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Classics wrote:
pagerank is just math. 900 links mean nothing. 900 PR0 links will get you a PR0. The quality of the links is a factor in the equation. One PR5 link is better than 900 PR1 one links (in terms of PR).

I agree, the quality of links is a huge factor, especially if the PR scale is nonlinear.

If the scale is linear, then one might argue that a PR1 page with only 2 outbound links is a better place to have your link than a PR5 page with 100 outbound links. If the scale was linear, then that argument would be correct.

Example:

PR5 page with 100 outbound links
5 / 100 = 0.05

PR1 page with 2 outbound links
1 / 2 = 0.5

Essentially the PR1 page delivers more bang for the buck.

However, this example is only correct if the PR scale is linear. Many people believe that the scale is logarithmic, with a base of 4, 5, or 6.

Say the base is 6. This means that a page with PR2 has 6 times as much power as a page with PR1. A page with PR3 has 6 times as much power as a PR2 page, and so on. If the scale was linear, then a page with PR3 would have 1.5 times the power of a PR2 page. (3 divided by 2 = 1.5).

Now, let’s look at Classics’ statement: “One PR5 link is better than 900 PR1 one links.” Assuming that his statement is true, we can estimate the acual logarithmic “base” being used by Google. This in turn will tell us exactly how much more valuable PR3 is compared to PR2, etc.

Here we go….

If one PR5 link holds more power than 900 PR1 links, we can write this equation:

(1)(5^y) > (900)(1^y)

In words:

1 link with PR5, raised to a power “y”

is greater than

900 links with PR1, raised to the same power “y”

We raise it to a power “y” because we are trying to find out how much more powerful PR5 is compared to a PR1. This “y” is the base that is being used by Google.

Using Excel (or a calculator) you can solve for y.

y = 4.23

What this means, is that each PR level is roughly 4.23 times as powerful as the previous level. So if you have a backlink from a PR5 page, it’s 4.23 times more powerful than a backlink from a PR4 page. Another example — you would need 5 links from a PR2 site to equal one link from a PR3 page (I say 5 links because 4.23 needs to be rounded up to 5).

This of course assumes that each link page has an equal number of outbound links. Also it assumes that Classics’ value of 900 is accurate.

If we apply the base of 4.23 to the linear example I used at the beginning of my post, we get this:

PR5 page with 100 outbound links
(5^4.23) / 100 =
(900) / 100 = 10

PR1 page with 2 outbound links
(1^4.23) / 2 =
(1) / 2 = 0.5

This shows that, even though the PR5 page has 50 times as many outbound links, it still packs 20 times as much power as the PR1 page.

It is still possible to have a better quality link on a lower PR page, though.

Example:

PR5 page with 100 outbound links
(5^4.23) / 100 =
(900) / 100 = 10

PR4 page with 25 outbound links
(4^4.23) / 25 =
(350) / 25 = 14

In this case the PR4 page is helping you more than the PR5 page.

900 was a random number used in another post.

“This means that a page with PR2 has 6 times as much power as a page with PR1”

PR is displayed in integers, but pages do not have PR in integers. A PR2.1032243 and a PR2.975243 and a PR3.83625 are related in very different ways, like a 5.1 and 5.9 and 6.8 earthquake.

There is no definitive agreement on the PR logscale, but no way is it less than 6. I’d say it is closer to ten than to six.

900 was a random number used in another post.

Ah yes, I see that now, thanks. Sharpgambler used that number in the other thread.

If you think the scale is closer to 10, then one PR5 link would actually be worth around 10,000 PR1 links. (There’s a difference of 4 PR units here (PR5 – PR1), and 10 to the 4th power is 10,000).

PR is displayed in integers, but pages do not have PR in integers. A PR2.1032243 and a PR2.975243 and a PR3.83625 are related in very different ways, like a 5.1 and 5.9 and 6.8 earthquake.

That makes sense, and that’s a good point. A 5.0 earthquake is 10 times more powerful than a 4.0 earthquake. A 5.3 earthquake is twice as powerful as a 5.0. (10 raised to the (5.3 – 5.0) power equals 2).

Likewise (if the Google base is 10), a PR of 5.3 is twice as powerful as a PR 5.0. Both will visually appear as a PR5 on the toolbar, but you would need two links on the PR 5.0 page to match just one link on the PR 5.3 page.

Also consider these two PR values:

PR 4.51
PR 5.49

The PR 5.49 is 9.5 times more powerful than the PR 4.51. And yet, they will both show up on the toolbar as PR5.