But I think your math is off.
- you need powerful people
- you need to know people well
- you need to know them IRL
- you need to know them if they know you
- one person can only help you get a job at one place
- the person must be in your line of work
However my experience has been rather:
- anybody has the potential to bring you an opportunity. They have friends, family and colleagues, and they talk. My first internship was from the cousin of a friend of my mother needing somebody. 3 layers of indirection.
- superficial relationships (met once in a meetup, sport club, whatever) do carry opportunity. When people are looking for a worker, they prefer somebody they know, but will rarely find it and settle for anybody they can assess.
- IRC channels, forum and social networks are all doors to get jobs. Even MMORPG, MOBA or RTS. Actually they are filled with geeks, they all work in companies having some need for a recruitment or the other. And they are having fun with you.
- Even if you don't know somebody, if the person knows your work, it's a start. Github is a great personal showcase. I personally don't send my resume first, but my link to my stackoverflow account because it's quite famous in the Python community.
- people can talk about you to somebody working at another company who heard someone needed somebody, etc. Actually it often works that way: informal networking is the way humans connect the best. This is something I learned in Africa where it's the way of life, it's a lost art in our countries, were we do it reluctantly if we have no way around it.
- I'm currently working for a transport facility. Because my flat mate, not an IT person at all, works for one of their contractor, and he knows the project manager for one stuff where they needed something to be coded and he hooked us up. How ? We played laser tag 2 years ago, and so they know me and we just had diner to seal the deal. It's that stupid. And it worked. I delivered the software and they were happy.