Twitter stats redefined - now measuring true influence?

I had a small revelation the other day while on Twitter and chatting with Alan Berkson. As you may or may not known, I'm a self-proclaimed statishist, meaning that I really get excited by statistics, or stats for short

I did a few calculations on 20 Twitter people, taking their latest 1,000 followers, and looking at their followers' followers and "friends"

Note: Twitter uses the term friends to indicate people you are following, it's an API term. These are not your friends, nor do these constitute people that you follow and follow you back. So, where ever I'm going to use friends in this post, I mean the opposite of followers; they're the people you follow

I hit two people, then three, then four and five, and I was astonished: people that I deemed similar had all followers with around 5,000 followers and friends on average each - wow!
I took a few others "of different style" and they averaged in between 2,500 and 3,000 each - oh my god I was on to something!!!

Then I looked a bit further and found that I just got lucky. A little bit further yet and I had chartered 20 people who all had at least 1,000 followers and I had to admit that my initial revelation had been great for my adrenaline which was now slowly wearing off...

But, that wasn't all, and I pursued my idea: playing with one's followers and friends, and one's followers' friends and followers. After all, "leaders have large followings" and it is very interesting to see who among those followers are leaders themselves - seems to me a good indication of influence. Of course it's nice when you control the masses, but it's nicer to control the controllers, if you catch my drift

So, the first picture (click on any one to enlarge by the way) is what's usually used to measure leadership or influence: number of followers - and you can see that Twitter Lists are nicely "running along" in the hierarchy there

Note: these figures are formatted according to Dutch settings, where the decimal-point is a comma. 1.000 is one thousand and 1,0 is one - sorry for that

However, counting followers is a very rough one and the "I follow you just follow me back" approach has resulted in mere mortals reaching the same numbers as leaders. So, another measure is to compare one's followers to one's friends: if you have a large following but a relatively small amount of people who you follow yourself, then you must be a leader - right? Here's a picture of that:

(The FR:FL column shows the results of the division of friends by followers)
The order changes significantly: where the first one showed the "icons" on top, this one shows what I'd call - wait, maybe you can fill in the blanks here? These are people who don't only speak, and may listen themselves, but they have people following them who want to listen to what they have to say, more (that is, in a greater quantity) than they do so themselves.
Let's name them thought leaders for now, OK? Humour me please

Then, off to my new lovechild: one's followers' followers. Again, I took the most recent 1,000 followers for each of these people, to assure a current view and a good-size "testbed". The column Fs' Followers shows someone's followers' followers.

What a difference that makes! An entirely different order, now showing people who - I don't know? Well I do: these people have a follower crowd that consists of a large follower crowd themselves. I'd say this top 5 has a great opportunity to amplify whatever they're saying.
Then again, how "serious" is this followers' follower crowd? How can we find out more about themselves? Easy: same way we did in picture 2, by comparing their friends to their followers.
So, here's a new list ordered by the ratio of one's followers' friends to their followers (are you still with me btw? Hang in there, we're almost done)

And yet, again, an entirely different list. The FFR:FFL column shows the results of the division of someone's followers' friends by someone's followers' followers.What we see here is that the top has followers who have more followers than friends themselves. One would say that these followers are considered thought leaders themselves, or at least have more people that listen to what they say, than they listen to others themselves? Tough...
In pop-speak: these people here have a thought leader audience - well at least that does sound nice, doesn't it?

But if we really want to know who's boss, we should compare one's own audience with one's audience's audience, shouldn't we? Take the friend:follower ratio of themselves, and the friend:follower ratio of their followers, and then compare those. Right? Right

There's a slight issue there though:
If you follow 1 person yet have 10 followers, and all those on average follow one person yet have 10 followers themselves, you get 0.1 and 0.1. If you divide those, you get one.
If you follow 10 persons and have 1 follower, who also follows 10 and only has one follower himself, you get 10 and 10.
Dividing those by each other would also render one; so we need to do something else - and it's called multiplication.
That would result in 0.01 in the first case, and 100 in the second. OK, here's the last picture:

The F:OWN column shows the FFR:FFL column (one's followers' friend:follower ratio) multiplied by the FR:FL column (one's own friend:follower ratio). I didn't round any of those or these, it's only showing one or two decimals, and then sorted - hence when you do this exercise yourself you might wonder; well just don't
It's maddening but in this 20-people sample case, that top-5 is exactly equal to simply looking at one's followers' followers and friends

And for the quick and alert among you: the entire order is almost exactly equal. Statistically, I'd claim it is...

What does that imply?

I haven't the foggiest, really - but I think I'm onto something. What do you think?