# How likely am I to die in a ball of fire?September 18, 2011 1:54 PM   Subscribe

Some help with general aviation safety related statistics. Do I really have a 7% chance of dying in a ball of flames if I fly for three hours a week in a fixed wing non-commercial plane?

I see here (page 5) that there are 1.19 fatal accidents in fixed wing non-commercial flights for every 100,000 hours flown. I'm working on my pilot's license now and I fly for about 3 hours each week. Let's say I continue to fly for 3 hours a week for the rest of my life (40 more years). That's 6,240 hours of flight.

With the per/hour probability of death being 0.0000119, am I right that I have a 0.0000119 * 6240 = 7.4% chance of dying in a plane crash?

Am I handling these numbers correctly?

By the way: I have no fear of flying whatsoever. My wife, however, has asked me to look into the safety of my new hobby. I was hoping these numbers would be comforting for her, but I'm finding that they may not be.

Note: I already know that safety always depends on individual conditions and the individual pilot. But they are helpful when we're trying to figure out what general trends look like. Thanks.
posted by crapples to Sports, Hobbies, & Recreation (27 answers total) 1 user marked this as a favorite

With the per/hour probability of death being 0.0000119, am I right that I have a 0.0000119 * 6240 = 7.4% chance of dying in a plane crash?

No, because with that logic, if you had a 50% chance of dying each hour, you'd have a 50% * 2 = 100% chance of dying after two hours, which you don't; it's 75%, as you have to win two coin flips to stay alive.

In fact what you want to do is estimate your chance of not crashing every hour and multiply them all together, which is (1 - 0.0000119) ^ 6240 = 92.84% chance of not dying = 7.16% chance of dying.

So actually these numbers turn out to be pretty close. This is because (for mathematical reasons I could go into in more detail), if a probability p is very low, (1 - p) ^ n is very close to 1 - pn.
posted by dfan at 2:16 PM on September 18, 2011 [1 favorite]

I was about to say that you should look at the reverse case, and that in each hour you have a .9999881 chance of not dying... but .9999881 ^ 6240 gives roughly the same answer (7.2%). (On preview, dfan has it.)

I think the fallacy here is that each hour isn't an independent event, which is how I'm treating it. The 1.19/100,000 figure probably includes things that are better treated with conditional probabilities.
posted by supercres at 2:18 PM on September 18, 2011

My experience has been that no matter how much reassuring evidence you can present, people who are nervous about flying in small aircraft will continue to be nervous about it. There's very little convincing you can do with facts and figures.

What I have done in the past (and you're going to have to wait until you get your license for this) is to convince people by taking them for quick joyrides. Pick a perfect, calm, sunny day and spend maybe a half hour in the air. The best thing you can do here is be thorough, so take your time with the preflight, explain out loud everything that you're doing, anytime the airplane makes a noise tell them what it is.

What you're trying to do here is not to show that flying in general is inherently safe, but that you know what you're doing and know how to handle emergencies. Therefore, you are safe and your passengers don't need to worry.

The last time I took up a nervous flier I actually broke most of those above rules, but the one I did stick with was that I told them everything that was going on. It was a cloudy, bumpy day, and I mentioned ahead of time that it might be bumpy but there's nothing unsafe about it. I showed them the whole preflight, how to turn on the engine, and after every radio call told them what just happened - "We're just about to take off but there's one plane landing before we can get on the runway." "They just told us to make a turn, so here's a slight turn to the left." Stuff like that. My passenger fell asleep on the way to our destination, so I felt like that was an accomplishment.
posted by backseatpilot at 2:19 PM on September 18, 2011

Statistics . You're doing it wrong.

The general overall statistic that you gave is far too broad to generalize to just you.
Just some factors to consider in one's chance of experience a fatal incident could be:

- amount of total pilot time
- amount of recent flying experience
- what kind of weather a pilot chose to fly in
- age of the pilot

Only when all the above (and I am sure many more) factors are grouped in could a meaningful statistic that might be applied to you be generated. I am a pilot with over 1500 hours experience and a former flight instructor. Enjoy your flying. If you want to keep safe always keep current and never be tempted to exceed your actual abilities ( always underestimate your flying ability)
posted by Poet_Lariat at 2:27 PM on September 18, 2011 [2 favorites]

You are not handling the numbers correctly, although miraculously the answer you get is pretty close to correct. Let me explain.

Suppose that instead of 1.19 fatal accidents per 100,000 hours flown, there were 1 fatal accident for every 2 hours flown. Then the chance of death per hour is 0.5. By your logic, if you flew for two hours, you would have a 0.5 * 2 = 100% chance of dying. But this is clearly false.

If you treat each hour as an independent event (which is not really the case, but we're simplifying here) then you can calculate the probability as follows. Suppose that the probability of having a fatal accident in any given hour is p, where p is a number between 0 and 1. Then the probability of not having a fatal accident in that hour is 1-p.

If you fly for N total hours (and if we treat each of the N hours as independent events, meaning that they are not statistically linked to each other), then the probability of not dying in that time is (1-p)N. Since dying and not dying are mutually exclusive and exhaustive, the probability of dying is then 1-(1-p)N

In your case, plugging in p=0.0000119 and N = 6240 gives a probability of not dying approximately equal to 0.071566426, or about 7.2%.
posted by number9dream at 2:30 PM on September 18, 2011

My experience has been that no matter how much reassuring evidence you can present, people who are nervous about flying in small aircraft will continue to be nervous about it. There's very little convincing you can do with facts and figures.

To be fair, there's going to be blessedly little convincing you can do when the figures you are showing me say you have a chance of death that exceeds 7%.
posted by DarlingBri at 2:31 PM on September 18, 2011 [3 favorites]

Are these statistics uniform across the US? I remember reading that general aviation in Alaska is substantially more hazardous than that in the lower 48. It could be that a higher rate up there is driving the statistics overall, but I can't tell from the report.

Also: the fatal accident rate for commercial fixed-wing is about half that for non-commercial fixed wing, implying a fatality rate of 3.5% across the same time period for the same amount of flying - something that doesn't smell quite right.
posted by scolbath at 2:49 PM on September 18, 2011

To be fair, there's going to be blessedly little convincing you can do when the figures you are showing me say you have a chance of death that exceeds 7%.

True, but like Poet_Lariat says, I think the statistics are a little misleading. It's like saying you have a 1 in 500 chance of being killed by an alligator. Maybe over a general population, but if you live in Canada I think your odds are slightly different than that.

Just like any other activity that involves risk (which is... well, pretty much anything) you can mitigate your risk by thinking about safety. Don't eat the chicken that's been sitting on the counter overnight. Don't drive drunk. Don't fly when you don't have the proper skillset. If all you're doing is flying in clear, calm air - which is mostly what you're doing as a student pilot - your risk factor is going to be much lower than someone who's flying into unknown weather in a plane he's not familiar with.

I had a flight examiner tell me once, "After this checkride, you will be the safest pilot you will ever be." At that point, you know what you need to know and you're still uncertain enough about your proficiency to not do stupid shit. After that it's all downhill.

That is my roundabout what of saying, simply, "Don't do stupid shit."
posted by backseatpilot at 2:51 PM on September 18, 2011

I'm a pilot too and like being alive. I've read various discussions of how dangerous general aviation is and the conclusion seems to be it's about the same risk as riding a motorcycle. It's a reasonable comparison: a mode of transportation that's more dangerous that cars, has some conveniences, and is often done for fun.

One key thing about the danger of little airplanes is most of the risk factors are in your hands. Motorcycle riders get killed by idiot drivers in cars. Plane pilots mostly kill themselves. You may want to look at the Nall reports on GA accidents. 72% of fatal accidents are because of pilot error. A lot of those errors are things you can prevent by being a careful pilot: make sure you have enough fuel, don't risk dangerous weather, etc.

You may also find The Killing Zone interesting. I haven't read it, but the gist is that pilots get complacent after getting their license and get sloppy. More info here.
posted by Nelson at 2:52 PM on September 18, 2011 [1 favorite]

As has been said, your chances really are about 7%. That still leaves cancer and heart disease as top risks. Flying is a wonderful hobby that can be shared with family members and friends. It can also save commute time for some people. Overall, it's going to be a net gain in the amount of quality time you enjoy in your life unless you are a very unfortunate person. Even in that case, your family won't know that your alternative wasn't to die young another way (good luck selling that to your spouse, though.)
posted by michaelh at 3:14 PM on September 18, 2011

Not a pilot here; ignore should you choose.

If Nelson is correct, and the numbers are close to the same as motorcycles, then there will be wildly swinging variables/possibilities/probabilities, not only all of those brought up by Poet_Lariat but also the overall caution and care of the pilot, his attitudes.

The only way to stay alive on a bike over long periods of time is to be incredibly cautious, especially around other drivers but also just overall, not go 110mph on that road you know so well just because it's fun, damn sure not to do so often. The one man who I've known to have bikes his entire life, and have them as his only way around, he is remarkably cautious, he is always aware, awake, he is alert to everything.

