So why are there so many, and how accurate can we expect them to be? Has anyone done an experiment with this?
The weight of a backlink depends on so many factors: How many other links are on the page your backlink is on; how related your page is to the page the backlink is on; the page rank of the page the backlink is on; whether or not you're linking back to the page the backlink is on; and probably more that I'm not aware of. Nobody can keep track of all that, so just try to get as many good backlinks as you can and provide original content and you can be sure Google will take notice.