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Old 03-10-2010, 01:30 AM   #1
cmac0420
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The REAL odds of being in a plane crash

So I set out to find the actual odds of being involved in a commercial airliner crash on a per flight basis. I thought this would be easy to find. What I found was a whole lot of rhetoric about "your more likely to die on the way to the airport" and "you're safer up in the air than you are down here" type of answers, but I had a very hard time locating any actual numbers or statistics.

I kept searching

When I actually found the "statistics" that back these attitudes and expressions I was shocked at how flawed and purposely skewed these statistcs were. The "official" statistic that always seems to be thrown out there is this

1 in 11 million chance of being in a plane crash per person, per year.

And the way that they arrive at this number is just ridiculous. They divide the number of crashes in a year into the TOTAL POPULATION, and boom. 1 in 11 million. However, most people don't fly all that often, if at all. So that doesn't mean anything to someone who travels alot.

I concluded that there is millions and millions of dollars invested into making the average american feel safe on an airplane, and that these extremely flawed statistics that are put out there by supposedly "official" sources are pretty much propaganda, and I was determined to have my question answered.

What are the odds that MY specific flight crashes.

So I did some research and crunched the numbers and here is what I came up with:

average number of US commercial flights per year

divided by

average number of US commercial crashes per year

= odds of your specific flight crashing


SO

9,748,551(national airtraffic controllers association)

divided by

36.05(national transportation safety board)

= 1 in 270,417

1 in 270,417 that your flight goes down. And that's if your taking just one flight. If you take a round trip, it's 2 x 1/270,417. If you take a round trip with a connector flight each way, then it's 4 x 1/270,417.

SO

odds of being in a crash after
10 flights = 1 in 27,041
100 flights = 1 in 2,704
200 flights = 1 in 1,352

These don't sound nearly as appealing as that 1 in 11,000,000, do they?

Anyways I'm thinking of organizing all of this into an article, and the reason I posted this here is because I would like you math guys out there to "check my work" and see that my numbers are correct, or if you can add anything to my numbers or argument.
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Old 03-10-2010, 01:51 AM   #2
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by cmac0420 View Post
1 in 270,417 that your flight goes down. And that's if your taking just one flight. If you take a round trip, it's 2 x 1/270,417. If you take a round trip with a connector flight each way, then it's 4 x 1/270,417.
This isn't necessarily true. Longer flights are more likely to crash than shorter ones.
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Old 03-10-2010, 02:00 AM   #3
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by cmac0420
1 in 270,417 that your flight goes down. And that's if your taking just one flight. If you take a round trip, it's 2 x 1/270,417. If you take a round trip with a connector flight each way, then it's 4 x 1/270,417.

This isn't necessarily true. Longer flights are more likely to crash than shorter ones.
True, but the long flight crashes and short flight crashes are all included and accounted for, so it's all averaged out. also, I'm not sure about this, as it may be unfounded, but I have heard that flights are most likely to crash during takeoff/landing.
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Old 03-10-2010, 02:18 AM   #4
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Re: The REAL odds of being in a plane crash

Well, technically you cannot just add them up. So for 2 flights you need to figure the probability of NOT crashing. Which is 270416/270417. Then take that number to the 2nd power. .999996^2. Then subtract that result from 1. 1 - .999993 = .00000739597.

For 10: .000369738
For 100: .036311108
For 200: .137546825

But I don't really know what to make of this. What year's did you include in your calculation of the average? It might be better to know the number of flights and crashes for each year separately.
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Old 03-10-2010, 02:54 AM   #5
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Re: The REAL odds of being in a plane crash

Quote:
What year's did you include in your calculation of the average? It might be better to know the number of flights and crashes for each year separately.
1989-2009

http://www.ntsb.gov/aviation/Table5.htm
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Old 03-10-2010, 03:44 AM   #6
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Re: The REAL odds of being in a plane crash

As Sherman noted, your math is wrong.

