A statistician’s analysis of Ryanair seating plans has led to claims that passengers are more likely to win the lottery than be randomly allocated a middle seat as often as they are.

The calculations have prompted Ryanair to admit that it tries to “keep window and aisle seats free” but that the remaining seats are still “randomly allocated”.

Jennifer Rogers, the director of statistical consultancy at Oxford University, was given access to information on the number of free seats available at the time of check-in on four different flights and from this was able to calculate the probability of customers being allocated the dreaded middle seat - as each of them was, four times over.

Her sums suggest that the allocation of seating for passengers unwilling to pay to select a seat is not as random as they might think.

Ryanair has angered some passengers over the summer by suggesting that must they pay an extra charge in order to sit next to each other on a flight.

Whereas in the past, many swear blind that they would normally have been seated with friends and family if all were travelling on the same booking, this appeared to suddenly no longer be the case.

@Ryanair @TomWitherow where is our other 'random' allocated seat?there are all these free rows around..row 33!!To sit together £28 joke! pic.twitter.com/fSfZWPyYs6 — niki spiller (@sleepinbooti) July 3, 2017

Ryanair has denied on many occasions in recent months that it has changed its policy and said that it is not deliberately trying to split groups up with the way that seats are allocated.

One of the few people able to mathematically put this to the test however is Rogers, who could calculate the likelihood of certain, real-life seating situations arising after being privy to the airline’s seating plans.

She was asked by the consumer programme Watchdog to calculate the chances of four programme researchers being randomly allocated middle seats on all four flights, which is what happened.

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On their Manchester to Dublin flight, for example, she could see that there were 65 seats available at the time of check in, 15 of which were middle.

“Therefore, we can calculate the probability of being allocated four middle seats on this flight as 1 in 500,” she said. “Carrying out similar calculations for the other flights, and then combining these probabilities together, I was able to calculate the probability of four researchers being allocated middle seats on their four flights, if the seating allocation was indeed random, as 1:543,094,880. A tiny probability.”

So tiny, in fact, that you are more than ten times more likely to win the UK National Lottery (a probability of 1:45,057,474), she says, than for this to happen.

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We put this to Ryanair.

“No, this claim isn’t true,” said Kenny Jacobs, Ryanair’s chief marketing officer.

“When a customer does not purchase a seat, they are randomly allocated a seat. The algorithm changes on each flight and each route by reference to demands for reserved seats.”

He went on say that, while the airline did withhold window and aisle seats from “random-seat” customers, they were still able to allocate the remaining seats for them at random.

“Some random seat passengers are confused by the appearance of empty seats beside them when they check-in up to four days prior to departure,” he said.

“The reason they can’t have these window or aisle seats is that these are more likely to be selected by reserved seat passengers many of whom only check-in 24 hours prior to departure.

“Since our current load factor is 97 per cent, we have to keep these window and aisle seats free to facilitate those customers who are willing to pay (from €2) for them.”

Just checked-in my wife & 17 mates on RYANAIR random seats, not 2 have been seated together, option to buy seats, rip off! pic.twitter.com/2HcAodGExd — John P J D (@johndoran21) September 5, 2017

Still confused? Us too.

“This is entirely a matter of customer choice,” Jacobs explained. “We are very happy to facilitate any customer who wants a free of charge random seat but we are also going to do our best to facilitate customers who are willing to pay for a reserved seat (usually window or aisle) which start from €2.”

In what has, in many ways, become a battle of semantics, Rogers puts it this way:

“I don’t think they do allocate seats randomly. Ryanair have said that they save the window and aisle seats. I think the rows will be randomly allocated, but you will be given a middle seat and then they fill up from there.”

Ryanair also denied that it was concerned about reports that some passengers, upon boarding, then try to find people to swap seats with in order to reunite groups.

“No,” replied Jacobs when asked if it was a concern, “as all customers sit in the seats they have been allocated and the issue doesn’t arise.”

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Telegraph.co.uk