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First Published: June 2004
Last Update: June 2004
Author: Bob Wakfer
PageRank: The Background
Google's PageRank (PR) is one of the most sought after, and yet misunderstood, web page attributes. PageRank, named after one of the founders of the Google search engine, Larry Page, was the innovative foundation that the Google search engine was built on.

The theory was that a link from one web page to a web page of another site was in essence a vote for that page. The reasoning was that webmasters would only link to pages that they thought were interesting and of value to their viewers. Google used the number of inbound links (IBL) to a page to judge the importance and relevance of that page, and based on this calculation, and other factors, decided where to place that page on the search engine results page (SERP).

They devised a scale of measurement for PageRank from 1 to 10. Then for the information of webmasters and interested people they produced a toolbar that can be deployed in Internet Explorer that will indicate the PageRank value of any page being viewed in the browser. These values have become known as PR0 to PR10.

Since PR values are a result of IBLs, Google decided to give them their own name and refers to inbound links as backlinks. As part of the toolbar there is a quick lookup of the number of backlinks that Google reports for the page that is currently being viewed in the browser. This search can also be done without the aid of the toolbar by simply typing "link:http://www.yourURL.com" into the Google search box.

The one trick to this link search is that Google does not display all backlinks. At one time it was thought that they only listed pages with a value of PR4 or greater. Today however, you will find backlinks reported from pages of lower PR values. So, at best, Google's backlink search seems to present some sample of pages linking to the site. Suffice it to say that this search is not a reliable measure of all IBLs to a page.

How is PageRank calculated?
In simplest terms PR is calculated by the sharing of PR from all the IBL links to your page. This is not strictly accurate because Google also uses the internal links within a site in the calculation of PR. Each link to a page carries with it and passes PR value to the target page. The PR points or value passed depend on the PR value of the page they come from, and the total outbound links from the page. It is generally agreed that a page will only pass about 85% of its value to the page it links to. So a PR5 page with a single outbound link will pass 85% of the value of a PR5 page to the page it links to.

But virtually no page has only a single link -- remember internal links are also used in the total outbound link count -- so the value passed to any page is 85% of the PR, divided by the total number of outbound links.

The question now becomes what is the PR point value of the different PR levels. Most observers believe that the relationship between PR levels is logarithmic rather than linear. In other words PR5 is not worth 25% more than a PR4, but may be worth 4 to 6 times more.

It is also understood that a PR value is not a single number, but is in fact a range of values. So not all PR6 ranked pages are equal. As the chart below shows a PR6 maybe just on the upper boundary of a PR5 or it maybe just short of the entry point for a PR7.

The chart that follows shows the range for each PR value. It also shows how much PR value or PR points a page with 50 outbound links will pass depending on of its own PR rank. From this I have calculated the number of links required from each value of PageRank necessary for a page to attain a desired page rank.

Here is the PageRank Calculation Chart.
Page Rank Calculation

PR Start End Median Median Links Links Links Links
Range Range Value PR Passed for PR5 for PR6 for PR7 for PR8

1 6 30 18 0.30 16,803 92,414 508,277 2,795,522
2 30 164 97 1.65 3,055 16,803 92,414 508,277
3 166 900 533 9.06 555 3,055 16,803 92,414
4 915 4,948 2,931 49.83 101 555 3,055 16,803
5 5,033 27,213 16,123 274 18.362 101 555 3,055
6 27,681 149,670 88,675 1,507 3.339 18.362 100.992 555.456
7 152,244 823,186 487,715 8,291 0.607 3.339 18.362 100.992
8 837,339 4,527,522 2,682,431 45,601 0.110 0.607 3.339 18.362
9 4,605,367 24,901,372 14,753,369 250,807 0.0201 0.110 0.607 3.339
10 25,329,516 136,957,543 81,143,530 1,379,440 0.0036 0.020 0.110 0.607

Assumption: 85% of median value passed
Assumption: 50 links per page average

The assumptions and the mathematics:
For those who are interested I have used logarithmic values of base 5.5. In other words the value range for a PR1 lies between 5.5 to the power of 1 and 5.5 to the power of 1.99, and PR2 lies between the value of 5.5 to the power of 2 and 5.5 to the power of 2.99 etc. The rest of the chart is fairly straight forward. It assumes that there are 50 links per page and that 85% of the PR value is passed to the recipient page.

The number of links required to attain any ranking is based on the median value of the donor page and the entry threshold of the desired PR value. In other words to achieve a PR5 you need 5,033 points and the average points available from a PR6 page with 50 links is 1507.

The chart was calculated with an Excel spreadsheet and it can be downloaded if anyone wants to play with the calculations and assumptions. It might be interesting to work with a different base number for the logarithmic calculation. And it is also interesting to see the impact of more or less outbound links from a page.

Are these findings valid?
Nobody knows for sure how Google calculates PR. I have shown this chart to a number of knowledgeable people and they have all agreed that my calculations look reasonable. One search engine optimization (SEO) guru from a major firm said the results were very similar to independent research that his firm had conducted.

So take it or leave it. It is probably a fair reflection of how PR is passed and accumulated.

The lesson that can be drawn from this explanation and chart is that if you want to increase your PR you need a few links from pages with equivalent or higher PR, or a great many links from sites with lower PR.

For more information on methods for actually accumulating links see part 2 of this article.

About the Author
Bob Wakfer is the owner of Computer Partners and a long time student and practitioner of SEO. Computer Partners offers web site design, hosting and search engine optimization for its clients. If you would like to discuss any of these services with Bob you can email him at bob@compar.com.

 

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