So I'd think that the more you fly, and the longer you fly, the safer you will become, as your abilities increase. Those numbers you quote include everyone, whether they've just gotten their license and also pilots who have been flying their entire lives. An old school friend started flying in high school, we're now in our mid fifties, I'd fly anywhere with him without a second thought.
posted by dancestoblue at 3:28 PM on September 18, 2011

I think people are doing you a small disservice with all the caveats and such, crapples. It is true that you can mitigate your risk such that your own chance of dying is likely less than 7% over the number of hours you postulate. But that is still mitigating risk from a much higher baseline than most people accept regularly.

I'm not saying what you should or should not do. But neither can people handwave away the very real dangerous nature of general aviation relative to most other risks we take, including driving an automobile.
posted by Justinian at 4:15 PM on September 18, 2011

If Nelson is correct, and the numbers are close to the same as motorcycles

The numbers I've seen indicate it is significantly more dangerous than motorcycling.
posted by Justinian at 4:16 PM on September 18, 2011

True, but like Poet_Lariat says, I think the statistics are a little misleading.

But they're not. They are legit numbers, published by the Aircraft Owners and Pilots Association. Small craft flying is statistically dangerous. Even telling me that pilot error causes 74% of those accidents doesn't help, because even the most careful pilot has a 1.8% chance of fatality in an air accident.

It's fun, it's convenient, it's cool, it's exhilarating, it's amazing. All of those things are true. Pretending that it isn't also high risk just because you don't like the numbers is engaging in magical thinking. Believing it isn't so is not an inoculation against the occurrence.

Frankly, were my spouse utterly committed to this as a hobby, what I'd want to hear is that he would do his absolute best to minimise pilot error, that the children were grown up, and that we had extensive life insurance specifically for aircraft pilots.
posted by DarlingBri at 4:53 PM on September 18, 2011

Another way to compare this is that lifetime auto accident risk is about 1%. There's a reason life insurance won't cover private pilots without significant additional cost.

Another aspect to look into is what effect regular flying has on the overall death rate. I have heard it said [citation needed] that flying should not be an occasional thing.
posted by wnissen at 5:37 PM on September 18, 2011

But they're not. They are legit numbers, published by the Aircraft Owners and Pilots Association.

A number and the proper interpretation of that number are two very different things. Anyone with a 6th grade education can take the total number of pilots, the total number of fatal accidents and do a division. Interpreting what those numbers actually mean and to whom takes a certain degree of thought.
posted by Poet_Lariat at 5:45 PM on September 18, 2011

I tried to find statistics backing up the claim that general aviation is about as risky as motorcycles but didn't have much luck. I did find this interesting article on John King's opinion of aviation safety. King and his wife are some of the best known aviation instructors in the world and their attitude towards risk and training is worth paying attention to it.

He claims "you're seven times more likely to have a fatality in a general aviation (GA) airplane than you are in a car, per mile". No citation, unfortunately. The article is most interesting for what he has to say about risk management.

I'm very wary of the high school probability math being thrown around in this discussion. OTOH, it's certainly true that flying an airplane is more dangerous than not flying an airplane. We take risks in our lives all the time, both out of necessity and for pleasure. People tend to decide whether the risk is worth it more on the emotional value of the reward than the mathematical probability of the risk.
posted by Nelson at 6:03 PM on September 18, 2011

People tend to decide whether the risk is worth it more on the emotional value of the reward than the mathematical probability of the risk.

True as that may be the OP's question is about the high school probability math you are leery of, not about whether the rewards in this case are worth the risk. This question isn't "Is flying worth the risk?" it is "How risky is flying?".
posted by Justinian at 6:07 PM on September 18, 2011

I tried to find statistics backing up the claim that general aviation is about as risky as motorcycles but didn't have much luck.

Here we go:

From the FAA we see that the last couple of years have a fatal accident per 100,000 flight hours rate of between 1.1 and 1.2. So roughly 11,500 fatal accidents per billion flight hours, or two and a half times the rate per hour of motorcycles.

So a rule of thumb appears to be that general aviation is 2.5x as dangerous in terms of fatal accidents per hour than riding a motorcycle. That sounds pretty dangerous to me.
posted by Justinian at 6:25 PM on September 18, 2011

Wow - this has all been very enlightening. Although I've never even had a flash of fear while up in the air, I have to admit that these numbers and this discussion are giving me pause. I have a family and I, like someone said above, enjoy being alive. I hadn't even looked into the safety numbers before this weekend - and now I'm wondering if I'm not being a little irresponsible. I'll have to give this some thought.