The formula should be:

(1-x)^y = chance of no crash
where x is the chance of crashing (1/270417), and y is the number of trials (flights).

Here is what I get:

assuming 1 in 270,417 is right

1 flight: 99.99963% no crash
Roundtrip = 99.99926% no crash
roundtrip with connector (4 flights) = 99.99852% no crash
10 flights = 99.99630% no crash
100 flights = 99.96303% no crash
200 flights = 99.92607% no crash
6000 flights = 97.80563% no crash
187438 flights = 50.00008% no crash

So, don't ever take a 187,439th flight. You are sure to die.

Last edited by DMMx69; 03-10-2010 at 04:06 AM.
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Old 03-10-2010, 03:55 AM   #7
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by DMMx69 View Post
As Sherman noted, your math is wrong.

The formula should be:

(1-x)^y = chance of no crash
where x is the chance of crashing (1/270417), and y is the number of trials (flights).

Here is what I get:

assuming 1 in 270,417 is right

1 flight: 99.99963% no crash
Roundtrip = 99.99926% no crash
roundtrip with connector (4 flights) = 99.99852% no crash
10 flights = 99.99630% no crash
100 flights = 99.96303% no crash
200 flights = 99.92607% no crash
6000 flights = 97.80563% no crash
187438 flights = 50.00008% no crash
Yes. This is right. Something didn't quite feel right about mine. I should have kept going and I would have found the mistake. For 200 I took 1-(270,217/270417^200), instead of 1-(270416/270417^200). Good catch.
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Old 03-10-2010, 04:06 AM   #8
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Re: The REAL odds of being in a plane crash

Quote:
1 flight: 99.99963% no crash
Roundtrip = 99.99926% no crash
roundtrip with connector (4 flights) = 99.99852% no crash
10 flights = 99.99630% no crash
100 flights = 99.96303% no crash
200 flights = 99.92607% no crash
6000 flights = 97.80563% no crash
187438 flights = 50.00008% no crash
can you express these as ratios?
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Old 03-10-2010, 04:08 AM   #9
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Re: The REAL odds of being in a plane crash

Here is a hastily drawn graph of the function for variously selected numbers of flights. You would need close to 1M to have a 95% chance of being in a crash...which is nice I suppose.

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Old 03-10-2010, 08:33 AM   #10
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by cmac0420 View Post
So I set out to find the actual odds of being involved in a commercial airliner crash on a per flight basis.
The data you used is for "accidents" not "crashes". The number of fatal crashes is far lower than 36 per year. I have a hard time believing that most crashes have no fatalities.

I would be interested in knowing what is included in "accidents".
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Old 03-10-2010, 11:03 AM   #11
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by cmac0420 View Post
36.05(national transportation safety board)
Most of these are private planes, many of which don't have professional pilots. Seems like you should only restrict to commercial flights on decent sized planes.
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Old 03-10-2010, 11:47 AM   #12
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Re: The REAL odds of being in a plane crash

Remember that all donīt die in every "crash". Have you taken that into account?
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Old 03-10-2010, 12:21 PM   #13
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Re: The REAL odds of being in a plane crash

Yes, there is a difference between being in a crash and dying. I sort of assumed the OP meant being in a crash and dying. Clearly he just meant being in an "accident" which is unlikely to just include crashes. It probably includes two planes bumping into one another while taxiing or something.

In any case, here are two graphs with the Fatality data.



As the first graph makes clear, the probability of being in a fatal plane accident (fatal accidents per departure), has been on a decline since 1989. This suggests that simply averaging the results from 1989-present is a mistake. However, for simplicity I did it anyway (p = .000000637) and plotted the probability of being in a fatal accident as a function of the number of flights taken. So even after 1M flights, you would only have a 30% chance of being in a fatal plane accident.
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Old 03-10-2010, 01:22 PM   #14
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Re: The REAL odds of being in a plane crash

What are the odds for an average flight pilot to be in a accident during his career (respectively to "not be among us anymore" due to a flight accident)?
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Old 03-10-2010, 03:14 PM   #15
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Re: The REAL odds of being in a plane crash

Quote:
The data you used is for "accidents" not "crashes". The number of fatal crashes is far lower than 36 per year. I have a hard time believing that most crashes have no fatalities.

