Just for balance, Pegasus have been flying 737s (they started with -400/500s before moving to the -800) for 30 years, the A320ceo (of which they have 15) was only introduced to the fleet just over 6 years ago. The Neo is obviously an even younger fleet, so comparing a snapshot of the 737 only comprising 40% of their fleet now isn’t quite historically accurate.
It is worth considering why one airline, with a fleet of 82 narrow-body aircraft has had 3 runways excursions since 2018, 2 in the space of a month. Their fleet is roughly split 50/50 between two aircraft types, of similar type - i.e. they are modern, narrow body, twin engine aircraft. There are thousands of flights safely competed every day, on both types, all over the world. On the face of it
three events seems a lot for a single operator. It is curious that all the incidents are confined to one type in the fleet and that they have been operating the 737 for 30 years yet laterally begin to have runways excursion events. So there may be a training and operational issue on the 737 fleet.
Equally the A320 seems
to have a lower rate of runway excursion. Ryanair and easyJet both fly similar fleet sizes, the primary difference being aircraft type. To my knowledge FR have had one excursion with the 738, easyJet have had none. Given the regulatory environments that FR and U2 operate in, their T&C's and source of pilots you would expect the pilot pools to be comparable - the huge numbers employed should normalise variables like age and experience. Granted the numbers of incidents are small and there are a lot of variables - but looking at the rate of excursion is not unreasonable.
A cluster of incidents could be explained by "bad luck". I work in an extremely litigious branch of medicine. I have read report after report which assumes "bad luck" in what are actually symptoms of underlying failures in training, communication, risk assessment and management. Sometimes the equipment is an issue - but human factors and poor training uncover poor design or redundancy. Ignoring clusters is a bad decision, understanding the reasons for the clusters and redesigning processes, training and equipment is vital for improving safety. If that means that old techniques and equipment have to be replaced, that is what must be done. Playing with the statistics isn't the way forward. Most statistics can be brought to a normal range by selecting a long enough time to study.