I have a question that seems a bit off topic, but what does qualify as a principle? what does qualify as roots of certain way or ideology/DNA in football?
Those terms are used in very flexible ways during argument.
Is Pep way and Crujif way the same principles? Is Lucho a Barca DNA? Naggelsman? Tuchel? Bielsa?
If I may answer this using my professional knowledge,
IN GENERAL (not in football in particular, but it applies to everything that has principles) a principle is a proposition standing at a very high level of abstraction.
The more abstract the proposition, the more close to that being a 'principle'.
The more concrete, and tied to specifics, it is, the further it drifts away from being 'a principle'.
A principle is always foundational: It acts as the base of other -less abstract- principles, derived by it when it becomes concretized.
Which other principles, in turn, can become concretized themselves in less abstract propositions, until you reach a threshold where you don't even talk about principles, as you don't have sufficient abstraction in them.
Some examples from a non-football domain:
"The essence of man is his moral being" -> that's a principle at the highest level of abstraction you can get.
"Honesty is the highest virtue of morality"-> that's a principle at a lesser level of abstraction compared to the above.
"Telling the truth, even when unpleasant, is an act of honesty" -> Likewise, here there is a even less abstraction. This one is questionable if it is principle, it's a borderline case. I would call it a maxim.
"If you have second thoughts on an issue, disclose them"-> that's not even a principle. It does not have the sufficient level of abstraction to be one. IT's a practical rule of conduct.
Some examples in football now:
"Having the ball most of the time is a value in football" -> That's a principle at a very high level of abstraction
"A team should have its players expand the pitch to keep possession" -> Principle at a lower level of abstraction than above
"To expand the pitch in possession, you need the wingers to not drift centrally" -> Likewise, one step below in abstraction
"A team should play 4-3-3 to have wingers stay out wide" -> Even less abstraction here. That's a borderline case, IMO it's more a maxim than a principle.
"The current Barca should play 4-3-3 to keep possession the most" -> That's not a principle at all.
It's a current directive stemming from principles standing at a higher level of abstraction, when applied to a very specific setting.
What I should note, is that stepping down a level of abstraction every time, is neither simple nor straight-forward,
and that's quite crucial...
PS: Lastly, about ideology in football,
I would say it's a collection of principles that form a coherent whole all together.