There's no doubt that the probability of a bad outcome goes up with the number of things that can go wrong, but it might not be factorial.
Let's say that a person is involved in a highly risky activity where he will break his left leg in one out of 6 trials (equivalent to rolling a 6 on a single die). Let's also say that for a totally different reason (different independent failure mode), he will break his right leg in one out of 6 trials of the same activity (equivalent to rolling a second die).
So it's as if the person rolls a pair of dice and will break a left leg if the first die comes up with a 6 and will break his right leg if the second die comes up as a 6.
If we assume that the dice are independent, then there are 36 equally likely outcomes of rolling the two dice. We can write them all down as:
11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
Now if we count the cases where the left leg is broken, we'll find 6 of them (all in the bottom row). If we count the cases where the right leg is broken, we'll find 6 of them as well (in the right column). So there are 12 broken legs in 36 trials. In other words, we can say that a 1/6 chance of breaking a leg on a single trial becomes a 2/6 chance when we consider 2 legs (2 modes of failure).
Now if we were horses and a broken leg was considered fatal, then we would be just as dead if we broke two legs as if we broke one. So the case where we break both legs is still only considered one fatality. So in that case, we end up with 11 fatal outcomes out of 36 actual trials which is less than 12/36. The equation in that case is:
1/6 + 1/6 - 1/36
In other words, since we can only die once - even with multiple contributing causes - the actual chance of death is slightly less than 2 out 6. But to keep the math simple, we'll ignore that and simply add the probabilities. This will give us a slightly more pessimistic prediction but not by much (12 out of 36 instead of 11 out of 36 for the dice example).
Fortunately, we're flying hang gliders instead of rolling dice, so our odds of injury for any given failure mode are much less than 1 in 6. If the chance of death due to a lock out is 1 in 50,000 tows (just a number, not even as good as a wild guess) and the chance of death due to a jammed release is 1 in 100,000 tows (also just a number and not as good as a wild guess), then in 100,000 tows you might expect 2 deaths due to lock out and 1 death due to a jammed release.
That's a long way of saying that the cumulative probabilities of bad outcomes due to additional independent failure modes tend to be more addative than multiplicative.
Having said all of that, I do believe that the probabilities of bad outcomes are higher for towing than for foot launch. But that's just my own guess, and the actual probabilities would require knowing the real numbers of deaths and launches of each type (foot or tow). I don't believe even USHPA has that data since the actual number of flights (or flight hours) are not generally logged at the national level.
Of the people I've personally known over the past 12 years of my hang gliding career, I know of 2 deaths related to powered flight, one death in towing, one death in aerobatics, and one death due to equipment failure. Of course, that's a statistically insignificant sample, and I may be forgetting some as well.
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by JoeF » Thu Mar 03, 2016 3:17 pm 
