How much page rank flows through a link?

[BakerStreet]

Hey, just a technical question here. Lets say there's webpage.html and it is toolbar PageRank 2. webpage.html has 10 hyperlinks and each go to a unique webpage. One leads to AnotherPage.html. How much PageRank would AnotherPage.html have?

My answer is .9.

You first take 10^2 since PageRank is log10 metric. That is 100. Then 100/10 is 10. So 10 raw page rank points flow through the link. Then there's a dampening factor of 15% so it is 10*.85 which is 8.5. Then you take log10(8.5) which is about .9.

Is this right or am I totally wrong? I'm asking because I put this as a test question in interviews and no one got it right. They all say 2/10 = .2, but I know that is wrong because it does not take into account log10 nor dampening.

 

[Jesse]

The actual formula is on Wikipedia, and it comes to about 0.32 using a 0.85 dampening factor. I have no idea where you pulled the rest of that from.

The simplified formula is giving the 0.2 that they all keep telling you.

You can ask ChatGPT to do the math for you if you don't want to or can't do it yourself. It can pull the formulas and format everything in a pretty way.

 

[Ryuzaki]

I think your logic is correct, and while I haven’t looked at the Wikipedia info, I’d assume they don’t have their hands on the most current or accurate formula (nor do the old browser extensions have current info). It’s all close enough, though, considering how many other variables and re-ranking occurs with classifiers and click-stream data there are.

One thing that occurred to me reading and thinking through your math is that none of us are privy to what the original scores are before the normalization takes place to neatly reduce and fit it into the 0 through 10 score. The higher the magnitude of the allowed scores, the more skewing occurs.

We also don’t know what treatments are added after the calculation. While we know a PR10 is massively larger, exponentially so, than a PR3, we don’t know (even ignoring all other factors and only considering page rank math) if a score of a 3 is treated the same as a 10. Obviously trust, relevance, age, anchor text, and all of that is applied eventually, but despite that, we don’t know.

Not that that’s what you were asking. Just more to consider. The real figures are so obscured from us that a ballpark answer should suffice. And for future employees, I’d be testing less for an answer you want and more for the ability for them to research and form a decently-informed answer that didn’t require too much time-waste or esoteric knowledge, since none of us know the right answer.

 

[BakerStreet]

The actual formula is on Wikipedia, and it comes to about 0.32 using a 0.85 dampening factor. I have no idea where you pulled the rest of that from.

The simplified formula is giving the 0.2 that they all keep telling you.

You can ask ChatGPT to do the math for you if you don't want to or can't do it yourself. It can pull the formulas and format everything in a pretty way.

There's a difference between ToolBar PageRank and Raw PageRank. Here's a post from 2002 that discusses this https://ianrogers.uk/google-page-rank/ .

When people say their site is PageRank 2, they meant that the toolbar says their site was PageRank 2. This scale is 0-10. However that score was expected to be logarithmic, as the author in the post states. People don't know the real scale but it was always assumed to be log10. The author in that post used log10 too. Therefore you need to turn the toolbar PR score into the raw PR score by taking 10^x, where x is the toolbar PR score.

Then once you found the raw PR score, you divide it equally across all hyperlinks on the webpage. Then you apply the dampening factor.

And yes, I checked with ChatGPT about the answer and ChatGPT just said .2 "with no dampening factor applied." But we all know the dampening factor is there None of the applicants stated what the dampening factor is.

so IMO there was three steps to the problem:
1.) turn toolbar PR into raw PR
2.) divide by the number of hyperlinks on the page
3.) apply dampening factor.

All applicants just got step 2 right and so did ChatGPT.

I think your logic is correct, and while I haven’t looked at the Wikipedia info, I’d assume they don’t have their hands on the most current or accurate formula (nor do the old browser extensions have current info). It’s all close enough, though, considering how many other variables and re-ranking occurs with classifiers and click-stream data there are.

One thing that occurred to me reading and thinking through your math is that none of us are privy to what the original scores are before the normalization takes place to neatly reduce and fit it into the 0 through 10 score. The higher the magnitude of the allowed scores, the more skewing occurs.

We also don’t know what treatments are added after the calculation. While we know a PR10 is massively larger, exponentially so, than a PR3, we don’t know (even ignoring all other factors and only considering page rank math) if a score of a 3 is treated the same as a 10. Obviously trust, relevance, age, anchor text, and all of that is applied eventually, but despite that, we don’t know.

Not that that’s what you were asking. Just more to consider. The real figures are so obscured from us that a ballpark answer should suffice. And for future employees, I’d be testing less for an answer you want and more for the ability for them to research and form a decently-informed answer that didn’t require too much time-waste or esoteric knowledge, since none of us know the right answer.

Yup, good points. If any of the candidates stated anything like click-stream data affecting the flow of PageRank through the link, they'd get the job

And yes I agree, I'm looking for their reasoning and how they approach the problem. They can get a different answer and still pass. What is bad is when someone's a total idiot and don't know what they're doing and copy and paste what ChatGPT gave without question. That person can not be responsible for SEO at my company! Fuck that!

 

[Jesse]

Ignoring that toolbar PageRank was retired almost a decade ago and may not be useful to quiz about for new hires in 2025, one problem with the format of the question is that a toolbar PageRank of 2 doesn't mean that the raw PageRank is 100 (assuming a base of 10). It means it's somewhere between about 32 and 316 because of rounding since the toolbar only showed whole numbers.

Nonetheless, here's the formula for anyone interested. PR_source is the raw PageRank of the page, L_source is the number of outbound links and d is the assumed damping factor.

In the example @BakerStreet is trying to arrive at, you have PR_source = 100, L_source = 10 and d = 0.85, giving a PR of 8.65. For reference, the simplified formula comes in at 10.

Again, if someone doesn't want to use LaTeX or similar to format this kind of thing or is otherwise challenged in the math department, ChatGPT can do the formatting and calculation for you.

 

[BakerStreet]

Ignoring that toolbar PageRank was retired almost a decade ago and may not be useful to quiz about for new hires in 2025, one problem with the format of the question is that a toolbar PageRank of 2 doesn't mean that the raw PageRank is 100 (assuming a base of 10). It means it's somewhere between about 32 and 316 because of rounding since the toolbar only showed whole numbers.

Nonetheless, here's the formula for anyone interested. PR_source is the raw PageRank of the page, L_source is the number of outbound links and d is the assumed damping factor.

In the example @BakerStreet is trying to arrive at, you have PR_source = 100, L_source = 10 and d = 0.85, giving a PR of 8.65. For reference, the simplified formula comes in at 10.

Again, if someone doesn't want to use LaTeX or similar to format this kind of thing or is otherwise challenged in the math department, ChatGPT can do the formatting and calculation for you.

I am math challenged and my answer, .9 toolbar PR, was right! I left out the (1-d) part of the equation but even without that, when you take log10(8.65) you get toolbar PR .94.

But yes good point, the toolbar PR is rounded and it can be anywhere from 10^1.5 to 10^2.5.

As for how useful this is for new hires, I'm trying to filter out those idiots who watched a few YouTube videos about SEO and now think they are an SEO expert. You would be shocked at what self proclaimed "experts" stated before. The issue here in Germany is that, once you hire someone, it is really hard to fire them, hence a question like this.