Risks in Cave Diving

[Gary]

I took some simple assumptions an looked at risk involved in choosing a safe air reserve. The results were fairly sobering... I realize this could be bashed and twisted in any number of ways but the idea is still worth considering.

I took a rough estimation on cave diving risk is 1 death per 10000 events. And for the risky end a rough guess on the order of a 50% chance of surviving a dive to half gas (whether or not an accident/silt out or whatever may or may not occur).

In the range of gas reserve from 2/3s to 1/2 we are looking at a factor of 5000 times the chance of dying on a per dive basis. 2/3 of 3000 = 2000 psi, 1/2 of 3000 = 1500 psi. For every hundred pounds difference might increase or decrease risk by a factor of 10 times!

I ran the theory over a fitted normal distribution curves and it seems to agree with this general theory. With these assumptions the risk factor is predicted closer to 15 times per 100 psi in the vicinity of 2/3 reserve.

In the graph the 2/3's reserve being the assumed basis for the 1 in 10000 ratio we get the predicted 50% chance of death after 10000 dives. But the cumulative effect of additional risk or safety is clearly evident in repetitive diving as any 10 times risk is multiplied over a larger number of dives.


Whatever the assumptions used for the comparison the risk factor of 10 times per 100 psi would seem to be fairly universal. The cumulative effect of additional risk/safety over multiple dives could well decide your lifetime as a cave diver (or lifetime in general). Even over as little as 10 to 100 dives the tiniest violations of 1/3s has a noticeable effect on survival chances. And for those planning for a long career in cave diving additional safety margins might be worth considering.

<disclaimer: I'm neither a mathematician nor a dive instructor but figured this was interesting enough to share>

[MengTze]

Interesting concept. What is missing in this set of assumptions is that with each 100 dives (or pick a number), experience increases, comfort increases and thus the chances of survival increase all things being equal.

Can you add that to the numbers machine and pump a new graph?

[Gary]

Interesting concept. What is missing in this set of assumptions is that with each 100 dives (or pick a number), experience increases, comfort increases and thus the chances of survival increase all things being equal.

Can you add that to the numbers machine and pump a new graph?

I certain I don't have to data to calculate it that way. If the complexity of the dive grows with the diver's experience and the gas reserves are pushed to the same limit it is possible that there might be no advantage. I was actually kind of thinking that experience would tend to push one towards greater gas reserves and that would tend to increase safety. It would seem that whatever the value of experience a change in reserve gas would make much more difference.

I included the data mostly because it is easier to show the basic assumptions and methods than explain them. The data fit better than I would have expected making sense over a huge range of tank reserves (not just the interval in question). Anyone can take the numbers and do whatever they want with them to change the assumptions to fit better - or use another method.

Whatever assumptions and methods though are going to have to traverse and explain a tremendous risk factor (on the order of 1/10000 vs 1/2 = thousands of times) over a very small change in reserved gas. Any reasonable facts are going to show that small changes in reserve gas have a far higher risk multiple than I, or I think most people, have ever considered.

[aainslie]

Gary,

What exactly is your model? I can't work out how you got those graphs. Could you tell us a bit about your methodology?

[Gary]

The basic model is the "known" overall risk of cave diving death (~1/10000) assumed to be at aprox 2/3 reserve gas vs a reasonable guess of survival in no flow diving to half. 500 psi makes up the difference between these two values and needs to be distributed "somehow". Roughly 5 decades in 500 psi seemed one way to do it.

To test the theory and produce the derived graphs I assumed that for large numbers and distributions that a normal distribution curve including the two known points and risks 50% and .0001 would provide the best fit I was likely to come up with. .9999 is way out in the 4th or 5th standard deviation (Normal Distribution Curve reference)

Lacking the tools to fit a normal distribution curve to the data I produced a normal distribution curve and fitted the curve to the two points. The first column is fitted air reserves to the distribution curve and the following columns are a normal distribution curve produced by 51 coin flips (thus .5 ^51 - ignoring the .05 ^ 51 typo). [more coin flips would have provided better resolution on the graph and extended the numbers farther above 80% and 20% reserves - but the shape is the same and the values above 80% and below 20% are virtually certain anyway.]

The assumption of 1/2 gas reserve = 50% chance made the distribution very balanced over the volume of the tank which would also make good sense. But I don't think it changes much in the 1/2 to 2/3 gas range regardless of the number assumed for survival at the 1/2 reserve level.

Having the odds for a single dive it is merely a matter of raising the survival chance to any given power to determine the chance of survival over a larger number of dives.

Using the normal distribution curve for distributing the risk factor of 5000ish over the range gives a range of about 2 to 15 times per ~100 psi rather than a general 10 times risk per 100 psi.

The graph, of course, is no better than the very rough assumptions that went into making up the data. But the numbers are so stark minor variations in the method or assumptions make very little difference. I would think that to significantly change the results reapportioning the 5000 times risk factor linearly instead of geometrically would make the numbers less extreme but I don't think that model would hold up to much scrutiny.

In any case the start and end points are assumed but the trends and risk factors seem fairly reliable. I doubt many would consider the minimal gains an extra 100 psi would give is worth increasing their risk by ten times (or even 2 times).

The safety gained from even a small amount of extra gas is well worth the effort of bringing an extra bottle in most cases.

[FW]

About experience, and comfort level..........

There is an alarming trend for cavediving accident victims to be trained cavedivers. 40 years ago, it was only OW divers that didn't know any better. Today even OW divers know the dangers of overhead.

Most of the fatalities, among trained cave divers, have no gas left in their tanks. It is EXTREMELY obvious that some emergency caught them with insufficient reserve.

The accident analysis "rules" are for everyone, not just new divers.

I am like Phillip. I add 50-100 psi, or more, to turn around, for things like:
New Buddy
Low/silty passage
Major restrictions
Long dives
New exploration
Mapping
and anything else that *might* delay my exit

In the last couple of years, I have ended most of my dives with half to 2/3 of my gas remaining. If you don't believe me, ask some of my buddies.

[cloudboy55]

Reading this reminds me of those speeding signs that I used to see up north where they posted the fines for each level of violation. The discerning speeder could choose his level of risk...

Seriously, though, it would appear that some speculation went into producing this graph, although I'm not sure how one would produce such a graph without these methods.

-- cloudboy55

[jj1987]

I took a rough estimation on cave diving risk is 1 death per 10000 events. And for the risky end a rough guess on the order of a 50% chance of surviving a dive to half gas (whether or not an accident/silt out or whatever may or may not occur).

50% chance surviving a dive to half gas? I've yet to have a reg/post failure in a cave. Even in my one silt-out incident, it didn't take more gas coming out than going in. My Apprentice class in JB where we had portions lights out, sharing air, and portions just lights out, we didn't use more gas coming out than going in, though it was very close. Thinking about it, I don't know of many people who have had a failure such that they required their reserve air. That means that every dive, I could have gotten away with diving to 1/2. I guess this would qualify as a proof by counter example?

I would also say that it's fairly obvious that the calculation of risk would HAVE to factor in things like silt, low flow, new system, new buddy, new cave diver, frequency of dives leading up to the dive you're calculating, how well the system is marked (IE Ginnie with arrows every 100ft or a rare system), siphon or spring, etc. One thing that cave training makes VERY clear, is that diving to 1/3 in JB/LR/Manatee/Ginnie has a much greater safety reserve than diving to 1/3 in Peacock. You can easily prove that by looking at a dive log of someone who records dive end pressures, and I can almost guarentee that they end with less gas from a peacock dive than a Ginnie dive.

Before I fall for this too hard...I'm not sure if your post was serious or stirring the pot? I mean, you've got a graph and spreadsheet and haven't mentioned any confirmed source of data, so maybe I'm taking this way too serious

[cloudboy55]

...you've got a graph and spreadsheet and haven't mentioned any confirmed source of data, so maybe I'm taking this way too serious

[FW]

50% chance surviving a dive to half gas? I've yet to have a reg/post failure in a cave. Even in my one silt-out incident, it didn't take more gas coming out than going in. My Apprentice class in JB where we had portions lights out, sharing air, and portions just lights out, we didn't use more gas coming out than going in, though it was very close. Thinking about it, I don't know of many people who have had a failure such that they required their reserve air. That means that every dive, I could have gotten away with diving to 1/2. I guess this would qualify as a proof by counter example?

Before I fall for this too hard...I'm not sure if your post was serious or stirring the pot? I mean, you've got a graph and spreadsheet and haven't mentioned any confirmed source of data, so maybe I'm taking this way too serious

You may be mis-reading Gary's intent. If you turn at half gas, in a no-flow cave. there is a good possibility that you would exit with zero gas, if you got out at all.