditions (i.e in every universe jumps happen under the exact same conditions and at the exact same time, until a fatality puts you out of the game in that universe). With the same parameters, you will be left standing in 77 of these universes at age 40. These 77 universes continue in parallel until the infinite cosmic coin flips whittle the survival rate down to zero.

The shitty part is that we don't get to choose which universe we are playing in. Right now we are all still in the happy area below the curve that represents survival, but that can all change on the next jump based on the cosmic roll of the dice. The good news is we can influence somewhat the odds of the dice roll going poorly (types of jumps, preparation, proper gear, advances in technology, throwing good-luck gainers and intricate pre-jump handshakes etc.), and thus in reality we all have a different risk per jump than the statistics from Kjerag referenced for the model. The bad news is that we are still fundamentally playing a game of chance. Overall, I think this model is a simple yet incredibly powerful and humbling tool to show current and experienced jumpers alike. Like any model there are assumptions made that complicate application to reality, which I'm sure someone will be quick to point out, but for educational purposes I find it plenty robust. Don't get wrapped up in the exact percentages, instead use it as a graphic shorthand for the risk level you are exposing yourself to and the ways you can affect that risk.

An interesting extension would be to remove some of the assumptions in the model, particularly the assumption that each jump is independent. This would allow us to play with the idea of "experience," and see how risk changes based on experience level. Intuition would tell me that the odds of survival would increase up to a certain point and then either plateau or more likely decrease as jumpers begin testing the boundaries (aerials, terrain flight, push conditions), and it would be a really interesting experiment to see what is actually true. You could also try to capture the concept of "currency" as another example. The data for these kinds of analyses would be much harder to come by and work with, and their results would probably be more difficult to interpret reliably because of the messiness that comes from dependent variables.