### Estimating the view count distribution on TikTok

TikTok is unusual in that the views of video get are fairly unpredictable. Unlike other social media platforms like Facebook or Instagram, most views through TikTok are driven by a recommendation algorithm (rather than who you follow) so views can vary dramatically based on unpredictable nuances of the algorithm. Within the same week, I've had videos whose success differs by a factor of 10,000.

I want to get some sense of how likely my next video is to be successful. Merely looking at the average of my most recent videos is not very predictive, because of how random the view counts are. This post details a method for creating these predictions, as well as a calculator so that you can protect your own future success.

## Methodology

The view counts that videos get on TikTok are reasonably well approximated by a gamma distribution:

(Note that the x-axis is logged.)

This gives us a reasonable prior to use for a Bayesian update.

Recalling that the conjugate prior of a gamma distribution is a gamma distribution (i.e. it is self-conjugate), we can first create a gamma distribution over the parameter $$\beta$$ of our gamma distribution as a prior, then add in the evidence from my view counts, resulting in a posterior distribution over $$\beta$$.

(It's going to get very confusing that we are using a gamma distribution to estimate the parameters for a second gamma distribution. Through the rest of this, $$\alpha,\beta$$ are the parameters for the distribution which estimates view counts, and $$\alpha_0,\beta_0$$ are the hyperparameters for the distribution that estimates $$\beta$$.)

1,000 samples of 200 videos each were created and a gamma distribution fit to each of them. I pulled out the parameter $$\beta$$ from each distribution and made a histogram (blue rectangles), then fit a gamma distribution (orange line) to them.

Wikipedia tells us that if our prior is $$\Gamma(\beta; \alpha_0, \beta_0)$$ then our posterior is $$\Gamma\left(\beta; \alpha + n\alpha_0, \beta_0+\sum_{i=0}^n x_i\right)$$ where $$n$$ is the number of samples and $$x_i$$ is the (logarithm) of the view count of sample $$i$$.

Plugging this in, we can see how the posterior distribution of $$\beta$$ based on my videos differs from the prior:

You can see that the posterior distribution is shifted the left, indicating a lower value of $$\beta$$ (and hence a larger expected number of views, because I'm so popular):

The update from @charlidamelio is slightly larger:

Resulting in a very different probability distribution of her view count:

As the expected value of a gamma distribution is simply $$\frac{\alpha}{\beta}$$, it's simple enough for us to calculate the expected values here:

 $$E[\beta]$$ $$E[\log(views)]$$ $$E[views]$$ Prior (average for the TikTok community) 0.647 2.197 157 Me 0.485 2.934 859 @charlidamelio 0.185 7.665 46,244,645

## Calculation

Okay, so what does this all mean for you? You can estimate the expected number of views that your next video will create through the following steps:

1. Calculate $$n$$, the number of videos you've published, and $$s$$, the total number of views those videos have received
2. Calculate $$\alpha_0 = 53.865+ n$$ and $$\beta_0 = 83.099 + s$$
3. Calculate $$\beta =\alpha_0/\beta_0$$
4. Calculate $$\log_{10}(views) = 1.42158 /\beta$$
5. Calculate $$views =10^{\log_{10}(views)}$$
Or you can use the following form:
 Number of videos you've published: Total number of views your videos have recieved: Expected number of views for your next video:
Research done in collaboration with @lilweehag

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