All very well stated.
When I broke down the numbers the other year, going back to the start of 8 classes, it was pretty evident that:
Among elite programs that private schools held a competetive edge, but nothing necessarily crazy. Observationally this isn't hard to believe with the two most trophied schools by a long shot both being private schools. A standard that the LWEs and Main Souths can't eclipse, but do compete well against.
Then the next tier was your tier of schools that was not quite elite, but consistently strong. In this tier any private-public difference was totally wiped out.
Then in the lowest tier, programs that will almost never reach a semis let alone finals it was likewise nearly equal to perhaps a slight public edge (razor thin).
But why the perception? I think there's a statistical fallacy we don't notice when we just compare private school verse public school record, which is a common stat used in these arguments.
Think of two equally matched schools competing for the state title, one private and one public. We can probably do this at any of the 6 classes that are split this year.
The public school may very likely have made it to the finals beating all public schools along the way. Maybe they beat one private along the way. So we get perhaps no new data all along the way. The private school on the other hand may very well have beat 3 or 4 public schools along the way. So we get a 3-0 tally to add to our overall private v public record. Conversely whenever there is a weak private school that's bounced in round 1 we only get a 0-1 record to combat the other direction. They can't go get beat again to reinforce their lack of success. Or perhaps they get bounced by a private and we get NO data displaying a weak private even if a large number of public programs may have beat them as well. You can play out this same story in your tier two programs. In your typical private v public quarters matchup its likely we accumulated a 2-0 private-public record one way and a null record the other. Even if the public wins, that quarter of the bracket yields a 2-1 private-public record edge.
Basically the private schools are just a more extreme representation of the have and have nots that define the entire state of HS football. And the difference in opportunity of matchup helps skew that imbalance into a greater public v private divide when we only scratch surface of total record.
So where do we go? Private schools on average should be playing slightly higher than their enrollment than a comparable public school and the waiver program should IMO be eliminated or based on more structural components than a 2 year rolling record that yo-yos private schools up and down every two years.
To the extent that success is a component of classifications it should be applied to both private and public schools. Though I tend to also think it should be zero factor. The objective IMO should be : fair opportunity to field a competetive team. Equality of outcomes shouldn't be the goal, but rather access to opportunity. So enrollment should still be a big factor. Lena Winslow or Byron are top 50 programs if you beleive a ranking system like Massey, but it'd be pretty silly IMO to say they'd be a high-mid seed school in a second best playoff that would match them with tons of 7A and 8A schools if you could line up all schools on a strictly rating basis.
As to football enrollment: it matches regular season to playoff better. Naz absolutely has benefited from having a tough regular season record that preps them well for 5A. It's a totally valid competetive advantage that nearly any small to mid size team could take on in theory. Obviously there's other advantages and disadvantages too, but that goes for every school - just a matter of how you use those advantages. But maybe that opportunity shouldn't exist : you play against the size of school in the playoffs that got you there. Not unreasonable. It would certainly help elevate private school classifications on the whole (with perhaps a slight modification needed that doesn't drag down some of the 8A schools to 6/7A).
