Friend speed

How fast can I get Facebook Friends?

41,23 friends per hour!

Awesome! You must wonder what that means and where I get this from.

A while ago I registered for a Facebook profile because:
1) All the cool kids are doing it
2) I want to watch holiday and baby pictures from friends
3) I wanted to do an experiment

Everyone I spoke about opening a FB account told me you get friends really fast. So I set out to see if this was true.

The experiment

When you don't change anything on the original settings you get an e-mail message about everything that is happening. That's why people switch this off immediately. You're on FB 24/7, you don't need see the messages twice, right?
I left the settings as were and registered every friend request and all the request I sent myself. The graph below shows you how that looks like. Yes, this was tedious work.

Most of it is quite clear I guess. On the horizontal axes we see the time in hours, and on the vertical axes the total number of friends, and the number of requests I sent myself. The numbers in the top are just the days, so we start on day one somewhere in the morning.
Funny thing is, within one minute of registering I received two friend requests without any other action then signing up.That means that those people somehow saw that I had joined, not sure how that works.
I sent maybe two or three requests, but I waited to see what would happen. The number of friends is rising, what happened?

Well in this case one of my first friends made friend suggestions and since I was in need of friends I clicked them all I guess. During day two I didn't do anything and I noticed that the rate at which my number of friends was growing was slowing down.

Sending requests

Therefore I sent out a lot of requests on day three, which you can clearly see from the quick rise of the blue line. And yes! I got an immediate response and my total number of friends sky rocketed. Let's zoom in on that event.

Total number of friends after sending lots of requests.

In this picture we can see that the total number of friends start to grow quite fast until.... people go to sleep. You can see  it stops at about hour 72 which is the end of day 3. A bit more than eight hours later it picks up again.

Friend speed

So I mentioned speed, or 'friend speed' as I like to call it. How do we calculate that? There are a couple of ways to calculate that. You could for instance look in every hour how many friends were added. Downside is, that in most hours no friends were added at all and in some others maybe four of five. This would be a very non informative graph.
A second method is calculating the time between two confirmations. Plus, you get a value for all the data points. Minus, some friends sent their confirmation at the same time (the same minute). That means the time was zero between them and so the speed was infinite at that moments. Infinite works very bad in graphs.

To solve that problem I let R (used in the graph making) draw something of an average through the data points, which is called an LOESS fit as can be seen in blue in the image below.

Blue line depicts a LOESS fit on the friend datapoints.

I think you lose 90% of your crowd with every graph you use, so I'm down to 0.1% of my readers.
On this line I performed this calculation I just mentioned of calculating the time difference between two events which should be an approximation of the speed. In the image below you can see the calculated 'speed' compared with the total friends data.

As my number of friends is rising very promising we see a terrifying event. The speed of gaining friends is dropping. We see what we expect, at nightfall the friend speed drops to almost zero, and during day 4 the speed is very low. But there is something wrong in my opinion about the speed data. Of course we used this LOESS fit as an approximation of our data which will give rise to errors. But, in this graph it looks like during day 3 the friend speed is decreasing at a constant rate. And for those who love differentiating and integrating and all, that would mean that the total number of friend should be parabolic. I therefore don't trust this graph all too much and tried it in a third way.

Tangents

Since some regions in the graph seem almost linear it's easy to draw a tangent line there and use that to estimate the speed.

Tangent lines to estimate the friend speed.

In day 3 it looked there were two areas. One in the beginning consisting of people who responded as soon they got the friend requests on their mobile device and some hours later people checking in later.
In the first section the climbed was huge and I estimated it to about 41,23 f/h !! (friends per hour of course). During the rest of the day it settled to a more moderate 3,66 f/h and the next day it dropped to a sluggish 0,70 f/h.

Conclusions

So what the message to take home? When you ask to become friends of FB, they respond pretty fast. The number of friends has to reach a maximum because you only know that many people and most friends you gain comes from the people you invite yourself. So automatically to speed slow down. Good thing too, if the speed stayed of about 40 friends per hour I would so may friends by now I wouldn't be able to keep up with the news feed.

Lesson two: you can't really say anything on such a small dataset and especially on something that is not reproducible. So there is no real science here, I just wanted to make pretty graphs.

(note 2 self: repeat experiment until friends no longer respond)