Does the risk eventually catch up to everyone?

[antonija 0]

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Statistics should catch up with everyone eventually.

No they don't. Statistics don't hunt people, and they won't tell you what's going to happen to any particular person.

They do actually... it's just that statistics never tells you what is going to happen to specific individual (or any specific event), but rather what is going to happen with entire population. So while statistics do catch up "with you" (and every other skydiver) you still can't predict the outcome of your next jump (or your next 1000 jumps for that matter) purely by statistics.

My point was that despite statistics you could die on your next jump, or maybe when you cross the street to get some coffee during your coffee break. No one and nothing can predict that (even though some claim they can). It's what makes our lives so beautiful and fun.

I understand the need for conformity. Without a concise set of rules to follow we would probably all have to resort to common sense. -David Thorne

[tombuch 0]

There has been lots of good discussion about this topic in this thread, and on other threads. I covered the issue of risk, specific to student jumps, in my book "JUMP! Skydiving Made Fun and Easy." The book was published by McGraw-Hill in 2003, and is now out of print, partially because I wanted the manuscript updated and they didn't want to spend any more money on a second edition. The original book is still available as a used book from many vendors, or Skydiving Book Service appears to have new copies in stock. And it is still available as an e-book or a Kindle edition on Amazon.

In any event, I have attached a copy of the Understanding Risk chapter as a pdf. Please note this is the draft version from the original manuscript, and not the edited version. You will find lots of statistics and a means of evaluating risk.

Tom Buchanan
Instructor Emeritus
Comm Pilot MSEL,G
Author: JUMP! Skydiving Made Fun and Easy

[awagnon 0]

Thanks, Erdnarob, for these numbers. More reassuring. I see from your profile that your occupation is math. It's been a long time since I took statistics in school. I vaguely recall a formula for cumulative risk. i.e. if the risk is 1 in 100,000 of getting killed on a single jump, what is the risk of getting killed in 1,000 jumps. I don't believe it remains 1 in 100,000 nor is it simply 1,000 in 100,000 or 1 in 100. Do you recall the formula? I know on any single jump, the risk is the same, but isn't there a cumulative risk over time? I think this is the point of the original post.

Alton

"Luck favors the prepared."

[NotBond 0]

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You can use probability to determine your odds of surviving Russian Roulette.

You can't use probability to determine your odds of surviving skydiving. It just doesn't work. Probability is use to describe things that are out of your control. More often than not, the things that will bite you during a skydive are in your control.

Very true. One can double inspect their gear every time, be at their mental, physical, and emotional peak, etc., and still get hit by a falling chunk of frozen urine from the 747 20,000 feet overhead.

You can REDUCE your chances by practicing due diligence, but never eliminate it.

Courage is being scared to death - but saddling up anyways... - John Wayne

[pilotdave 0]

We can't eliminate all risk, but we can eliminate specific risks. Statistics don't mean much unless you find the right statistics that apply to you. If you don't swoop, you aren't exposed to the risks of swooping. If you don't wingsuit, you aren't exposed to the risks of wingsuiting. And the list can go on and on and on to include everything skydivers do. We have a lot of control over our risk level. But no matter what, jumping out of a plane isn't safe. As long as you are exposed to the risks of boarding a jump plane, you're not safe.

Dave

[erdnarob 1]

Since jumps are "independent" events statistics or better, probabilty remains the same for each jump ie. 1 fatality for 96,052 jumps made (Internationally). When you throw a coin, it's 50% tail or head, if you throw the coin again it's still 50% to get a head or tail. When you draw a card from a set of 52, probability changes after each draw if you don't put back the drawn card in the set.
1 in a 100,000 makes 0.01 in a 1000 (same thing)
You can argue that jump after jump you gain experience and that makes statistics better to stay alive which is true. But you know that with more experience you will do things more complicated like speed landing or big formations which can make statistics bad for you. Now we have to check if experience is balanced by more complicated stuff which seems not the case since 41% of fatalities happen with perfectly open parachute.
Statistics are important and comprise 3 things: 1) keeping a good record of what happens 2) getting a significative sample 3) doing a good analysis and interpretation.
Only the most advanced countries have a statistics department. It's the only way to know where the country is going and use appropriate actions to maintain or correct.
I guess the formula you are refering to is the one involving CONDITIONAL PROBABILITY where one event chance to show up is linked with another probabilty.

