Page Rank Theory...true not matter what the Page Rank?

Is this a correct theory behind increasing Page Rank and is it valid?

[riadn]

Ok first i'd like to start by thanking you all for teaching me more about SEO than 100 other websites put together...

Its common knowledge that if a particular page on the web has 1 backlink and the page which gives the backlink has a Page Rank of X then the page receiving the backlink will have a Page Rank of X - 1 or in some cases X.

This is true no matter the value of X(2 - 10).

Now a similar point.

It seems true to say that increasing your Page Rank from X to X + 1 would require N links from pages of rank X.(lets discount backlinks from pages with rank higher than X).

Surely this again is true no matter the value of X(0 - 9).

Therefore it follows that regardless of the Page Rank you need N links of Page Rank 4 to increase your page Rank from 4 to 5 and N links of Page Rank 7 to increase your Page Rank from 7 to 8 where N is the same value in both cases.

The question therefore follows... what is the value of N?
From your own experiences... or is it that simple?

[rfgdxm1]

PR is a logarithmic scale. Thus, your N is the base of the log. I've seen estimates that N is around 6, and from my observations seems ballpark accurate. Please note this. Since this is a log scale, if N is 6, to go from PR4 to PR6 means that you'll need 36 PR4 pages more to link to your PR4 to go from a PR4 to a PR6. This is why moving up to higher PR values tends to be so difficult.

[riadn]

really? I was thinking N was closer to say 20.
So from what you're saying to get from a PR5 to a PR6 I need 6 links from pages which have a PR5 linking to my PR5 page?
Surely its takes more than 6 links?

[NickCoons]

riadn,

<Its common knowledge that if a particular page on the web has 1 backlink and the page which gives the backlink has a Page Rank of X then the page receiving the backlink will have a Page Rank of X - 1 or in some cases X.>

Hold on, hold on.. this is not necessarily true.

There is PageRank, and there is Toolbar PageRank (which we often refer to as PageRank, because we're usually talking about the Toolbar representation).

The *real* PageRank is a number that Google will not give to us. This number is represented from 0-10 on the Toolbar, with 1 being N times more than 0, and 2 being N times more than 1, and 3 being N times more than 2, etc (N probably being somewhere around 6, as previously mentioned by rfgdxm1).

So if page A links to page B, then page A is going to give its PageRank, minus a dampening factor, divided by the number of other links on the page, to page B. So page A's contribution to page B is as follows:

Contribution = (PageRank of page A * X%) / Links on page A

Where X% is probably somewhere around 85%.

This contribution is then added to all of the other contributions that page B has been given, and the PageRank is shown to us on the toolbar represented by the Toolbar PageRank from 0-10.

So you cannot really use the Toolbar PageRank to determine how much real PageRank, or Toolbar PageRank, a page is going to contribute to another page; but you can use it (along with the other links on the page) to determine if a page is going to contribute more PageRank than another page.

That being said, a page of Toolbar PR X linking to another page may give that page a Toolbar PR X-1 always, often, sometimes or never, in practice.. but there is no rule that says that this is true, and it cannot be relied upon.

[NickCoons]

riadn,

<really? I was thinking N was closer to say 20.
So from what you're saying to get from a PR5 to a PR6 I need 6 links from pages which have a PR5 linking to my PR5 page?
Surely its takes more than 6 links?>

I think he means that it takes 6 *times* more links to increase the Toolbar PR by one.

[steveb]

"So from what you're saying to get from a PR5 to a PR6 I need 6 links from pages which have a PR5 linking to my PR5 page?"

Nooooo. Ignoring whether six links is the correct number or not, it takes maybe six links from PR5 pages to make your page a PR5 page, not a PR6.

[rfgdxm1]

>I think he means that it takes 6 *times* more links to increase the Toolbar PR by one.

To be more specific, what I meant assumed that your page was PR4, AND the additional pages linking to you were PR4, AND the link to your page was the ONLY link on that page.

[tedster]

Don't forget another big factor - a backlink PR "vote" is split equally among ALL the links on the page.

It helps to look at the basic PR equation. I know that the notation can make it seem complicated, but it is straightforward - especially when you focus on the section that I've highlighted in blue:

PR(A) = (1-d) + d(PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))

PR(Tn) is the PR of the n^th backlink page
C(Tn) is the total number of links on the n^th backlink page

Add up all those little quantities (page PR divided by the number of links.) Then multiply that total by a "damping factor", and also add in 1 minus the damping factor. But, since the damping factor is always the same for every web page, the size of the transfered PR is dependent on only two factors: the PR of the linking page and the number of links on that page.

That "number of links" factor is the main reason it takes so many backlinks to raise the PR from 5 to 6, for instance.

***
In order not to oversimplify this, on the real web, PR "votes" are often reciprocal. Even more frequently, linking patterns will loop around for a while, and come back to the original page after a few hops.

Because of this, the equation must be "iterated" or calculated over and over as the PR values shift -- until the PR of all the pages starts to approach a limit. And it's the damping factor that ensures all the PR actually WILL approach a limit.