#### dTal

##### Member

- Joined
- May 1, 2016

- Messages
- 34

We are not looking at a single curve. This is the superimposition of at least three different demographics.

Demographic 1: The people who were poised over the keyboard ready to order as soon as they were allowed. This is viewable as a virtually instant spike. Eyeballing it, I model this as

**130 people.**

Demographic 2: Forum members (who didn't order within the first hour). As far as I can tell, this is about

**350 people**. I arrived at this by assuming that all of those ordered in the first 5 or 6 days, and treating the curve at that time as linear and finding its y-intercept. I model this as a

**step response**with a time constant of 1.3 (eyeballed):

**350*(1-e^(-x/1.3)) .**This part could probably stand to be tweaked a little more but it's unimportant.

Demographic 3: Everyone else. The tricky one. Initially, this appeared linear, but in recent days a falloff is becoming apparent; I decided to model this as a step response as well. From day 5 to 15 roughly 12.65 Pyras per day were sold - I will conservatively round this *up* to 13 and treat it as the initial slope for the step response, which makes the equation

**13*n*(1-e^(-x/n))**, where 13*n is the total number of non-forum goers who end up preordering. I experimented with different values of n to achieve the best fit with the observed falloff -

**50**worked well, for a total of

**650**"outside" preorders. Rounding the initial slope down to 12 and making n=70 make a slightly more optimistic final prediction of

**840**"outside" preorders. These are pretty much the outer limits of the model, so it's not all that sensitive to the exact numbers you pick.

Putting it together: my prediction for now is that Pyra preorders are described by the curve

**P(t) = 130 + 350*(1-e^(-t/1.3)) + 650*(1-e^(-t/50))**

On this basis, I predict that we will hit 800 preorders sometime around day 34, and 900 sometime around day 52, should preorders stay open that long. Total preorders are unlikely to exceed 130+350+840=1320.

Obviously, real life is not math, and I will be quite surprised if this turns out to be accurate. Nevertheless, here's a fun graph showing the fit: