DCS--Playing the Odds

[MargaritaMike]

For a simpler illustration: If you roll a die ten times, the probability of scoring a six at least once, is 84%. Still if you've rolled the die nine times without scoring a six, the chance of scoring a six on the tenth attempt is still only 17%. Because what has happened in the past has no bearing on the future.

I agree totally. Well, almost. I think your percentage on the 10th roll is a little high, BUT the concept is spot on. That's why I dive as if my next dive is the one.

 

[tursiops]

I agree totally. Well, almost. I think your percentage on the 10th roll is a little high, BUT the concept is spot on. That's why I dive as if my next dive is the one.

This is why I suggested Baysian statistics, which take into account this kind of thing. If you have not rolled a particular number, say 6, after 9 tries, one possible conclusion is that the die is imperfect and weighted/shaped to make a 6 less likely than any other number. After just one roll, there is no way to know this. After 10 rolls, you get a hint. After 100 rolls, not getting your 6 by then is highly unlikely if all numbers are equally likely. You need a way to take into account your data, which is additional information it is silly to ignore.

But this gives the opposite conclusion to the one quoted above. If you haven't been bent after 100 dives, there is no additional information there, because the odds were very low you'd get hit with so few divas. If after 10,000 dives, no hit, you're getting a hint. After 100,000 dives, the chances the next dive is "the one" are very low, even lower than when you started diving. You've taken the data into account, which is information additional to DAN's reports.

This may be nonintuitive, and is certainly arguable (the argument has raged for hundreds of years!), but the Baysian statistics are in daily use in lots of places for lots of things and allow solving some real-world problems frequency statistics can't touch because of poor data or lots of confounding variables. Like, DCS.

 

[boulderjohn]

This is why I suggested Baysian statistics, which take into account this kind of thing. If you have not rolled a particular number, say 6, after 9 tries, one possible conclusion is that the die is imperfect and weighted/shaped to make a 6 less likely than any other number. After just one roll, there is no way to know this. After 10 rolls, you get a hint. After 100 rolls, not getting your 6 by then is highly unlikely if all numbers are equally likely. You need a way to take into account your data, which is additional information it is silly to ignore.

In the opening scene of the play Rosencrantz and Guildenstern are Dead, the two main characters are flipping a coin, with the one calling correctly keeping the coin. Rosencrantz calls heads every time, and he wins 92 times in a row. He is unthinkingly excited about the fact that he keeps winning, while Guildenstern contemplates what might be causing this staggeringly unlikely possibility.

But this gives the opposite conclusion to the one quoted above. If you haven't been bent after 100 dives, there is no additional information there, because the odds were very low you'd get hit with so few divas. If after 10,000 dives, no hit, you're getting a hint. After 100,000 dives, the chances the next dive is "the one" are very low, even lower than when you started diving. You've taken the data into account, which is information additional to DAN's reports.

Exactly. You would likely conclude that you are not DCS prone, and the dive algorithm you are following is very much right for you. Your next dive will thus very likely be a safe one.

In contrast, I was once part of a small group of divers who followed a specific algorithm for decompression on dive trips of less than one a month. With 8 DCS cases in our group in a couple of years, I concluded that the algorithm was not a safe one and never dived it again.

 

[dmaziuk]

While it is true to some extent that the more you dive, the more likely you are to be bent, I would say that is only true if those extra dives are more risky than others.

Only assuming that repeated subclinical stress does not add up. Between that and slower recovery due to aging, are we sure our tissues won't get inflamed from the same amount of "silent bubbles" exposure that 10 years and a 1000 dives ago did absolutely nothing?

 

[MargaritaMike]

For a simpler illustration: If you roll a die ten times, the probability of scoring a six at least once, is 84%. Still if you've rolled the die nine times without scoring a six, the chance of scoring a six on the tenth attempt is still only 17%. Because what has happened in the past has no bearing on the future.

@Storker I apologize. I misread your post the first time and made your roll of the die more complicated. I agree with your percentage (1 in 6 rounded up)

Exactly. You would likely conclude that you are not DCS prone, and the dive algorithm you are following is very much right for you. Your next dive will thus very likely be a safe one.

This is what I have been saying. You just say it more eloquently.

Cheers - M²

 

[Neilwood]

Exactly. You would likely conclude that you are not DCS prone, and the dive algorithm you are following is very much right for you. Your next dive will thus very likely be a safe one.

In contrast, I was once part of a small group of divers who followed a specific algorithm for decompression on dive trips of less than one a month. With 8 DCS cases in our group in a couple of years, I concluded that the algorithm was not a safe one and never dived it again.

If you are getting that far along (1,000+ dives) without getting bent, it is safe to say the algorithm and how you are using it (with regards to conservatism, ascent rates etc) is a good fit for you.

The 8 cases within 2 years is definitely well above the expected ratio so it is safe to assume there is something wrong with the algorithm or its use.

 

[MargaritaMike]

Only assuming that repeated subclinical stress does not add up. Between that and slower recovery due to aging, are we sure our tissues won't get inflamed from the same amount of "silent bubbles" exposure that 10 years and a 1000 dives ago did absolutely nothing?

This is why what @Bob DBF said makes good sense.

The good news is if you have been diving a long time with a lot of dives, you are in a position to make good decisions on the the amount of risk you will take. Personally, I won't make the dives I would years ago. Hell, in the last 10 years or so I got a computer, ascend at 30'/min, make a safety stop, and don't go out in bad weather as much.

And dive conservatively. When I use to fly tactical aircraft and found myself in air combat (fortunately training only), the way to win was to fly on the edge of the envelope (high speed, maximum g's, hard turns, etc.). Now with my diving I approach it like flying an airliner - no excessive angle of bank, no g's, gradual turns, and relaxed. Not that airline pilots don't earn their money. They do. But my diving NOW is much more conservative and relaxed. I think that is what age has brought to compensate for my tissues getting inflamed from the same amount of "silent bubbles" exposure that 10 years and a 1000 dives ago did nothing.

Cheers - M²

 

[Cowfish Aesthetic]

Only assuming that repeated subclinical stress does not add up. Between that and slower recovery due to aging, are we sure our tissues won't get inflamed from the same amount of "silent bubbles" exposure that 10 years and a 1000 dives ago did absolutely nothing?

Is there any evidence that this is a factor? I tend not to worry about hypothetical risks until there is some reason to believe that they exist.

 

[dmaziuk]

Is there any evidence that this is a factor? I tend not to worry about hypothetical risks until there is some reason to believe that they exist.

Oh, I'm just keeping up an idle conversation. For all I know it's quite the opposite: it builds up tolerance and a 60 yo with a 1K dives under his belt can shake off more "silent bubbles" than would send a 20 yo w/ 10 dives to a chamber.

You dive, you may get DCS. You most likely won't, but the term "undeserved DCS hit" exists for a reason.

 

[Storker]

If you have not rolled a particular number, say 6, after 9 tries, one possible conclusion is that the die is imperfect and weighted/shaped to make a 6 less likely than any other number. After just one roll, there is no way to know this. After 10 rolls, you get a hint. After 100 rolls, not getting your 6 by then is highly unlikely if all numbers are equally likely.

While I agree in principle, I think you're taking the hint too early. In the die case, there's a 16% chance for not rolling a 6 in ten tries. That's not particularly long odds, and quite a bit higher than the 5% normally required for a "statistically significant" conclusion.

And sometimes probability and statistics just mess with us: