Page Rank Calculation

BobMutch:

This is some of the best info I have ever seen posted on any subject in any forum, ever.

Kudos to you for sharing.

AJ

 

Spyware Remover:Well er, thanks. If you want some good articles to read on PR I suggest you read Phil Craven's article Google's PageRank Explained and Ian Rogers article The Google Pagerank Algorithm. I also think Bob Wakfer's PageRank Calculation Chart is very useful.
This thread is currently discussing this chart and I am waiting for a responce from compar to my questions.
compar: Do you have some time Sir to address the questions I raised in my last post to you.

 

Four variables: how do we deal with them and make the numbers meaningful that are in the chart?
In some ways there appears that there is additional calculation that are required to use the chart, and it would seems those calculations would vary from site to site.
If the numbers from the chart can't be applied to any case, and I am not say they can't be, without some changes to the number then how can the numbers in the chart be used?
Do the numbers in the chart only apply where the links are to a single page that is not connected to any other pages?

Variables:
1. Chart is worked out for medium value PR -- no way to know if PRx is close to a high PR(x-1) or close to a low PR(x+1).
2. Chart is worked out for inbound links to have 50 outbound links -- no way to revalue if the links are greater or less. (I addressed revaluing in my article.)
3. Chart seems to not take into consideration internal link structure. For example inbound links to the home page in a 6 page site that has a fully meshed link structure will retain more PR than the same links going into a 14 page site that has a fully meshed link structure. (Phil Craven's Page Rank Grid Calculation shows this.)
4. Chart doesn't have any way to calculation the effect of outbound links on the page receiving the links or outbound links on any other pages in the site that the page recieving links is linked to.

Compar HELP!

 

I been thinking about doing a controlled study.

9 different single page sites with 3 sites getting a differnet set each of 101 PR4 links, 3 sites getting a differnt set each of 18 PR5 links and 3 sites getting a differnet set each of 3.339 PR6 links.
The links would be revalued using the revalue rule 6.25(PRx/TOL) PRx from my Page Rank Calculation article.

Then using the same links set up 9 sites with a 6 page fully meshed linking structure and 9 sites with a 12 page fully meshed linking structure.

This study would address the following issues.
1. Compare the numbers from Wakfer's Chart to a real life controlled study.
2. Show the effect that adding a single page to a fully meshed site will have on the page that is receiving the links.

Different variables addressed:
1. Using 3 sites with 3 different sets of links will address the issue of the chart using "medium value" PR.
2. Using the revalue rule 6.25(PRx/TOL) PRx to revalue the links being received will address the issue of links having different numbers of Outbound links. If 3.339 PR6 link with 50 Outbound links each give a page a PR5. Then 1 PR6 with 15 (50/3.339 = 15) Outbound links will give a page a PR5.
3. Introducing the 9 single page sites into 6 page and 12 page sites with a fully meshed link structure will reflect the PR retained when moving an isolated page study into a real life site.
4. Now testing the effect of outbound links I will have to think on these things.

Who would be interesting in be involved in such a study? I can put up 27 domains, handle the hosting and construct the sites.

We would need some one that is very good at statistics, and a number of people that have conections for obtaining PR links easily.

What you all think?

 

Bob:

Truly THE most valuable post I have ever read and seen.

Thanks!

 

Spyware Remover: Have you read Phil Craven's article or Ian Roger's article on page rank. Now those are good articles. All I do is ask a bunch of questions.

 

I think that is a freaking great idea and somebody needs to pick up your beer tab for a month if you undertake this endeavor!

 

Scoreboard: hehehehe well it all fun and games, it is sandbox work for me, I love internet stuff eheheheh.

 

Everyone: I changed my rule 4 formula as I found an error in it for calculating anything other than a PR8 and it also was to complicated. Here is the new rule. (TOL = Total Outbound Links)

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.

I also made quite a few changes in the article Page Rank Calculation.

 

Ok! I've been absent for a couple of days so let me set you all right on this.

1. As I clearly said in my original article PR is passed both by internal and external links to a page. In fact Google makes no distinction between internal and external in their listing of backlinks.

2. What you guys are talking about is commonly known as PR bled. The theory is that if a page has many outbound links, like a home page linking to all the pages in the site it belongs to, or just a home page with many links to other sites, -- it makes absolutely no difference either way, that is why this discussion of internal structure is meanlingless -- that it will pass less PR to all the pages it links to.

This is correct and is reflected in my 50 outbound links per page assumption. Once again whether those are links to internal pages or external pages make no difference.

So if a page has PR of a certain value and suddenly added 10 more internal or external links, then it would be passing less PR value to all pages. Assuming that these pages link back, which is normally the situation with internal pages, then after multiple calculation iterations each of these pages would have less PR to pass back, and on subsequent iterations the home page would have less PR to pass etc. etc.

3. For the purposes of my article and the understanding of the subject I think it is valid to assume that the internal linking structure of a page is fairly static. So new or additional inbound links will pass the values that I suggest. And no matter what the internal structure is this doesn't change the PR value received from an additional inbound link.

And if you guys think my article is too simplistic then don't read the fucking thing, and don't publish other articles that piggyback on it and try and capitalize on the popularity of my original work.

 

I have made some updates in my Page Rank Calculation article. There were some mistakes in the calculation for revaluing links up or down to 50 total outbound links. I have also written up a new article that may be of interest called Sell Page Rank. This compares the values of different page rank text link ads that are being sold on different auction on the internet.

 

compar: While it may not make any different whether the links are internal or external as far as concept and effects, the current accepted view of page rank is that links cause page rank bled. Even when there is a direct link back there still is page rank bled even though it is less.

According to general accepted views on page rank there will be a difference between a stand alone page with no outbound links at all, that has for example 18 medium PR7's (with 50 outbound links) linked to it, and the same page that has a non returning link to another page whether it is external or internal.

I don't see the question to be is there a difference in retained page rank but the real question is, is the different enough to affect the page rank value in the 1 to 10 scale that we see displayed on the little green bar.

If the difference in retained page rank is so small that it wouldn't change the green bar value except in an case where the page rank of the page is at the very bottom of the scale, then links don't matter except in the extreme case where the page rank value is at the bottom of the scale.

It is an accepted page rank view that whether you have 1 or 100 non returning outbound links you get the same bled. While returned links limit the page rank bled, the issue of whether the links are returned or not will have no mater if there is not is not enough bled in a non-returned links to effect the the green bar.

As I see no problems with agreeing to the above then the question remains, how much page rank is bled when an outbound link is made.

According to your chart it takes 18 medium valued PRx page links to product a PRx. If this is correct then each PRx link is transfering 1/18th PRx. Like wise when an outbound link is connected to a PRx page, 1/18 or 5.6% of the page rank will be transfered from that page.

If that calculation is correct and 5.6% of the PR is transfer then there wouldn't be more than that bled. If this is the case it is quite clear that the linking structure, be it internal, external, one way or fully meshed has little or almost no effect on the calculations and doesn’t need to be considered.

As far as my referring to yours or others published article or papers in the articles I write, this is an accepted practice in all fields in most countries except where there is totalitarian rule. It is also an accepted practice to question the results and theory's of publish papers. This is a good thing. This pratice enables proposed theories to be discussed, challenged, put to the test, revised, changed and even discounted where they are incorrect.

As a seeker of truth I welcome this process to any and all the articles I write.

 

compar: Also another thing, can you explain to me how 18 PRx's transfering only 1/50 (18 links with 50 total outbound links) of their PR can product a PRx on the page they link to? Wouldn't that be the same as a 0.36 of a PRx with only one out bound link producing a PRx?

I am revaluing the outbounds with 50/TOL = New Link Number

18/(50/50) = 18
18 medium value PRx with 50 outbounds each = 1 PRx

18/(50/25) = 9
9 medium value PRx with 25 outbounds each = 1 PRx

18/(50/5) = 1.8
1.8 medium value PRx with 5 outbounds each = 1 PRx

18/(50/1) = 0.36
0.36 medium value PRx with 1 outbound each = PRx

Now if you say my revalue calculation is incorrect then lets just look at 18 sets of PRx links producting 1 PRx 50 times. If it can product it once with 1 of the 50 outbound links then it can product it 50 times. That would mean that 18 PRx links can product 1 PRx 50 times. This doesn't seem possible.

That would be 1 PRx page producting 2.77 PRx pages (2.77x0.36 = 1).

If you roll back your outbound links to 18 instead of 50 (a huge 64% change) you still have 1 PRx producting 1 PRx. Or 18 PRx's producing 1 PRx 18 times.

Do you see an error in my calculations.

 

What I think I see is that you really don't understand the math behind my chart or the entire concept.

Have you downloaded the current PR Calculation Chart? If you do you will find that I have changed the 50 outbound link assumption to 40 as I said earlier because this correlates so closely with the actual results that Rustybrick reports with his latest link statistics tool.

However all you have to do is substitute whatever number of outbound links you wish to experiment with in the field -- cell C19 -- that presently has "40" and the entire chart will recalculate on that basis.

I just reduced the outbound link assumption to 20 and it says that you then only require 7 links from any PR value to give a page the same value.

 

compar: I have not looked at the math behind your article so I am not going to fully understand the math. I will download the current PR Calculation Chart and take a peek at it.

I think my question was concerning the results of your chart. The old chart says that 18 PR8s of medium strength with a total of 50 outbound links, linked to a page will product a PR8. My comment was that this is the same as saying that 18 PR8's each linked to 50 different pages result in PR8 on those 50 pages. I just don't see how it that is possible. How can the links from 18 PR8's result in 50 PR8 pages?

 

I don't think that that is what the chart says or implies at all. It say that if a page had nothing else but 18 inbound links from pages with PR8, and assuming that the average number of outbound links from each of these pages was 50, then the recipent page would probably be given a PR8 rating. Or saying it another way the recipent page would have been passed enough PR points to cross the PR threshold. The other assumption here is that the Average PR points of each of the donor PR8 pages was the median of the PR8 point range.

Look at the math. The median value of a PR8 is 2,682,431. If a page passes 85% of its value then a page with 50 OBL passses (2,682,431*.85)/50 which equals 45,601 PR points. Do the arthmetic yourself. It works.

Now the threshold point for a PR8 is 837,339. If you divide this by the 45,601 PR points that each of the 50 links pass then you will see that it only takes links from 18.362 pages to achieve the threshold value of 837,339.

The secret, or explanation for, this is the assumption that each PR8 in question has the median value of the PR8 range.

 

compar: Ok I see where I when wrong. I didn't take into consideration that the PR8's would be lower value PR8s.
The PR8 has a value of 837,339 to 4,527,522 with the medium value being 2,682,431. ((2,682,431*.85)/50) * 18 = 820,823 which is a tad short of a entry level PR8. The inbound 18 PR8's need to be an average of 2,736,402 or better to result in a bottom value PR8.

The multiplier is 0.306 [(0.85/50) * 18 = 0.306]

Lets look at the rest of them.
PR1 6 30 18 Short 5.5
PR2 30 164 97 Short 29
PR3 166 900 533 Short 163
PR4 915 4,948 2,931 Short 896
PR5 5,033 27,213 16,123 Short 4,933
PR6 27,681 149,670 88,675 Short 27,134
PR7 152,244 823,186 487,715 Short 149,240
PR8 837,339 4,527,522 2,682,431 Short 820,823
PR9 4,605,367 24,901,372 14,753,369 Short 4,514,530
PR10 25,329,516 136,957,543 81,143,530 Short 24,829,920

Lets check you 3.339 PRx results in a PR(x-1) [(0.85/50) * 3.339 = 0.0567]
Ok I ain't going to write them all out. All the calculations seem to be short.

[(0.85/50) * 19 = 0.323] works for all but the PR1, so it takes 19 medium PRx with 50 PRx to get a just-over-the-line PRx.

I suggest you modify your chart to give more than a just barely over the line PR. You may want to aim at a 1/4 value PR or even a 1/2 (medium) value PR.

I agree with cutting back to 40 inbounds and it seems to be a common number of external outbounds that people are using when they sell text link ads for there PR value.

The number of medium PRx's required to result in a medium value PRx is 59 medium value PRx's that have 50 outbounds. [50/0.85 = 59]
So it will take 59 PR8's of medium value with 50 outbounds to product 1 PR8 of medium value.

My next question is, what is you view on linked back internal links. Would you count those as outbounds also?

Oh by the way compar, I enjoy these discussions very much!

 

Geeze so many numbers ---lol I gotta tell you - im so confused!

 

same here man.

I think a respectable someone in the field should filter through all the rumors and come up with a comprehensive guide one of these days. The study of the internet has come into it's own.

 

david sakh: Well it is all theory any way, but it is interesting to put forth theorys and discuss them.