Learn from others mistakes, you will never live long enough to make them all.

[DJL 232]

"First, let me define what a "consistent skydiver" is exactly: A consistent skydiving is a licensed skydiver who completes at least 5 jumps per year with no more than 2 recurrency jump required."

For starters, I improve my safety by going no-where near this dude that does 5 jumps in a year and has to keep getting recurrency training. F-that!

To answer your question, the risk is not the same for every jump - just for those who treat every jump the same. Your risk decreases with experience; talent and knowledge. You're still subject to the same risks as everyone, you just learn to deal with them better. The two attitudes I hate the most are "Shit Happens" and "I AM a 1000 jump skygod, therefor I can." If you think that shit happens or that your jump numbers mean you can do more dangerous things, then you're not going to figure out WHY shit happens and avoid it and you'll think you can do maneuvers or jumps that you have no business trying.

"I encourage all awesome dangerous behavior." - Jeffro Fincher

[awagnon 0]

Each individual jump risk is the same and independent of other jumps. Like flipping a coin. Each time you flip it, the chance is 1 in 2 that you will have heads. However, the chance that if you flip the coin 6 times you will never see heads is only ? 1 in 64 or 2 to the 6th power. So lets pretend for a minute that your chance of getting killed skydiving is 1 in 2 each time you jump after removing all variables like swooping, wing suits, etc. It remains 1 in 2 every time you jump. However, after 6 jumps, your chance of being alive is only 1 in 64. This is the question I have about cumulative risk.

Alton

"Luck favors the prepared."

[pilotdave 0]

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Each individual jump risk is the same and independent of other jumps.

Unfortunately (or fortunately) it doesn't work that way.

The risk of each jump varies. Skydivers build talent and risk decreases. Then they take more chances, jump smaller canopies, try new things, and risk increases. Then they get better and more experienced at those things and risk decreases. Then they try new, more dangerous things and jump smaller, faster canopies. Risk goes up again.

The risk on a hop n' pop is not the same as the risk on a bigway head down jump. You can't apply simple statistics to risk in skydiving.

Dave

[DJL 232]

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Each individual jump risk is the same and independent of other jumps. Like flipping a coin. Each time you flip it, the chance is 1 in 2 that you will have heads. However, the chance that if you flip the coin 6 times you will never see heads is only ? 1 in 64 or 2 to the 6th power. So lets pretend for a minute that your chance of getting killed skydiving is 1 in 2 each time you jump after removing all variables like swooping, wing suits, etc. It remains 1 in 2 every time you jump. However, after 6 jumps, your chance of being alive is only 1 in 64. This is the question I have about cumulative risk.

But if flipping the coin is in the subset of A and then add that to a series between 1 and N-Factorial then the answer is 42. So, you're back where you started....

"I encourage all awesome dangerous behavior." - Jeffro Fincher

[JohnMitchell 14]

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So, perhaps I'll remain a student forever. It's safer and plenty exciting for an old fart like me.

If you always keep the attitude that you're still learning, don't know everything, and can get killed if you mess up, you can be a student forever. I still am in my heart.

[antonija 0]

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... It remains 1 in 2 every time you jump. However, after 6 jumps, your chance of being alive is only 1 in 64. This is the question I have about cumulative risk.

Now just take true value for probability of you not dying during one jump and multiply it with the number of jumps you think you'll make in your lifetime. What you now get is another specific event (or one series of events, that is all your jumps in your lifetime) so you still don't have your answer. There are many skydivers who will make "n" jumps in their lifetime and the risk you get from your calculation will still be distributed between all of us.

But then again this is the whole point of the statistics: It is used to discover and monitor trends in populations (of skydivers, animals, molecules and atoms, money, etc.), not individuals. So while none of us can't say anything specific about his/her skydiving career, we all get the shared probability of being killed on your next jump. Kinda makes it clearer why relationships between skydivers are a bit different than between other social groups.

I understand the need for conformity. Without a concise set of rules to follow we would probably all have to resort to common sense. -David Thorne

[awagnon 0]

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But if flipping the coin is in the subset of A and then add that to a series between 1 and N-Factorial then the answer is 42. So, you're back where you started....

I thought factorials applied to increasing probabilities. Like the previous example of drawing an ace of spades from a deck of cards where a card is removed each time if it isn't the ace of spades. Or, the chance of getting a "6" when you roll a die six times. Or 6 factorial, since you stop if you get a six. Perhaps factorials do apply to skydiving since the probability stops if you get killed. I don't know the answer. It's been way too long since taking basic statistics.

I believe the original post was simply a question about the more you jump, is there an increasing chance of eventually having a fatality, not counting increasing or decreasing your odds by experience, swooping, etc. I believe there is based on cumulative odds, but it can be modified both ways by changes in behavior, training, equipment, or technique as most of the posts have pointed out.

As a several posts mentioned, statistics are based on populations or groups and shouldn't be used for assessing an individual's risk. I disagree. That's how statistics are used They can be applied to an individual. "Hey doc, what is my chance of dying of my pancreatic cancer?" Well, your chances are "x" based on statistics from a population of patients with pancreatic cancer IF you don't do anything to change those statistics (surgery, radiation, chemotherapy, etc.).

I agree, the odds of a fatal jump (statistics) are constantly changing for an individual skydiver.

Alton

"Luck favors the prepared."

[labrys 0]

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84% of those fatalities appear to be caused by human error. (That means attitude is the most important)

Well, perhaps this is true, Andre... but I think it's also important to consider that in high stress, and possibly high speed circumstances, even someone with the best possible attitude has a "statistical" chance of screwing up.

The high percentage of pilot error fatalities might reflect more on the chances of anyone, regardless of attitude, surviving a mistake.

So what are the odds that even the most careful skydiver will drop the ball?

Owned by Remi #?

[erdnarob 1]

If each jump is really an independent event it's not cumulative. This simplified assumption is OK only if conditions remains the same. We know that in the reality they vary. I have an idea of what you have in mind like if the risk to have a car accident is say 1 accident every 100,000 miles based on a large population. Well more miles you travel and more risky it is. That means on an large population there will be an average of 1 accident every 100,000 miles or 2 accidents every 200,000 miles... That doesn't mean that after 100,000 miles you will have a car accident necessarily but if you don't some other people will have more than one but the average will stay the same.
But making more jumps certainly doesn't decrease the risk of fatality.
Coming back to your coin try this. Throw it the right way 100 times and record the results. You should have around 50 heads. Probability is the science of large numbers, more you toss your coin and more the number of heads (or tails) will approach 50%.

Learn from others mistakes, you will never live long enough to make them all.

[erdnarob 1]

Attitude is a way to express the word judgment. As a human being we should evaluate what we can do or not. Some are good at that while some other are not. The statistics I have posted show that students are well protected by the training system. The problem arises later on with experienced people. When we drive a car on the road we are continuously evaluating conditions around us and using our judgment. We have to do the same in skydiving and that includes the way we feel in shape or not. I have refused to sign up a student after the first jump course when after a conversation with him he told me he haven't had any meal since the day before because he was too much stressed. Other than that he was smoking too much that day. I will not suprise anybody if I remind the readers that skydiving is a high risk sport. We have to be always on alert mode while skydiving as I used to say. I believe in our great sport and provided we stay alert that sport can be done with a minimum of problem.
I don't want to scare anybody but here are my own facts about this subject.
On 35 years:
15 people I knew (having at least one conversation with them) died in skydiving
6 people I didn't know died in skydiving when I was there
4 aircrafts I have jumped from have crashed
There are old bold skydivers but there are no bold old skydivers

Learn from others mistakes, you will never live long enough to make them all.

