1. Link: command does not show you all the links, so the 8180 figure is totally useless.
1a. Not all links are created equal, so you cannot compare a site A (800 backlinks) against site B (10,000) and conclude merely based on those numbers that site A has a better link profile.
2. SERPs are not a reliable SEO tool because factors can't be isolated.
3. There are hundreds of factors.
Knowing all the factors will not help you nail #1 ranking; at the end of the day its a popularity contest and anchor bomb game. Rack up links that pass juice = you win. Waste months collecting links that will be devalued by Google in 1 or 2 years = you lose.