The Mechanics of Page Rank (PR) Calculations



The “Page Rank" or PR is calculated by taking into account a site's pages are linked to each

other, and also to other sites. Let's consider a tale of two pages, “A" and “B". A link from

one “page A" to “page B" is counted as a vote of confidence for “page B" and is referred to as

a “Back Link" from “page B"point of view. In effect “page A" is saying, yes, Mr. Google Bot, I

found this “page B" worth linking to and therefore this page has importance. Google Bot takes

this vote into consideration and boosts the value of “page B" or it's “rank". If “page A" had a

high enough rank to begin with, it's vote for “page B" would count for a lot more. The only way

“page A" would achieve this rank is by having a sufficient number of high ranked back links.

And, then it gets quite complicated.

The problem for Google Bot is that if everyone votes for everyone, by linking to everyone under

the sun, how would the Bot know if it's a real vote or just a global mutual admiration society.

From the Bot's point of view, when “page A" links to “offsite page X", some of the rank of

“page A" leaks. Therefore “page A" has a disincentive to link willy nilly to pages.

What happens on one site is a microcosm of the internet. The ranked pages often point to pages

on other sites(which is kind of why internet is useful). The Google Bot applies a similar

methodology to calculate the rank.

So, how can you see the page rank? You can use our tools(should be a popup tool which allows

input of a URL, and outputs the page rank) , or you can install Google toolbar.

Some stuff to keep in mind:

It's not a linear scale

The Page Rank that we see for a site is on a logarithmic scale. As an example(used for

illustration only), if 3 PR-1 incoming offsite links are required to give your site's homepage

a PR of 1, then you would need 18 or so links to achieve a PR 2. For PR 3 it would be 108, all

the way to more than 30 million for a PR-10. Very tough to be an overachiever!

Don't get involved with PR networks

Unfortunately, the “Page Rank" calculation has brought about a cottage industry of sites that

form a virtual network. Their sole aim is to boost the PR of all the pages, by linking to each

other and increase their mutual ranks. Such practices are recognized and frowned upon by the

bot's and the perpetrators are penalized. The worst offenders are dropped off the index. The

equivalent of being sent to a penal colony…on another planet!

Tread Carefully

We once got a referral for a client whose site dropped from PR-5 to PR-0 all of a sudden. We

were mystified, until we found that he had two similar sites which were linking to each other.

After a while, this person merged the contents of the sites and started redirecting one site to

the other. Since he didn't update his links, the Bot went from the first site to the second

site and got redirected back to the previous site on same page. This caused an infinite loop,

causing the Bot to drop that site's PR. Innocent mistake…grave consequences! However, once the

problem was fixed the site's Page Rank went back up on the next Google PR update .

Here's more explanation, if you really care about the geeky details and our Google Simulator is

not enough for you:

All the “ indexed " pages have a score of 1.00 when Google Bot first visits them. The Bot then

examines the structure of the links and reassigns weights. It uses the following formula

proposed by Larry Page(of “Page Rank" fame) and Sergey Brin. Here's a quote from their paper:

We assume page A has pages T1...Tn which point to it (i.e., are citations). The parameter d is

a damping factor which can be set between 0 and 1. We usually set d to 0.85. There are more

details about d in the next section. Also C(A) is defined as the number of links going out of

page A. The PageRank of a page A is given as follows:

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

Note that the PageRanks form a probability distribution over web pages, so the sum of all web

pages' PageRanks will be one.

Sounds complicated, but the idea is really quite simple. Let's look at the definitions.

PR(A) è The PR of “page A". The desired result

d è A damping factor. The Google founders proposed this number to be 0.85 but it

possibly has changed.

PR(Tn) è The PR of a page Tn providing “page A" a back link.

C(Tn) è The number of outgoing links from the page Tn

PR of the page A basically sums up these numbers. Assuming d=0.85 and there are two pages,

“T1"(PR 7, two links) and “T2"(PR4, 5 links).

PR(A)=(1-d) + d(PR(T1)/C(T1)+PR(T2)/C(T2))

Plugging in the numbers we get:

PR(A)= 0.15 + 0.85(7/2 + 4/5) = 3.80

But the story doesn't quite end here. It's because “page A" which started with PR 1, now may

be more or less than 1 depending on the number(and quality) of back links it has obtained. If

the page is not “dangling"(i.e. not linking to anything else), it will affect the PR of other

pages(say “page T1" and “page T2"),

Whoa! If we change the PR of “page T1" and “page T2" would we not be affecting the PR of page A

again? Round and round it goes, you say. And you would be right! Almost. The “damping" factor

d is chosen to allow the PR number to “converge". That is, if the PR calculation is repeated,

the final results don't change. A good reason to quit or “terminate". As you can well imagine,

in a world wide network of millions of sites, this calculation could take a very long time.

Fortunately, there are some mathematical shortcuts that allow faster convergence. In addition,

Google has tens(hundreds ?) of thousands of computers at it's disposal. Even then, the update

happens once every 10 weeks or so.

Please see: http://www.sofizar.net/improve-google-pagerank.php for further details, or write me

an email: art@sofizar.com