## YouTube Power Laws (a small experiment)

When learning about power laws in class, YouTube views immediately sprung to mind. Given the sheer number of videos on YouTube and the wide, wide ranges of views per video, it is incredibly likely that the view counts across the entire site follow a power law. But I wondered if I could find evidence of power laws in something a little smaller: a single YouTube channel. I run my own channel with a little over 1000 subscribers and less than 100 videos. The numbers are small, but I have view counts ranging from a few hundred to over ten thousand (and one video with 60,000 hits, which would certainly be an outlier). It seemed very possible that this data set could hold to a power law.

My views

The data seemed to indicate yes. Graphing it using Excel produced a nice looking, albeit sharp, curve. Taking the logarithm of the numbers and plotting them showed some small drops, though. As expected the 60,000 hit video is far off the line of the log chart, and there is also a sharp dip and level off towards the end. This is likely accounted for by the fact that I uploaded a series of videos which I had initially uploaded to a different site onto YouTube a year or two later, and most of the people who watch my videos watched them on the other site first.

These numbers seem to follow a power law, but I wanted something more definitive. I decided I needed a channel with more subscribers and more videos, and went with Retsupurae, a channel run by some friends. They have over 50,000 subscribers, and 400+ videos, as well as a range of 4000 views to 320,000 views per video. If a power law held in individual channels, it should definitely show up here.

Retsupurae’s views

After plotting their view counts, the data again followed a nice looking curve, and plotting the logarithms of the views produced an even smoother line than my channel did. In fact, the power law seems to hold quite strongly even when eyeballing the data: only 2 videos have over 300,000 views, while 10 break the 200,000 barrier, 76 have over 100,000 views, and 254 have over 50,000 views. There are a few videos that are far and away the most popular, but as we get to lower view counts the number of videos grows by leaps and bounds, resulting in that pretty curve linked above.

This is not definitive proof that power laws also rule over individual YouTube channels, but the basic pattern does seem to hold for these channels (to different extents). A possible factor that might have made my curve a little less smooth is the fact that my videos tend to be playthroughs of video games, which are best watched all together. The small sample size probably did not help either, and I hypothesize that as I upload more videos the pattern will grow stronger, as it seems to have when looking at the larger Retsupurae channel.