I don’t know about you, but I love data. But not just plain data without a purpose, instead I like to use data to look at trends and make predictions.
So, not too long ago I decided to start a second YouTube channel — Physics Explained. This channel is basically all of my physics explanations and problems. I started off with stuff for introductory-level physics, but I’ve found that more advanced physics (like classical mechanics) is both fun and popular. Here, check out a video.
But here’s the deal. In order to be able to monetize your channel (put ads on there so that you can get paid) YouTube has 2 requirements: 1000 subscribers and 4000 watched hours of video. Right now, I’m just waiting to get to 4000 hours. This is where the data comes into the game.
In July, I started recording the daily number of subscribers and total watched-hours. Here are some of my ideas about this data.
- I suspect that the watched-hours will be non-linear. At the very least, as I make more and more videos that should lead to an increased rate of watching — right?
- There should be some type of relationship between subscribers and the rate of watched-hour increase. If I have more subscribers, I think I should have more watch-hours per day.
- Finally, I want to project the date that I meet the monetization requirements. Let’s see if I get it right.
You know what comes next — a bunch of graphs.
Modeling Subscriber Data
Here is the plot of subscribers as a function of day. Oh, I should point out that I don’t have data for “day zero”, but I count days from the date of the first YouTube video.
After playing around with this, I picked a fitting function that is an exponential. It looks like this (I’m using t for the time variable and S for the number of subscribers).
This function doesn’t really mean much except that it’s a) exponential and b) seems to fit the data pretty well. Of course the one thing that I found troubling is that at t = 0, I would have 1060 subscribers. That clearly wasn’t true. Oh well.
Now, what about the watched-hours as a function of day? Here’s what I get.
Again, I get a nice exponential fit. In this case, I’m going to represent “watched hours” with the symbol “w”. This gives the following fit.
Again, this fit shows a large number of watched hours on day zero (1409) — which clearly isn’t exactly true. But maybe it’s not super crazy. It’s very possible that just starting the channel up had an initial “surge”. But anyway, this equation seems to fit the data quite well. Oh, also notice that the exponential factor for the watched hours is very similar to the subscriber exponential. This suggests that subscribers and watch-hours grow at the same rate.
When Will I Get 4000 Hours?
This is the question I want to answer. Let’s assume that the traffic for my channel continues along the same mathematical model. In that case, I can just find the time that gives a watch-hours of 4k. Let’s do that.
I will first subtract the 1409.43 term from both sides of the equation and then divide by 0.356. This gives:
Now I can take the natural log of both sides so that I can get to the value of t:
If I divide both sides by 0.0361, I will get the following expression for t as a function of w:
Putting in a value of 4000 for w, I get a time (day) of 246.33. Ummm…that’s just 16 days from now (right now I’m on day 230). I really don’t think that’s going to happen, but let’s just wait and see. I hope it happens.