In another tread Why did I loose PR I made several comments on Google PR. I used the comments as the basis of an article "The Value of Google PageRank" and have a draft at: http://cssdesignmagic.com/page-rank.htm. I would appreciate any feedback, suggestions, comments or criticism.

Just curious... what importance do backlinks have in your theory of PageRank?

Also, when you mention PR are you referring to PageRank or Toolbar PageRank?

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To be honest I haven't given it much thought. My initial thought was that links have an impact on PR but on re-examining some data I was unable to determine if links did indeed play a role. Let me give an example. Keywest.com will is #1 for "Key West real estate" in Google and Yahoo. Google shows the site has a PR5 and 30,700,000 links. I would reason that if backlinks had an impact on PR then it would be evident on keywest.com. Another example, groklaw.net has a PR6 and 4000 backlinks but averages 1-2 fresh articles everyday. Here it appears evident that the fresh content and the 100s of daily comments determine the higher PR.

I am leaning to the theory that PR is determined by non-link related factors. If this is correct, and I say if, then PR and links are two independent measurements that Google combines in some way for the SERPs. I reason that there is more value in them as independent variables than as backlinks influencing PR. That said there is one area that I can think of where backlinks likely play a role in PR and that is the anchor text. Why? Because when the anchor text matches site content it adds weight to the site's congruence.

I am referring to toolbar PR which, of course, is a discrete number, but I realize PR#s are not discrete and all PR with the same number are not equal. There is decent explantation of the differences at: http://www.webmasterworld.com/forum80/569.htm

offtopic: I believe I seen a post by you that had an example for mod-rewrite of the root url. Can you point me to it.

Thanks

Frobn,
I enjoyed reading your article, as do I enjoy reading all your posts. You seem like you put a lot of thought and energy in describing your theories. I can't think of anything that I really disagree with in your arcticle. I especially think your list, "Factors That Can Influence Google PageRank", is spot on.
Thanks for sharing the article.

Frobn and Kyle, if backlinks do not play a role in PageRank this will be news to many including myself.

Here is the thread I believe you're referring to:
http://www.realestatewebmasters.com/...ead.php?t=3501

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First, thank you for the link it was what I was looking for.

I am not ready to make a blanket statement that "backlinks do not play a role in PageRank."

The evidence as I and others are beginning to interpret it points to a separation between PR and Links. It is possible we are saying the same thing but in a different way.

I am seeing many webmasters and SEOs reason that:

a. Links help SERPs
b. PageRank helps SERPs
c. Therefore Links and PR must be related.

and they are right they are related but not in the casual way they believe.

I would often see this type of reasoning from first year grad students in my stat courses. When they locked two or more variables into the same frame they could not imagine any other relationship other than a causal one between all the variables. When the frame was changed they were able to see the many other possibilites. When I asked myself the question "what would prevent Google from taking measurements from two independent groups of factors?" My answer was 'there isn't any reason'. For the sake of argument I call one set of factors form and the other function (this is an idea I have for another article). Together form and function interact to give us the SERPs.

It is possible that I am missing something simple and that links do indeed have a central role in PR but I haven't any evidence for such a conclusion and intuitively I can not imagine any benefit but I can list a multitude of benefits if the two are independent. If 30+ million links do not raise PR then how many links would it take. I admit I am new to SEO analysis so I would appreciate any and all feedback that I can get.

First off, where are you seeing 30 million links? Did I miss something?

Next - until Google tells us otherwise I can guarantee that pagerank is evaluated based on the link of one site to another.

Source: http://www.google.com/technology/

Google IMO looks at a link in 2 ways (Anchor text vote, pagerank contribution) the anchor text is a simple cemantic comparison of the text of the linking site to the text of the linked site and then the anchor that connects them. The closer they are related the stronger influence (The more anchor points) awarded which helps in serps (This is why we always promote "relevant" vs "irrelevant" link exchange. I also believe that if 2 many completely unlrelated relationships are formed (Especially reciprocally) there will be a negetive awarded to the site.

Now as for PR, to my understanding it is still based off of the orinigal PR = (1-d) + d(PRt1/Ct1) whereby D is a # we dont know called the dampening factor (For the calculation it doesnt matter) and PRt1 is the PR (Which google knows but we dont) of the site linking out and Ct1 is the amount of links on the page linking out.

The reason D doesnt matter is as follows
Pr of an individual page in a system = 1
Pr must diminish if 2 pages are linked together otherwise with each iteration it would increase forever therefor the dampening factor must be some # less than 1 to work in the calculation.

Here is the math
If a page has no outbound links PRt1 and Ct1 = 1 therefore you can allocate any # as D (as long as it is below one and the algo will = 1
Observer
d= .85 in (1-d) + d(PRt1/Ct1)
(1-.85) + .85(1/1) = 1
and if d= .5 in (1-d) + d(PRt1/Ct1)
(1-.5)+.5(1/1) it also = 1 and so on and so on.

