The word "need" implies a cause and effect that doesn't exist. What I agreed with, Peter, is that if you have high rankings for a competitive phrase there is a statistical probability you will also have a high PR. If you are color blind, there is a statistical probability you are male. If you are retired, there is a statistical probability you won't grow any taller. The list of correlated effects in this world is nearly endless and, in isolation, meaningless. At best, they might tell us where to place out bets. But they can't accurately predict what will happen next. They can't, because effect correlations don't tell us WHY something happens.
Interesting though is that you agree with that in order to get high rankings for a very competitive phrase (I mean a phrase with a high popularity) you would need a high PR. This has been categorically denied by most others.
There *are* fields, such as particle physics, where statistical analysis plays an important role in making predictions. The weather, generally, isn't one of those fields, however, as predictions are still based on cause and effect. Tell someone in Kansas their home will be hit by a tornado next Thursday because, statistically, a lot of tornado occur on that date and they'll either laugh at you or (knowing those mid-Westerners) introduce you to a load of buckshot. The only time weather prediction even marginally enter the realm of chaos theory is when they are long-term, when the causes are in as much question as the effects. And I think we all know how useful *those* forecasts are.
SEO has absolutely nothing to do with chaos theory. No algorithm invented by man, not even a man with a PhD or two, will ever be described chaotically. Indeed, I'd go so far as to say that computer chaos is an oxymoron.
I commend your willingness to approach SEO scientifically, Peter, but would remind you that real scientists are as careful when publishing their results as ever they were in testing the results. No scientist, for example, would ever state you "need" to be male in order to be color blind, because that relationship just isn't true.
Which is pretty much what everyone here has been trying to tell you.