[Megatron 0]

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In any event, I have attached a copy of the Understanding Risk chapter as a pdf. Please note this is the draft version from the original manuscript, and not the edited version. You will find lots of statistics and a means of evaluating risk.

Thanks, that was exactly what I was looking for. It seems that if one takes a more conservative approach to the sport, many of the leading causes of skydiving fatalities can be eliminated entirely. The remaining inherent risk seems to be at a level that one may not live long enough and make enough jumps such that they will truly be tempting the odds.

[yarpos 4]

"So what are the odds that even the most careful skydiver will drop the ball?"

FWIW for me its been 1 in 600. I am very conservative and have two incidents were I was lucky to survive. One I "deserved" if that is the word , a very low reserve opening after hanging on to a mal for for too long. The other was more random... falling beside the prop of a chase plane on a formation load that ended up sliding under us on climb out, with me last out. The first one I learnt a big lesson from, the second one got me in a lot of new conversations with load organisers and pilots....always a good thing anyway

regards, Steve
the older I get...the better I was

[pchapman 262]

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I vaguely recall a formula for cumulative risk. i.e. if the risk is 1 in 100,000 of getting killed on a single jump, what is the risk of getting killed in 1,000 jumps. I don't believe it remains 1 in 100,000 nor is it simply 1,000 in 100,000 or 1 in 100.

What you are thinking of is this:

Chance of getting killed 1 in 100,000 per event (=jump).
Therefore chance of not getting killed is 0.99999.

To make 1000 jumps, you need to get "not killed" 1000 times in a row.

So it is .99999 for one jump, times .99999 for the next jump... and so on.

(Like a coin flip: .5 to get heads. So to get heads 3 times in a row it is .5 * .5 * .5 = 1/8 chance.)

So for the jumping, it is .99999 to the power 1000 =
.9900497 to not get killed.

Subtract that from 1.0 for the chance to get killed, =
.00995

= 0.995 % chance.

This is very close to the approximation where one just multiples 1 in 100,000 by 1000, equals 1 in 100, equals 1 %. The approximation only works when calculating events that are highly unlikely.

(When one gets into calculating something like how many malfunctions will I have in 2,000 jumps if people have a mal on average 1 in 500 jumps, that's a little different. One can still look at the simple average and say "4" as an approximation, but the real math gets a little messier, into binomial theorem stuff, because one is looking at the number of mals, which can vary, not whether or not one has a mal at all. In the death case, one only cares if one gets killed once as that puts the stop to further chances of jumping and getting killed again...)

[awagnon 0]

Thanks, Peter. Your reply answers my question about cumulative odds. Since my instructor has had 3,500 jumps, his odds of having had a fatal jump is about 3.4%. Actually pretty high.

Alton

"Luck favors the prepared."

[antonija 0]

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Thanks, Peter. Your reply answers my question about cumulative odds. Since my instructor has had 3,500 jumps, his odds of having had a fatal jump is about 3.4%. Actually pretty high.

Was about 3.4%. That would be statistical result for his jumping career. If he had 100 skydiving buddies who jumped as much as he did 3.4 of those 100 should be dead by now.

This would be the same as flipping the coin 100 times and than calculate the chance of getting the result you got from those flips.

I understand the need for conformity. Without a concise set of rules to follow we would probably all have to resort to common sense. -David Thorne

[labrys 0]

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Since my instructor has had 3,500 jumps, his odds of having had a fatal jump is about 3.4%. Actually pretty high.