Thanks for the thoughtful and excellent responses.
posted by crapples at 6:46 PM on September 18, 2011

I'm late to the party, but I don't think anyone has pointed out another mathematical fact here. You're calculating the chance now that you will die in a ball of fire some time in the next 6240 hours of flight. It seems to be true (notwithstanding all the other factors such as your skill, your general carefulness, the maintenance of your plane, etc) that the chance is ~7% over that entire time. However, every next hour that you fly is still only giving you a marginal risk of death of .001%. Once you survive the first 1000 hours, you will have much less than a 7% chance of death for the rest of the total hours you ever intend to fly. I imagine your skill will have increased also, which will decrease the marginal risk rate.
posted by RobotNinja at 7:11 PM on September 18, 2011 [2 favorites]

The problem with the GA category is that it contains a really wide range of aircraft types. For example, from the summary of the document you linked to:
In 2008, 228 amateur-built fixed-wing aircraft were involved in 226 distinct accidents[...] Sixty-one of these were fatal, resulting in 82 deaths; these [...] made up 26% of fatal accidents and 19% of all fatalities. By comparison, amateur-built aircraft logged less than 5% of the corresponding flight time. [...] The 27% lethality rate in these accidents was 10 full percentage points higher than that of accidents in type-certificated airplanes.
Are you flying an amateur-built aircraft? No? Then your chances are less than 7.2% (I didn't do the math). Other factors, such as type of aircraft, usage spectrum and your own personality, will also affect the probability (higher or lower). You need to look at the data carefully and then decide. A good starting point is to read the case studies in that report.
posted by Simon Barclay at 7:51 PM on September 18, 2011

General aviation is not what I think of as a safe activity. The pilots I've talked to say you can cut your risk considerably by the following measures, in order of magnitude of risk modification:

1) Stick to VFR conditions during daylight hours - and that means not setting out if you think your destination may get fogged in while you're in the air. This reduces your risk quite a bit.

2) Fly a plane model that has a good safety record. That obviously rules out ultralights, homebuilts, etc as mentioned above.

3) Fly a plane with enough hours on it that the bugs of the individual plane are worked out, but not so many that it's getting into the elderly, undetected-metal-fatigue age range. Apparently this is different for different planes.

There are probably statistics pertinent to these factors too - as has been pointed out, the remedy for overly broad aggregate statistics is to replace them with more narrowly applicable statistics - but I don't know where to find them.
posted by Protocols of the Elders of Sockpuppetry at 10:07 PM on September 18, 2011

So a rule of thumb appears to be that general aviation is 2.5x as dangerous in terms of fatal accidents per hour than riding a motorcycle.

Or roughly the same accident rate per hour as a motorcycle. Decide whether per mile or per hour makes more sense to you.

Where did you find the accident rate for motorcycles?
posted by Nelson at 10:07 PM on September 18, 2011

D'oh. Same rate per mile. GA planes fly about 150mph, or 2-3x faster than motorcycles.
posted by Nelson at 10:09 PM on September 18, 2011

Where did you find the accident rate for motorcycles?

Um. Wikipedia. I know, I know.
posted by Justinian at 10:22 PM on September 18, 2011

Just to pipe up with another answer that will be similar to the ones already given, but is closer to "correct" (at least, what would be given complete credit in a math stat course...):

If you have a period of time, and the frequency of events in that period of time, then we use the poisson distribution to work out the probabilities of events occurring. In your case, you have an accident rate of 0.0000119/hr, for 6240 hours. That is equivalent to having a rate of .074 deaths per 6240-hour period. What you want to know is the probability of >0 deaths, which is 1-e^-.074=.071. The similarity of this number to the other answers given above is due to a mathematical quirk discussed on the wiki page under "the law of rare events".

But the fact that that I said >0 deaths, rather than 1 death, should be a signal that something is not quite right. What isn't right is the fact that these are death rates over many people. The death events across many people might be well-approximated by a Poisson distribution; but that doesn't mean that the death probability of a single person is. There are all kinds of reasons to doubt that the analysis would hold for single people.

So, a caveat: Do not take the above analysis as evidence that YOU have a 7% probability of death. That would be buying too much into assumptions that are clearly false. However, that doesn't mean the 7% value is completely worthless. Take the above analysis as indicating that flying bears with it a certain amount of risk that cannot be ignored.
posted by Philosopher Dirtbike at 1:02 AM on September 19, 2011

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