I would be interested in knowing what is included in "accidents".
Quote:
Remember that all donīt die in every "crash". Have you taken that into account?
Yes, I included non-fatal crashes on purpose. See that was one of my problems with the 1 in 11 million statistic. It was 1 in 11 million that you would "die" in a plane crash. In other words if you're in a crash and end up paralized from the neck down from it, they don't even count you. Like that plane that crash landed in the hudson river a couple weeks ago is not counted. I don't know about you, but the thought of any plane crash is pretty terrifying, and deserves to be counted. I wasn't interested in odds of dying. I was interested in odds of being in a plane crash.

Quote:
Most of these are private planes, many of which don't have professional pilots. Seems like you should only restrict to commercial flights on decent sized planes.
Wrong. These statistics are restricted ONLY to major U.S. commercial airliners. If you were to include private planes, the number would be much, much higher.
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Old 03-10-2010, 03:20 PM   #16
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Re: The REAL odds of being in a plane crash

Can anyone turn these into statistics? I.E. "1 in xxx"

Quote:
1 flight: 99.99963% no crash
Roundtrip = 99.99926% no crash
roundtrip with connector (4 flights) = 99.99852% no crash
10 flights = 99.99630% no crash
100 flights = 99.96303% no crash
200 flights = 99.92607% no crash
6000 flights = 97.80563% no crash
187438 flights = 50.00008% no crash
you can leave out the last 2 if you want. I mean really, who's gonna take 187,438 flights?
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Old 03-10-2010, 03:22 PM   #17
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by cmac0420 View Post
Can anyone turn these into statistics? I.E. "1 in xxx"



you can leave out the last 2 if you want. I mean really, who's gonna take 187,438 flights?

the 6000 was supposed to represent a pilot halfway through his career.

and the last number: someone who wants to be more than 50% sure they don't end up in a crash.

turning the numbers into "statistics": use division.
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Old 03-10-2010, 03:39 PM   #18
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Re: The REAL odds of being in a plane crash

Quote:
turning the numbers into "statistics": use division.
No idea how to do that. You saw I already fudged all the numbers in my OP. I need help on this one.
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Old 03-10-2010, 06:54 PM   #19
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by cmac0420 View Post
Wrong. These statistics are restricted ONLY to major U.S. commercial airliners. If you were to include private planes, the number would be much, much higher.
Then I agree with Sherman, of those 36 per year, many probably don't have serious injuries.

They might be counting things like the failed Christmas bombing in Detroit or the pilots that were playing (online poker?) on their laptops and overshot their destination.

Do the stats detail the incidents in a year?
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Old 03-10-2010, 07:08 PM   #20
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by wamplerr View Post
Then I agree with Sherman, of those 36 per year, many probably don't have serious injuries.

They might be counting things like the failed Christmas bombing in Detroit or the pilots that were playing (online poker?) on their laptops and overshot their destination.

Do the stats detail the incidents in a year?
The table that is referenced above does not indicate what constitutes an accident. But I suspect that almost any incident at all has to be reported as an accident (e.g. bumping the plane into the jetway) for maintenance purposes.

The OP seems to think that many of these accidents involve serious, but non-fatal injuries. However, I am not sure I believe that. How many people in the Hudson river landing (in which that pilot became famous) were seriously injured? I don't recall hearing about any. Yet I am certain that is reported as an "accident" and probably a fairly major one by airline standards.
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Old 03-10-2010, 08:00 PM   #21
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Re: The REAL odds of being in a plane crash

Quote:
They might be counting things like the failed Christmas bombing in Detroit or the pilots that were playing (online poker?) on their laptops and overshot their destination.
Quote:
The table that is referenced above does not indicate what constitutes an accident. But I suspect that almost any incident at all has to be reported as an accident (e.g. bumping the plane into the jetway) for maintenance purposes.

