For SEO, a technical understanding of back links and Google Page Rank is essential to answering common questions asked by non-technical SEO clients, and to gain insights to improve the current SEO strategy. It has been proven many times, however, that Google PR equates to link popularity, and then high popularity means “importance” but does not necessarily equate to “relevance.” This is why we can see low PR sites appearing high in search engine results.

This article is NOT about improving Page Rank to improve rankings. This will not happen anyway. If you’re trying to improve your rank in the search engines, look to improve things that are more important than Page Rank (content, conversion rate, links from topical communities, etc).

However, this article will deeply examine the current relationship between the total amount of links pointing to the URL versus its Google Page Rank. As we all know, Google Page Rank has evolved a lot over the years (especially recently), and what we think we know now could be obsolete.

We can only achieve our goal by conducting a scientific study. This means gathering data, analyzing it, and then making conclusions and recommendations. “A single test is worth a thousand of expert opinions.” In this study we will use the Google PR toolbar value (1 to 10), since the real Page Rank, according to Google, is not visible to the public.

The experiment will be aimed at answering the common questions asked concerning Page Rank and back links:

- What is the current relationship between inbound links and Google Page Rank? How strong is it?
- How does Google convert inbound links to Google Page Rank as shown in the toolbar?
- What is the degree of difficulty of each PR climb? For example, how many links are needed to increase from PR 1 to PR 2? Is it the same amount of links we need to climb from PR 9 to PR 10?
- How can we use this study to improve the quality of a website’s back links?

If you are interested in learning more about this study, then keep reading.

{mospagebreak title=Methodology and Theory}

According to the classic Page Rank definition, the Page Rank of the URL is a function of all back links pointing to it. These back links comes from inside and outside the domain.

To measure this back link quantity, we will use Yahoo Site Explorer. First, we will enter the home page URL, and then click “Explore URL.” We’ll gather the “Inlink” data, which by default will measure the number of links from “From All Pages to ONLY this URL.” See the screen shot below:

It shows that there are 297,259 back links pointing to the home page of http://www.seochat.com coming from ALL pages (inside or outside the domain). These back links are responsible for the Page Rank value of this URL, according to the Page Rank papers cited above.

In order to provide a certain accuracy and precision to this study, the total back links and Google PR data will be gathered for a random sample of 100 websites. Then we’ll tabulate the data in an Excel spreadsheet.

The Google PR data will be gathered from the toolbar.

{mospagebreak title=Data Gathering and Analysis}

The data of the 100 sample websites has been gathered. See screen shot below for the snapshot:

A complete list of raw data is available.

To examine the relationship between total inbound links pointing to the URL and the Google Page Rank, we will use statistical regression analysis. Below is the plot of the raw data:

The Y-axis uses a logarithmic scale to properly show all the data in the graph. The regression plot helps answer the first question:

“What is the current relationship between inbound links and Google Page Rank?”

The answer is a direct/strong logarithmic relationship between Google Page Rank (toolbar) and total inbound links to the URL. The R squared (coefficient of determination in statistics) is 67%. This means that currently, back links account for 67% of the variation for Google Page Rank. It also says that the Google Page Rank algorithm is 67% back link dependent.

How does Google convert inbound link data to Google PR in the toolbar?

In the above plot, the regression model is:

Y = 13.418e1.4717x

Where:

Y is the total inbound links pointing to the URL and X is the Google Toolbar PR.

In practical application, we will be attempting to express Google Toolbar PR as a function of the inbound links. So we will solve for X.

Taking the logarithm of both sides (using the common logarithm, base 10):

Log10Y=Log1013.41e1.4717x

Applying properties of the logarithm and solving for X:

X= (log10(y/13.418))/ (1.4717log10e)

e is a constant in natural logarithm which is equal to 2.71828…

Punch that into the Excel spreadsheet and it will approximately compute the Google PR toolbar value given the total inbound links (y variable).

{mospagebreak title=Computing Degree of Difficulty}

Some of the commonly-asked questions in SEO are: “What is the degree of difficulty of each PR climb? For example, how many links are needed to increase from PR 1 to PR 2, or is it the same amount of links we need to climb from PR 9 to PR 10?”

The answer is the exact base of the logarithm used in Google Page Rank, which can be computed above. Note that we are using a base of 10 in computing for PR. We will attempt to express the above equation as:

X= log b (y)

Where b = the exact base of the logarithm that will translate to the difficulty of each Page Rank. X is the PR and Y is the total inbound links.

Equating for both PR equations:

(log10(y/13.418))/ (1.4717log10e) = log b (y)

And solving for base B:

Base (b) = 10(1.4717loge) (log13.418)

Using a calculator, the exact base is around: 5.26. This also simplifies the calculation of PR given the inbound links:

X= log 5.26 (y)

So every PR climb increases in difficulty by a factor of 5.26. Using this logarithmic base, the following is an example of a simulated back link table:

It shows that starting from one back link for a PR 0 site, you need four links to climb to PR 1. But to climb to PR 2 from PR 1, you now need 22 links. This difficulty further increases for each PR level; it is much easier to climb from PR 3 to 4 (a 620 link difference) than to climb from PR 9 to PR 10 (a 13,130,501 link difference). This is because the PR toolbar is logarithmic. It also explains why there are very few PR 10 sites on the Internet as opposed to lower PR values like PR 1 to PR 3.

How can we use this study to improve the quality of a website’s back links?

This study tells us a lot about the Page Rank algorithm. First, since 67% of the Page Rank depends on back links, it makes sense that in every SEO effort, a strong emphasis and plenty of resources will be invested in improving the quantity and quality of back links to the website. Several ethical techniques can improve back links. Techniques such as link baiting and putting up highly useful content to attract natural links are among the best ways to improve the link profile of a website.

It takes more than Page Rank to get traffic and customers from search engines. Make sure that when your link profile improves, and your PR increases, that you also see an improvement in the traffic and conversion rate of your website. This is where non-valuable websites fail and highly useful websites succeed.