# Thread: Formula to detemine exponent base for pagerank calculation

1. ## Formula to detemine exponent base for pagerank calculation

The numbers presented in the Google toolbar are not 100% accurate. They are tiered levels based on an exponential equation. Also if Google has not yet spidered a page, but it has spidered the root domain, they will guess a pagerank temporarily. You can tell if the pagerank is a guess or not by seeing if Google has a cache of the page (not a 100% way of telling, but good enough).

The pagerank scale is from 1-10 and its exponential, but what we do not know is what base the exponential equation is. Is it base 10, 2, 3, 4, 5, what?

I have thought of a way to test this so that we may know.

Consider having 9 pages:

A1
A2
B1
B2
C1
C2
D1
D2
X

Page A1 links to A2 and X. Page A2's only incoming link is from A1.

Repeat that situation for all the letters A-D.

So X has 4 incoming links, and all the "2" pages each have one incoming link.

The problem with calculating the PageRank formula has been that you cannot know how much each link provides. This would let us know the answer to that question.

The links to the "2" pages and the links to the "X" pages would both carry the exact same weight.

So we can look at the PR's of the "2" pages to figure out what all is going into the PR of the X page.

For instance if the X page is a "6" and all the "2" pages are 5's, then we could say that 4 5's is enough to make a 6. If all 5 of those pages are 5's then we can say that 4 5's are not enough to make a 6. Indicating that the exponential base is atleast a 5.

Considering how you can have a high 5 or a low 5 this isn't entirely accurate. You would need to run multiple trials in hopes you would get 5's (or whatever) from all over the range.

I have a way to use this method already in place. On the next Google update in a week or two here I'll be able to tell you data on how many 6's are needed to make a 7.

3. I will interested too. Personally I think its an exponent of 2 or 3.

4. ## Re: Formula to detemine exponent base for pagerank calculation

Originally posted by aspen
I have a way to use this method already in place. On the next Google update in a week or two here I'll be able to tell you data on how many 6's are needed to make a 7.
That'll be excellent Aspen

If too many people find out how the equation, or even part of the equation works, will Google change it??

5. Not likely, this equation would have no bearing on how you rank, it'd just let us know more about how that green bar in the Toolbar is calculated.

6. But surely Google aren't gonna like people having an idea of how many 6's are required for a 7.

7. I really doubt they'll care... you can still find that thesis paper online and that has plenty of formulas in it.

8. Fair enough I look forward to your findings

9. Okay here it is:

3 6's, 2 5's and a 4 = atleast a 7.

Also of course a single link from a 7, if there are no other links on the page, will give you another page with a 7.

10. aspen- Do links from forums like this count? For instance, if I have no links to my site and post the URL here (PR of 7) will I get a PR of 7?

11. Links from anywhere will count - if Google spiders the page.

No. The sessions information in the URL prevents a spider from spidering these forums.

Will spiders be able to spider the entire forum in vb3? Yes.

Will the links count then? Yes.

12. So does anyone who writes an article for SitePoint with their URL get an automatic PageRank of 7?

13. No, as mentioned above the amount of bonus you get from a link is found by dividing the rank of the source page by the number of links on that page.

http://www.webmasterbase.com/article/685

It has a PR of 6. There are probably about 40 links on it.

So each link on that page gets whatever PR6/40 is - and it is also modified further by the "dampening factor" which is a small amount applied to every link to bring total pagerank down.

If PageRank represents the probability that a surfer will randomly find your site by clicking on links, then the dampening factor is the random chance that on your site he just gives up.

14. Originally posted by aspen
No, as mentioned above the amount of bonus you get from a link is found by dividing the rank of the source page by the number of links on that page.

http://www.webmasterbase.com/article/685

It has a PR of 6. There are probably about 40 links on it.

So each link on that page gets whatever PR6/40 is - and it is also modified further by the "dampening factor" which is a small amount applied to every link to bring total pagerank down.

If PageRank represents the probability that a surfer will randomly find your site by clicking on links, then the dampening factor is the random chance that on your site he just gives up.
Oh, I see. Thanks for clearing that up.

15. Originally posted by aspen
Okay here it is:

3 6's, 2 5's and a 4 = atleast a 7.

Also of course a single link from a 7, if there are no other links on the page, will give you another page with a 7.
Good data.

So, the 3 6's, 2 5's and a 4 each have one link on them?

16. No.

It doesn't matter how many links are on the 6 the 5 the 4, those pages are just used to measure how much weight a link gets.

If A links to both A1 and X then it will give the same benefit to X as to A1. So A1 is only used to measure how much weight X is getting.

Then B links to both B1 and X, etc etc.

So you can see what scores went into X by looking at the scores of A1-N1...

Or if you want to think of it this way. If you add up all the incoming links to X in one column and the links to A1-N1 in another column the results will be identical.

17. Originally posted by aspen
Will spiders be able to spider the entire forum in vb3? Yes.

Will the links count then? Yes.
Other than the fact that the vast quantity of links on these forum pages will decrease the PR value, you have to be excited about how that'll help everyone's sites who they promote in their signatures. Especially if they have 5,000+ posts.

18. Google sees pages, not sites, right? That is, they don't give SP a PR of 7, the give SP a PR of seven, each of the inner pages a PR of 7 (I think it's 6, but hypothetically), and count links from pages, not sites?

So, with vBulletin 3, each of the 80,000 threads or whatever would have links counted individually (not as "SitePoint" links), correct? And there are maybe 15 linsk on a forum page, so if you post once, the link is worth however much, factoring in the PR of six and the 15 links per page?

What I'm getting at is, would people with 5000 posts (hypothetically let's say never more than one per page) get the links in their signitures counted 5000 times from pages with PRs of 6?

Good luck answering that, there are a LOT of question marks.

19. Yes.

The amoung of PR garnered from signature links will be small, very small. However 5000 of them should be fairly substantial.

I think after the implementation of vb3 here all of the regular posters should see atleast a slight PR increase.

20. So by the way, apparently the exponent base is atleast a 3, and maybe a 4.

More data is needed to know for sure.

21. Originally posted by aspen
Can we expect these forum pages to have a PR of about 6, or was that guess only because most sites' inner pages have one PR step lower?

The amoung of PR garnered from signature links will be small, very small. However 5000 of them should be fairly substantial.

I think after the implementation of vb3 here all of the regular posters should see atleast a slight PR increase.
I'll take anything I can get (which isn't much, because I have about 70 posts and no link in my sig).

22. By the way, aspen, I know you were in talks with SP about getting a book you wrote published. Is this going to happen? I'd be really interested in it (I'll tell SitePoint that if you need someone to argue for you )

23. SitePoint really liked the book, but they decided they wanted to focus on more technical material. I do not think it is a good idea but it's their business.

So I submitted it to a different publisher on friday.

24. aspen- Best of luck to you (both for yourself and for me- I really want to read it!). I know from what you've contributed here that you're knowledgeable, articulate, and that just about anyone would be lucky to have your knowledge (or at least a book filled with it).

I don't understand SitePoint's thinking either, they've turned down an article or two of mine because they were moving in another direction (which is odd because few people seem to be too concerned with technical aspects of running a site).

I can't wait to read your book, and I'm sure I'll get a chance.

25. Okay, new Data:

7+7+6+5+5+5+5+3 = 7

Previous data:

6+6+6+5+5+4 = 7

The theory that it has a base of 4 still holds true.

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