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You're right. I'm making an assumption of what Ryanair's system is based on the outrage people have at being deliberately assigned middle seats. Ryanair have admitted however that they prioritise window and aisle seats for paying passengers. My analysis took this to an extreme, which may not be the case.

And I agree, an R analysis is unnecessary but I've been telling people this conclusion for ages and they don't seem to get it!

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Ryan air might use a system where the probability of getting a middle seat is biased upwards, but not quite guaranteed. In that case, there has to be a critical point for the bias where it switches from "Better check in late" to "better check in early". Because with no bias (the first simulation) we have "better check in early" and with maximal bias (second simulation) we have "better check in late". I'd guess that this critical point depends on the proportion of pre-booked seats.

I wonder if Ryan air balanced the bias so it lies roughly at this critical point. This comes with the 'upside' of being more fair, as this system can't be gamed by changing your check-in time.

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