# The Significance of DCS Probability on a Single Dive Profile

If you consider only your risk of getting decompression sickness on any single dive, you might wonder whether it really matters (within reason) what risk level you choose.  What’s wrong with choosing a dive profile where the risk of decompression sickness is, say, .005 (being .5%, or 1 chance in 200) instead one with a more conservative risk of .0005 (being .05% or 1 chance in 2000)?  In either case, while there is some non-zero risk of decompression sickness, the most likely outcome of that dive is you won’t get bent. So, no harm, no foul? Not really, because you’re only looking at the outcome of a single dive.  Since, if you’re reading this, we can presume you intend to continue diving, your dive experience is likely to expand over time to hundreds or thousands of dives.   So it’s important to look at where seemingly small differences in risk level can lead you.

The  graph below illustrates how the probability of getting at least one hit varies both with the risk for a single underlying profile “p(dcs)”, and with the total number of dives in a series of dives undertaken on that profile. The dives here are all on air to a depth of 80 fsw with a 3 min safety stop at 15 fsw. The “risk”, or p(dcs) values  for each of these three profiles were determined (using the dive planner) to be: 0.00896 (.896%), 0.00414 (.414%), and 0.000845 (.0845%) for the dives with 40, 30 and 20 min bottom times respectively.

As with the other calculations, the probability of getting “m” hits in “n” identical dives is obtained from the general expression (from basic probability theory): In the graph below, the number of dives executed for each profile “n”, ranged between 1 and 10,000. Applying this expression, we find that the probability of getting zero hits ( m=0) over a series of  “n” identical  dives, whose individual risk is “p(dcs)”, is given by: so that the probability of getting at least one hit “P{}” is obtained from :  As you can see from the graph, by the time you get to even 100 identical dives at a single-dive risk of .00896 (roughly.9% or still less than 1 in 100) your chances of being bent at least once has passed the 10% point (reached after only 10 dives) and is starting to approach 100% which is essentially reached before the 1000th. dive.  Similarly, a single-dive risk of .00414 (just over .4% or still less than 1 in 200), while it doesn’t rise quite as quickly with increased numbers of dives, still reaches essentially 100% by the 1000th. dive.  On the other hand, a single-dive risk of .000845 (just over .08% or less than 1 in 1000), while it still rises with number of dives, remains under 1% risk after 10 dives and, after 100 dives, is still less than 10%.  By 1000 dives, the risk here too has risen significantly, but is still well below 100%.

#### The Significance of DCS Probability on a Single Dive Profile — 2 Comments

1. Craig Wood on said:

Hi Saul,

I really appreciate your last two blogs.

The MOD for 32% at a PO2 of 1.4 is 111 feet, many computers do not give a NDL beyond this depth,

I routinely ascend at 30 ft/min, it is not really very difficult. Whatever.

The cumulative risk of DCS is very interesting, however, nobody dives to the NDL on every dive. I have nearly 1800 dives using DSAT, without an episode of DCS. When I do dive near NDL, I often pad my SS to 5 minutes.

I do have a few additional questions regarding SAUL. How does SAUL deal with repetitive dives? I assume it tracks gas loading and calculates time based on the chosen risk value for DCS. How does SAUL deal with deco dives? I assume it is by a similar mechanism but wonder about deco times and residual risk.

• saul on said: