Page Rank Log Scale

[djtaverner]

Page Rank is done on a logarithmic scale, which is approximated in the tool bar as 1 - 10.

What log base do you think its operating on?

10, or other?

Dave

[roodle]

I've heard it's something more like base 8, but only from what I've read. I wouldn't know how it could be worked out.

R.

[pagano]

Here is a past thread:
[webmasterworld.com...]

In a very clear work, which gives a very good explanation of PageRank, I've read: "... In reality, the base is unlikely to be 10. Some people think it is around the 5 or 6 mark, and maybe even less. ..."

But in some other PR explanation I read it's around 8.

[Sally Stitts]

Last month, my observations, assumptions and calculations came up with base 6.

[michael heraghty]

Yeah, somewhere around 6 seems to be the consensus, though the jury is still out.

[GoogleGuy]

Whenever I hear this discussion, I say 42. I say that as a joke, but the fact is that PageRank isn't the end-all-be-all of rankings. My bet is that looking at visitor logs to see what terms people use to find your site(s) is a better use of time than trying to figure out log scale coefficients. Looking at referer logs usually turns up something interesting, at least; besides, who ever said that it was a single log scale for the toolbar display? :)

[pagano]

GoogleGuy,
I got a degree in statistic, and I totally agree with you!

[mil2k]

Yeah, somewhere around 6 seems to be the consensus, though the jury is still out.

Yes, many think its close to 6. Some of the maths guys around here think it maybe close to 7. Also remember that the base should change as the size of the Google index increases.

HTH :)

[rainborick]

GG apparently knows the answer to life, the universe, and everything. A misspent youth, no doubt ;-)

[jbgilbert]

Stats major here too, but a stats major with real world experience who has learned to get out of the trees when looking for the forest!

Who cares what the log base is!

The only possible use anybody could make of this is to get an idea of their actual PR... 5, 5.1, 5.21, 5.64, 5.2353746527........

[doc_z]

Yeah, somewhere around 6 seems to be the consensus ...

Personally, I think that even GoogleGuy's joke is closer to the real value than 6.

[ciml]

> Who cares what the log base is!

It's not the destination that matters, it's the journey.

I agree with doc_z if he's talking in relative, rather than absolute terms. That's judging from the last good set of data I had, which was not recently.

[rfgdxm1]

>Looking at referer logs usually turns up something interesting, at least; besides, who ever said that it was a single log scale for the toolbar display?

Hmm...could this be a cryptic clue? Toolbar PR could be more complex than the same log scale from 0 to 11.

[pleeker]

PageRank isn't the end-all-be-all of rankings.

Thank you for saying that.

Now, could someone at WebmasterWorld HQ please put that in big, block letters right underneath "News and Discussion for the Independent Web Professional" on the home page, or at minimum insert it prominently into the charter for this Forum? :)

[BigDave]

Who cares what the log base is!

Well, obviously too may people care. ;)

It changes from update to update. And more importantly, it simply doesn't matter.

All you really need to know is that PR7 is better to have than PR6.

No matter what the base is, or even if it is a log base at all, the result is the same. Getting more PR is a much better use of your time than trying to figure out a number that doesn't make any sort of real world difference.

Work on your site and get more links. Check your PageRank every couple of months to feed your ego.

Checking your logs can provide you with a lot more entertainment too. I just found that I am at #2 on a search term that had me doing a Bevis and Butthead impression.

[Sally Stitts]

After a closer look, I think I have a more polished estimation. I just eyeballed a bunch of sites in various areas, and came up with the following estimates :

PR - log base - Typ.# of links
0 - - - - 1 - - - - 1
1 - - - - 2 - - - - 2
2 - - - - 2 - - - - 4
3 - - - - 3 - - - - 12
4 - - - - 3 - - - - 36
5 - - - - 4 - - - - 144
6 - - - - 4 - - - - 576
7 - - - - 5 - - - - 2,880
8 - - - - 5 - - - - 14,400
9 - - - - 6 - - - - 86,400
10 - - - 6 - - - - 514,400
11 - - - 7 - - - - 3,628,800 (Google only, GG=11M, FAST=302K)

Final Conclusion: Starts out at about log base 2 @PR=2, and ends up at about log base 7 @PR=11.

Typ. # of Links = Approximate average number of backlinks associated with each PR value - varies like crazy - scattered, generalized estimates, but ones which fit a lot of cases.

Of course, this says nothing about the Quality of the backlinks, or the quality of the site, or it's competitive environment.

Creating this summary is time consuming.
That's why I don't usually do this.
I sure wish I could just post my Excel file, or a .PDF, or even just a JPEG of the data, the relationships, and my conclusions. Or just a link to it. Or maybe just a link to a link to it. Sorry. Disallowed by TOS.

When I want to post for feedback, I must do it elsewhere.

[rfgdxm1]

>Creating this summary is time consuming.
That's why I don't usually do this.
I sure wish I could just post my Excel file, or a .PDF, or even just a JPEG of the data, the relationships, and my conclusions. Or just a link to it. Or maybe just a link to a link to it. Sorry. Disallowed by TOS.

Hmm...have access to a Usenet binary posting server? Post those to alt.binaries.misc, with a clear subject line making in easy to find, or with an additional text post explaining what you are posting. I have Usenet access, and can handle even an Excel file. I actually think that you may be onto something.

[Sharper]

The problem with your summary is that it sounds like you did sites and not pages within sites. Site homepages tend to have higher pagerank than internal pages, one likely explanation for your scale varying upward.

[IITian]

Final Conclusion: Starts out at about log base 2 @PR=2, and ends up at about log base 7 @PR=11.

Very nice analysis. I too think that the base changes as you have described.

[stevenha]

Thanks for posting your data Sally Stitts. Some people just like to figure out how stuff works, whether or not it leads to anything useful. Being curious and testing ideas should be encouraged. So Thanks!

I just have a point about log scales... There are other kinds of formulas out there. Logs aren't the only game in town. Search for "classic equations commonly used by biologists" and you'll find formulas for One-site binding, Two site binding, and others, which describe curves that could be manipulated to fit the relationship between input-# of links and output-toolbarPR.

There are assumptions and simplicifcations used in this kind of analysis. One is to assume all incoming-links have the same average amount of PR transferred. It would be helpful if forum members could state their assumptions used for this.

Another thing that I've always wondered about, is what is the distribution of toolbarPR amongst all pages Google indexes. It's certainly not a Normal distribution (bell-shaped curve). It might be a log-normal distribution, or does the distribution simply look like a one-phase exponential decay curve. Does anyone know?