YOWgary has brought up two points that I think actually matter, and do not get discussed enough.

1. AC 123 on a 789 departing at 1200 is cancelled and replaced with AC 123 on a 789 departing at 1200.

That is technically a cancellation in the stats, but who cares. Nothing happened.

2. The 15 minute mark. We all agree that a 4 hour delay sucks. But without the actual data on delay lengths, what happens if airline X has 95% of its flights delayed 14 minutes, and airline Y has 95% of its flights delayed 16 minutes?

One has a perfect OTP, and the other has 5%. But to the passenger, it's identical.