The classic way that people have determined link value is by using Google PageRank. It is well known that Google doesn't use PageRank as a direct determinant of link value, but it remains convenient and available as a metric, so it's only natural that people continue to use it. If you're using Internet Explorer, you can get this information from the Google Toolbar, and third party tools that use the API can also display it:
People often refer to the home page of the linking site when referring to the value of a link: "I have a link from a PageRank 8 site" means that the home page of the site containing the link has a PageRank of 8, though the link can come from any other page on the site. If one is forced to rely on PageRank alone, there is some merit to this as it may communicate something about the level to which a link can be trusted, but clearly you should consider the PageRank of the linking page as well.
If the page is a brand new blog post, the PageRank meter will show zero, although that isn't the actual value – it just means that the PageRank database that tools access through the API has not been updated yet (it only gets updated a few times per year).
Google calculates PageRank for a page as soon as it discovers it. You just can't see the value yet.
In this case, the best way to determine the approximate value for the PageRank of the page is to look up the PageRank of other blog posts on the site that have already moved to archive status and that were on the site prior to the last PageRank update.
We have other measurements available for these types of metrics from Open Site Explorer (OSE):
And Majestic SEO:
OSE's Domain Authority and Page Authority have been around for a while and provide a different calculation of a PageRank like metric. Bear in mind that this is based on a smaller data set than what Google uses, and how Google has evolved the algorithm for calculating PageRank is also not known, so while the values correlate pretty well with PageRank you will not see a one to one match.
Majestic SEO's Citation Flow is an improved calculation of a PageRank like value from the ACRank metric they used to offer, and Trust Flow is interesting because it gives us a look at how trusted (duh!) a page is. Majestic's Flow metrics are new but look quite promising.
All these metrics are useful in their own way, and they do provide a simple measure of the value of a page, but as Google learned over the years, not a sufficient measure. So what else do we use to help us evaluate the quality of a link? I thought you would never ask!
The Obvious Additions
One early conceptualization is that is capture in this paper from Yahoo and Stanford. Majestic's TrustFlow metrics tries to capture this concept in their own way. Google says that they don't calculate a TrustRank, but that they keep several other factors related to the measurement of trust of a web page and website.
Google and Bing already determine what keywords are relevant to which websites and web pages. So determining whether a page implementing a link is relevant to a page that it links to would seem easy to do.
There is some debate in the industry about how much they leverage this, but it would seem obvious that a link from a trusted expert in your same space would be worth more from some other site, even if they are trusted in a different space.
The Not So Obvious Additions
Internal vs. external links
Of course, it's fair and appropriate that a page assume some trust and authority from the domain on which it resides (assuming that it is under control of the domain owner). But, it is also very good if the page also gets some direct attention from the outside world (i.e., other web sites link directly to it).
Google might pull that metric from Google Reader or even Feedburner (assuming that they are not sunsetting it):
If you were an average user, what would impress you more, a blog with a PageRank of 6 and 1,000 readers, or one with a PageRank of 4 and 5,000 readers? I would take Option B every time.
Of course, you can skew that conversation further – what if you were looking at two different music industry blogs with identical PageRank and the same number of readers and you knew that Simon Cowell of "American Idol" and "X Factor" fame read one but not the other? So the trust and authority of the various readers could matter too.
Social metrics for the site and/or the page in question
How often do articles on the site get shared or tweeted? How often did the page with the link get shared or tweeted?
These all have some influence on the value of the link. Do I know whether the search engines use metrics like these to value a link? I don't. But, as a human, I know that these types of things would matter to me, and I know that the search engines want to approximate the human measurement of content value (and link value) the same way users do.
Another thing to track would be how many times did tweets and social shares happen after after your link was added to the page? This is a different type of factor for those cases where your link is added to a page after initial publication. Is there evidence that the addition of your link devalued the page? Or, vice versa?
As with the tracking of subscribers, it's also interesting to see who is tweeting or sharing the page with your link on it. If authoritative people are sharing it, your page which is receiving the link is more likely to get noticed and spread.
Clicks on the link, or likelihood of clicks on the link
Is the link buried in the footer or on the right rail where it looks like an ad? This notion is the subject of a Google patent on the concept of the Reasonable Surfer. The patent talks about the likelihood of a link getting clicked based on its placement on the page.
Many link builders have tried to manipulate this concept by buying links through paid guest posts where their rich anchor text links are buried in the middle of the post. This leads to the next concept, that of artificial placement.
If the link looks artificial in nature that could counter what would otherwise be a strong "reasonable surfer" score. Or, Google could use Google Analytics data and simply measure whether or not the link actually gets clicked on.
Bounce rate of the page containing the link
No discussion would be complete without including bounce rate. Back in June, Matt Cutts stated that Google doesn't use "Google Analytics Bounce Rate" as a ranking factor. However, that doesn't mean they don't use more sophisticated metrics such as how many people click through to a page from a search results page, bounce back to the search results and click on another result.
But, we don't have the ability to measure that, and a straight bounce rate measurement can be a useful way for you to approximate a page's value, and therefore the value of a link from that page. The potential value of this type of signal was endorsed in June of 2011 by Google's John Mueller. You may not have access to the linking site's analytics, but you can look at third party tools such as Compete.com and get some indication of the user engagement with the pages on a given website.
Which of These Matters
In my opinion, they all do. If you're an avid reader of SEO related articles then you're probably aware of the great controversy about whether social signals are used as direct ranking factors by the search engines. This article gets to the heart of the matter. There is a very strong correlation between social shares and links.
The point is, if you do something that generates social shares, you're also doing something that will generate lots of links (assuming you aren't buying said shares, but earning them). And so it is with my link valuation metrics above.
All the metrics I outlined help give you one measure or another of the quality of a page, and the quality of a link that you obtain from that page.
Whether the search engines use only one of them, or some other measurement entirely, does not matter. Focus on the link quality metrics that can be available to you, and let the rest of the story take care of itself.
For example, if you obtain a link that has a reasonable chance of obtaining lots of clicks, chances are that it will also score well on metrics that Google and Bing actually use. If you focus all your attention on one metric just because you think the search engines are doing it, chances are that the algorithms will change on you soon enough anyway.
Focus on these types of things, and trust that the search engines will get continually better at seeing value the way users do.
While life as a digital marketer doesn't come with guarantees, focusing on links that have the most actual value (not taking SEO into consideration) will net you the links that the search engines want to value the most. Granted their execution is far from perfect, but they will continue to move in that direction as aggressively as they can. I would rather be in line with their goals than focus on trying to manipulate perceived holes in their present.