Now what happens when you add a couple of links, lets increase the outbound links to 1 Prt1=1 Ct1=2 (Ct1 = 2 because the page itself counts as the first link and each subsequent outbound ads one more integer we will keep .5 as d)

(1-.5)=.5
.5(1/2) = .25
add them together = .75

Thus a page with a weight of 1 (all pages start with a weight of one) can pass on .75 or 75% of its weight to the page it links to. Assuming that page had not been linked or was not linked to from anywhere else, it also started with a weight of 1 thus it now has 1.75 weight points (Pagerank points) Now imagine it links out to just one other previously unlinked page (Weight of 1) it can pass 75% of its weight (Assuming there is only one link) to that page, so it is .75(1.75) = 1.3125 so now the 3rd page in the system is at a weight of 2.3125

This is how pagerank grows in a linear system

Now the reason for the dampening factor
What if you go back to your first 2 pages, link page A to page B
We already know page A has a weight of 1, and can also contribute .75 to page B thus with the one link page B becomes 1.75 but what happens if page B links back to page A? All of a sudden page A is recieving 75% of 1.75 back to itself and becomes 2.2135 - But wait isnt page A linking to page B? So it's now sending 75% of 2.2135 to page B which has 1.75 so again it grows (This is all due to the fact that pagerank allows pages to pass a % of their weight to another page via a link while still keeping all the pagerank it has. So if there were no dampening factor the #'s would just grow and grow into infinity. With our d=.5 this means that the amount of pagerank in the system that can pass is diminished by 50% each time (With the exception of the initial one point which becomes obsolete in an iteration loop) Thus for those of you familiar with Limits in Calculus, as the amount of iterations approaches infinity x=0 (X being the amount of pagerank that a page can pass)

The amount of iterations this takes depends on what you set d as, and d is one of the factors that I believe google plays with when messing with the importance of pagerank (Want to make pagerank important in the algo? Set d to a high # want to make it less important set d to a low #

What does all this mathematical rambling which might only make sense to me mean? It means that I think pagerank is 100% dependant on links.
The End
Morgan

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Whoops, didn't realize that "backlinks" was left out.

LOL. I must say that I was a little confused by all that math. It all got cleared up in the end.

I apparently made a mistake on the 30+ links. When I first checked the site it did show 30.5 million links and on a second check it showed 30.7 million. I went back this morning and now the site shows 211 links so obviously there something wrong with the first check with either myself or a quirk in the results. I apologize.

Very interesting post. Where do I start. Perhaps with the conclusion first. I am sure that the math is fine and the conclusion that follows is valid based on the math. But there are problems with it which I will come back to. Your conclusion that "pagerank is 100% dependent on links" would mean that PR is not a measurement of anything, has no unique value and is merely a rough estimate of where the web site is in the linking 'derby'. I say rough because PR is believed to be logarithmic and not linear (http://www.webworkshop.net/pagerank.html). No problem, Google could use PR as an ornament and many people are convinced that is all it is.

I agree with most of your statement:

I said something similar in another thread but labeled it "congruence" because congruence better describes what is happening.

We agree that there must be relevancy, but relevancy to what? For relevancy there has to be at least two separate factors. I had proposed that PR made up one set of factors and links a second set but if PR is 100% dependent on links then there is nothing to compare. What are the external links being compared to? I would reason it has to be non-link factors such as congruence, content and other non-link factors. Google tells us such non-link factors are important and google wouldn't fib us, would they?

What does this mean? Even if PR is wholly determined by links non-link factors are needed to rate the relevancy of the links and in a round-about way will contribute to PR. My main motivation in the discussion and the article is to direct some energy away from the linking frenzy and to attend to other factors which may be just as important and that add meaning to web sites. I belive the suggestions I made on optimizing a site are sound and balanced even without PR in the equation. Please note that nowhere do I say or advocate that you should give up linking.

Now back to the problems. There is much evidence that pagerank is NOT 100% dependent on links. If it were 100% dependent then ALL web sites with decent PR would have a fair amount of links. This is simply not the case in many web sites I and others have examined. Besides the ones I mentioned in other posts I will leave you with a puzzle on a more problematical web site for your conclusion. Last year I developed a web site for a green living energy expo put on by the Univ of Florida with about 30 pages http://keysglee.com. There was zero optimization. In the first Google PR update the site had a PR4 on the main page and PR3s on all the other pages. Two updates later the main page dropped to a PR2 but two pages http://keysglee.com/sponsor.php and http://keysglee.com/master.php went to a PR5 and most of the internal pages keep PR3 and PR4. Google shows zero links. If PR is 100% dependent on links how can this be?