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Ryanair make around 725,044 flights per year. This They have been operating for 35 years, so have accrued around 25,376,540 flights.

They have also never had any fatal incidents or even major injuries related to a flight. Statistically, they should have had around 2 or 3 by now at least.

How and why is this airline so much safer, statistically (based on average commercial aviation fatality statistics) than almost any other airline in the world? (Easyjet being the closest with a similar perfect safety record).

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    $\begingroup$ Statistically, they should have had around 2 or 3 by now at least. I don't think that's how statistics work. $\endgroup$
    – zymhan
    May 13, 2019 at 12:59
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    $\begingroup$ I don't think you'll get a definitive answer here, but with a large number of airlines it's always likely there will be one or two airlines which are outliers by chance. You would need to test the null hypothesis with something like chi-square to be sure. Lots of work.... $\endgroup$
    – Dannie
    May 13, 2019 at 13:00
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    $\begingroup$ It's like saying, "My grannie drove her whole life without a speeding ticket, when most people get a couple in their lifetimes. How could she do that?". Reminds me of an old comic strip gag where a guy with a clean driving record for years and years is complaining about his insurance rates skyrocketing. Insurance agent says "you're due". $\endgroup$
    – John K
    May 13, 2019 at 13:24
  • $\begingroup$ A seemingly minor but very important detail. Are you asking specifically about Ryanair, or did you look through a list of aircraft accident rates and are asking about the lowest one? If the real question here is the odds any airline go without any fatal incidents, well that's probably 50 times more likely. $\endgroup$
    – Cody P
    May 13, 2019 at 16:25
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    $\begingroup$ Your number of total flights are way off. They have operated for 35 years, but haven't had that number of flights per year for long. Their fleet numbered 383 aircraft in 2017, but just five years earlier it was around 100 less. I can't find historic numbers, but according to Wikipedia but during the first few years they only had a handful of routes. $\endgroup$
    – bjelleklang
    May 14, 2019 at 7:48

2 Answers 2

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First of all, Ryanair has more than 700,000 flights per year now, but not during their entire 35 year existence. The total number of flights you give is therefore too high.

Assuming aircraft accidents are purely statistical (which is not true, of course), one can estimate the number of accidents you expect using a Poisson distribution: the probability of having $ k $ incidents with $ \lambda $ expected incidents is given by

$$ P(k) = e^{-\lambda} \frac{\lambda^k}{k!} $$

To get the expected number of incidents, we take the overall accident rate of 1 in 2.5 million flights (aviation-safety.net, for 2018, has been higher during the last 35 years) and multiply it with the total number of flights. For 25 million flights this would be $ \lambda = 10 $. This results in in a probability for 0 accidents of only $ P(0) \approx 0.004 \% $. Even when assuming 12.5 million flights in total (as suggested by David Richerby in the comments assuming a linear increase from 0 to 700,000 flights per year), one still obtains $ P(0) \approx 0.67 \% $ with $ \lambda = 5 $.

This means Ryanair is indeed safer than the average airline flight world wide, but so are many other EU or US airlines. Safety is not just a statistical coincidence, regulations are very strict in Europe and training is good resulting in higher than average safety records.

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    $\begingroup$ Indeed, if we assume that Ryanair started with zero flights per year (which they did!) and have linearly ramped up to their current volume (which is less accurate), then we estimate that they've had about half the number of flights that the asker claims. In that case, the claim of "should have had around 2 or 3" accidents needs to be revised to "should have had around 1 or 1.5". Well, it's not so surprising if a number that "should be" 1 or 1.5 turns out to be zero. $\endgroup$
    – David Richerby
    May 13, 2019 at 13:53
  • $\begingroup$ @DavidRicherby thanks, I added the estimate to my answer. $\endgroup$
    – Bianfable
    May 13, 2019 at 14:07
  • $\begingroup$ @DavidRicherby Also, the 1 in 2.5 million statistic applies to incidents, fatal incidents however are much more uncommon at around 1 in 11 million flights. $\endgroup$
    – Cloud
    May 13, 2019 at 14:08
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    $\begingroup$ @Bianfable Apologies... that is surprising. Next you'll be telling me my roulette technique is wrong (I wait for 3 reds or blacks in a row and then bet on the opposite colour, since although each spin should be a 50/50 chance, the likelihood of 4 in a row is much smaller than 50%)... $\endgroup$
    – Cloud
    May 13, 2019 at 14:14
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    $\begingroup$ @Cloud - not sure if that was a serious comment but yes that roulette technique is wrong. $\endgroup$
    – Martin Smith
    May 13, 2019 at 14:44
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Each time you interpret statistical values, you need to look at both, the mean value and the mean deviation.

The mean value of incidents per flight per year gives you the expectation value. That would be the 2 to 3 that you cited. Now you have to look at the distribution. Many statistics are shaped like the famous Gauss bell. The statistic of accidents per airline probably has a different shape because of the small numbers involved. A Poisson distribution maybe comes closer.

The point is, if you are reading a statistic result, where the expectation value is 2.5, and the mean deviation is 3, then 0 incidents would mean no significant deviation. There wouldn't be enough data to tell if the airline is safer or just lucky.

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