The OP seems to think that many of these accidents involve serious, but non-fatal injuries. However, I am not sure I believe that.
Accident

As defined by the NTSB, this is an occurrence associated with the operation of an aircraft where as a result of the operation of an aircraft, any person (either inside or outside the aircraft) receives fatal or serious injury or any aircraft receives substantial damage. The occurrence is also not caused by the deliberate action of one or more persons and that leads to damage or injury. The NTSB definition, which is also used by the FAA, divides accidents into four categories:

1.Major - an accident in which a 14 CFR 121 aircraft was destroyed, there were multiple fatalities, or there was one fatality and a 14 CFR 121 aircraft was substantially damaged.
2.Serious - an accident in which there was either one fatality without substantial damage to a 14 CFR 121 aircraft, or there was at least one serious injury and a 14 CFR121 aircraft was substantially damaged.
3.Injury - a nonfatal accident with at least one serious injury and without substantial damage to a 14 CFR 121 aircraft.
4.Damage - an accident in which no person was killed or seriously injured, but in which any aircraft was substantially damaged.

The failed christmas bombing, and the pilots overshooting they're destination would not be recorded as accidents. And neither would a runway bump unless it caused substantial damage.

These would be recorded as incidents, and not included in the afformentioned accident statistics

Incident
An occurrence, other than an accident, associated with the operation of an aircraft that affects or could affect the safety of operations.

Last edited by cmac0420; 03-10-2010 at 08:11 PM.
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Old 03-10-2010, 08:14 PM   #22
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Re: The REAL odds of being in a plane crash

Can anyone turn these into statistics/ratios? I.E. "1 in xxx"


Quote:
1 flight: 99.99963% no crash
Roundtrip = 99.99926% no crash
roundtrip with connector (4 flights) = 99.99852% no crash
10 flights = 99.99630% no crash
100 flights = 99.96303% no crash
200 flights = 99.92607% no crash
6000 flights = 97.80563% no crash
187438 flights = 50.00008% no crash


anyone?
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Old 03-10-2010, 08:50 PM   #23
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by cmac0420 View Post
Can anyone turn these into statistics/ratios? I.E. "1 in xxx"
anyone?
Apx:

1 flight: 99.99963% no crash = 1 in 270.270
10 flights = 99.99630% no crash = 1 in 27.027
100 flights = 99.96303% no crash = 1 in 2.705
200 flights = 99.92607% no crash = 1 in 1.353
6000 flights = 97.80563% no crash = 1 in 46
187438 flights = 50.00008% no crash = 1 in 2
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Old 03-10-2010, 09:23 PM   #24
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by cmac0420
Can anyone turn these into statistics/ratios? I.E. "1 in xxx"
anyone?

Apx:

1 flight: 99.99963% no crash = 1 in 270.270
10 flights = 99.99630% no crash = 1 in 27.027
100 flights = 99.96303% no crash = 1 in 2.705
200 flights = 99.92607% no crash = 1 in 1.353
6000 flights = 97.80563% no crash = 1 in 46
187438 flights = 50.00008% no crash = 1 in 2
Thanks buddy

Quote:
odds of being in a crash after
10 flights = 1 in 27,041
100 flights = 1 in 2,704
200 flights = 1 in 1,352
So I really wasn't that far off in my OP.
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Old 03-10-2010, 09:43 PM   #25
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Re: The REAL odds of being in a plane crash

Quote:
Originally Posted by cmac0420 View Post
Accident

As defined by the NTSB, ...

3.Injury - a nonfatal accident with at least one serious injury and without substantial damage to a 14 CFR 121 aircraft.
A quick review of the NTSB database shows that most accidents are this type where a flight attendant or un-buckled passenger is injured when the flight encounters turbulence. Hardly a crash.

Here's the link. And remember, keep those seat-belts buckled.

http://www.ntsb.gov/NTSB/query.asp
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