No, it just doesn't work that way. Those kind of cumulative odds only work when the outcome is completely predictable, as in a quarter will land heads or tails or on an edge and the quarter itself can't influence it's own behavior. The quarter has 3 options and nothing else.

A skydiver can be reckless or safe...can use questionable gear or good gear. The 1/100,000 odds reflect a combination of behaviours. 1/1000 reckless skydivers might die compared to 1/1,000,000 safe ones.

Owned by Remi #?

[fred 0]

I find that people who complain about statistics are usually people who will say, "You can make statistics say whatever you want them to say." People who understand statistics are the people who extend this by adding, "... by asking the right question."

Whenever you see/read/hear statistics, you have to pay attention to "What question was being asked?" You can skew the final numbers quite a bit by changing the question very slightly.

Ask the simple question: If a person is going to jump out of an airplane tomorrow, what are the odds that he/she will suffer a fatal accident. The answer is simple. It's about 1/100,000, or 0.01%. From this, you could read that skydiving is very safe.

But change the question: If a USPA member is going to jump out of an airplane tomorrow, what are the odds that he/she will suffer a fatal accident within the next year. When I run those numbers, I come up with an answer of about 1-2%.

If you try to refine that question further by specifying an active jumper (however you define 'active'), or by discipline (student, swooper, CReW, FF, tandem, etc), it's a lot harder to find the numbers. My educated intuition is that the numbers are lower for students/tandems, and higher for the other disciplines, with a significant spike for swoopers.

My rough calculations say that the average non-student USPA-registered jumper has about a 2% risk of a fatal accident if he jumps an average amount during the average year.

This is, admittedly, much higher than I expected.

But I expect that if you sample the dz.com population, you will find that they are better informed and generally safer than the skydiving population as a whole. 2% is not outside the realm of possibility for the general population.

[erdnarob 1]

Hi Peter, as you said the problem is not as clear as it appears. Here we have a binomial "experiment" as you said because there is only 2 possible results since each jump can be a success or a failure. Maybe we should talk here about Mathematical Expectancy of a binomial experiment. The formula is quite simple : E(X) = np where 'n' is the number of tries and 'p' is the probability of each event or jump to be killed.
Therefore if Awagnon's instructor has 3500 jumps what is the Mathematical Expentancy for him to be killed if the probability of being killed is 1 every 100,000 jumps.

p=1/100,000
E(X) = (1/100,000) x 3500 = 0.035 or 3.5% which is almost the result obtained by your approach which is: 1 minus (0.99999 to the power 3500) = 0.0349 or 3.4%

What is amazing with your approach for 100,000 jumps is that you get the following result ie. 0.63 or probability of 63% to be killed.
If you use my method we get: E(X) = pn = (1/100,000) x 100,000 = 1 (probability of 1) or a probability of 100% to get killed while doing 100,000 jumps which is more normal mathematically speaking...Thank you Awagnon, you gave me the chance to review my Probabilities. But I still have a doubt !!!!

Learn from others mistakes, you will never live long enough to make them all.

[ufk22 32]

Any probability that come out 100% has obvious problems. The probability of 100,000 coin flips and no heads is not 100%, but.........
Statistics can't tell you much about YOUR chances of survival in this sport. Much more relevant is you personality and attitude, ability,equipment, and currency .
Look at the deaths from true double malfunctions, ie, properly deployed main, chop, and properly deployed reserve at proper altitude. This number is so extremely low as to be almost non-existent.
IF you stay current (not less than 40-50 jumps a year, more if multi-discipline), have some degree of physical and mental ability, have an AAD and/or Skyhook/RSL, don't fly a canopy too small for your experience level, don't do radical hook turn landings, and don't overestimate your abilities (this is the tough one), you can still die. Your chances are just much, much lower.
Statistics don't catch up with you.
Fatigue does. Being unprepared does. Ego does.

This is the paradox of skydiving. We do something very dangerous, expose ourselves to a totally unnecesary risk, and then spend our time trying to make it safer.