Page Rank Calculation
The question is often asked, how many links do I need to get a Page Rank (PR) of 5 or 6? Pagerank at its best can be confusing for those that are familiar with it, and Page Rank is almost uncomprehendable for those that have no experience working with it.
The purpose of this article is not to discuss whether Page Rank is lost or bleed, or how Page Rank is voted, passed, accumulated or calculated, but to lay out a few simple rules that will help answer questions like the one above.
Bob Wakfer's PageRank Calculation Chart will be used to answer these questions and to form a number of simple rules. While no one knows for sure how Google calculates page rank, Bob Walfer's pagerank calculation diagram has been shown to a number of knowledgeable people and they have confirmed to him that his page rank calculations look reasonable.
Wakfer's paper takes the position that Page Rank can't be bleed or lost and that all outbound links, whether internal or external to the domain, are given an equal PR vote. This position means that inbound links in his chart apply to a web page no matter where the web page is located in the web site and no matter how many outbound links (internal or external) that page has.
Bob Wakfer's paper states that the inbound links in his chart are voting 1/50th of their PR (have an average of 50 outbound links, internal or external), and are calculated as having a Page Rank of medium value. He gives each toolbar Page Rank value (1-10) a starting range and an end range. That is to say that when you see a PR5 on the Google toolbar, that PR5 might be just a bit over a PR4 (5,033) or it may be just a bit under a PR6 (27,213) according to the numbers in Wakfer's chart.
In any given toolbar PR value the number of low values is greater that the number of high values as the PR scale is a logarithmic scale. Therefore if you take a large number of PR5's they will not average out to be medium values. This means when you see a PR5 there is a higher chance of it being of a lower value than of a higher value. Keep this in mind as you use these calculations.
I don't want make things to confusing, but I do want to stress the point that the values used in the chart calculations are medium values, (the PR5 medium value is 16,123).
This point is as good as any place to spring another one on you. The PR values producted according to Wakfer's chart of all lower level values. This of course is the only way that, as we will see later, 18 medium value PR6's could product 50 PR6's -- 18 medium values producting 50 low values.
From the chart we will be able to determine how many links from a medium value PR6 page it will take to give you a PR5, a PR6, or a PR7. Let's take a look.
We find from the PageRank Calculation Chart that it takes 18 medium value PR5 links to get a PR5. So there is our first rule. Rule 1: it takes 18 links of PRx to get a PRx.
Next thing we can note from Wakfer's chart is that it takes 3.339 PR6 links to get a PR5 and 101 PR5 links to get a PR6. From these results we can make a couple more rules. Rule 2: it takes 3.339 links of PRx to get PR(x-1) and Rule 3: it takes 101 links of PRx to get PR(x+1).
I haven't made rules for PR(x-2) or PR(x+2) but all you need to do is look at the chart and you can see the value for PR(x-2) is 0.607 and for PR(x+2) is 555.
So here is a first set of rules and examples.
Rule 1: 18 PRx links to get PRx (i.e. 18 PR5 links to get a PR5).
Rule 2: 3.339 PRx links to get PR(x-1) (i.e. 3.339 PR6 links to get a PR5).
Rule 3: 101 PRx links to get PR(x+1) (i.e. 101 PR5 links to get a PR6).
The next question that needs to be answered is what if the links have more or less than 50 outbound links? All the numbers in Wakfer's chart are worked out for the links to have a total of 50 outbound links.
The PR voted from a link that has more that 50 outbound links needs to be devalued. Likewise the PR voted from a link that has less that 50 outbound links needs to have its value increased.
The links can be revalued in a very simple way. If your link is from a page that has 50 outbound links you received, 1/50th of the PR is voted. So to revalue a link that has more or less than 50 outbound you divide the number of outbounds that that link has into 50. So if the link only has 25 outbound links, you now received 1/25th of the PR vote which is twice as much. If the link has 100 outbound links you new receive 1/100th of the PR vote or half as much.
Let's see how we can apply this calculation to our first 3 rules.
If 50/TOL = Number of links, then here is our new rule.
Rule 4: Revaluing links: 50/TOL = New Link Number (i.e. 25TOL = 2 Links; 100TOL = 0.5 Links)
You then take these revalued links and use them over in rules 1 though 3.
With the first 3 simplified rules or calculations we can now tell how many links of a certain PR it will take to get your desired PR. With rule 4 you are now able to revalue the links that you are considering that have more or less than 50 outbound links.
Written by Bob Mutch Aug 1/2004; Last Revised Sept 14/2004