Current statistics and some predictions

[dTal]

Well, this stats game is addictive. Here's my analysis.

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:

 

[levi]

I didn't order immediately because I was away visiting friends at the beginning of the month, and knew I had my place reserved by a pre-preorder anyway. I'm not sure if I upgraded to a preorder on the 5th or the 6th day, which'd shift me from group 2 to group 3 in your model.

 

[Djoga'Ro]

Well, this stats game is addictive. ...

Statistics is devil worshipping. No wonder it has qualities like being addictive.
Who's idea was it to call it mathematics, anyway?

 

[Binky]

@Binky Sorry, I don't understand "sig. fig.s". ?

Significant Figures:
How precisely a number is recorded
The more precise a number, the more digits its worth quoting accurately.

<lecture>

Example:

Suppose a national census receives 35,678,541 replies.
That probably isn't a perfect measure of how many people are in the country. Illegal immigrants, emigrants, etc. It could be off by a few thousands, so you might round it and say:
"The population of this country is 35,679,000"
That number is correct to five significant figures
If you asked me in conversation what the population was, I'd probably say
"About 36 million"
That would be correct to two significant figures.
If I were being really lazy, I might just say
"40 million"
Which is only correct to one sig fig.
​

In a scientific context, the number of sig figs used implies the precision of the value.
A weather-forecasting computer might predict that the wind speed at 16h 32m 06.422s today will be 21.639m/s
While that may be the mathematically precise result of the calculations involved, it would be inappropriate for those results to be published in that form, because weather forecasts are never that accurate. It would be far more reasonable to quote 16h30m and 20m/s when reporting the forecast.

When doing calculations, it is pointless (and misleading) to give answers that are more precise than the original data.
In the case at hand, the input data (number of Pyras sold so far) only has three digits - and people aren't buying fractional pyras. That means that FBnil's equation...

y = 112.3626812 ln(x) + 348.0876387
(Where y is number of Pyra preorders, and x is time)

...is unreasonable, because the prediction is not accurate to the nearest 0.0000001 Pyras!

</lecture>

 

[FBnil]

Here's my analysis.

Yes, exactly that. The data can not be modelled to simple regressions because each part follows a different model.
So we already saw that the logarithmic model (good for modelling, say, how much CO2 is going out of your soda, or how a zombie infestation would go) actually starts to stall asyntotically (becomes a straight line) too early in time compared to the data.
This difference is actually the amount of new people flocking in. And that looked linear, however, as DTal pointed out... it is stalling too (not good)
It should not be a line, it should have spikes when newschannels/mediaoutlets/websites talk about the Pyra and new people join. But maybe paychecks have not come in yet, and we will see a spike when the paychecks come in (this chainsaw effect is seen with stores that sell luxury items).

As for the "Demographic 1", this is accounted for in any regression, it is the + c (constant) that is added to each formula. Even stretching that to remove the data of the first 3 days, and make that the constant, then modeling with the remainder data does not yield calculated points with little error...

For example, a big error was seen with the 4th power poly, which actually started decreasing the amount of pre-orders...

 

[comradekingu]

Its a graph, when you assume it to continue, it is a prediction.
And it is accurate for that first part, which is the same as saying one pyra per high resulution unit of time.

 

[Djoga'Ro]

Thanks, @Binky. I know the concept, just didn't know the abbreviation and couldn't figure it out from context.
[doublepost=1463863595,1463863514][/doublepost]Has anyone tried it with DFT, yet?

 

[dTal]

As for the "Demographic 1", this is accounted for in any regression, it is the + c (constant) that is added to each formula.

True, but I was not attempting a blind regression, but a model. And it was not initially obvious that at t=0 preorders should not also = 0 (since in reality of course, they were). But the initial spike was so rapid it made more sense to treat it as a y-intercept.

 

[levi]

Has anyone tried it with DFT, yet?

A discrete fourier transform is a technique I know from sound processing, so I suspect any curve reconstructed from a DFT will oscillate around the 0 point - that is it'll go up, then go down, then go negative and then go back up again. You could probably get a retrospective prediction to fit the curve as is, but it would almost certainly almost immediately tail off, so be useless for future predictions.

Edit:

 

[Djoga'Ro]

Well, one could use it on the growth not the totals. There even have been negative values. It also spits out a 0 Hz component, i.e. a constant baseline.

 

[Caine]

How about this one:

def g(x):
  return 8 * x + 552 - 344 / x + 134 / x**2

With estimates:

 1:  350  2:  429  3:  476  4:  506  5:  529  6:  546  7:  561  8:  575 
 9:  587 10:  599 11:  610 12:  620 13:  630 14:  640 15:  650 16:  659 
17:  668 18:  677 19:  686 20:  695 21:  704 22:  713 23:  722 24:  730 
25:  739 26:  747 27:  756 28:  764 29:  773 30:  781 31:  789 32:  798 
33:  806 34:  814 35:  823 36:  831 37:  839 38:  847 39:  856 40:  864 
41:  872 42:  880 43:  888 44:  897 45:  905 46:  913 47:  921 48:  929 
49:  937 50:  946 51:  954 52:  962 53:  970 54:  978 55:  986 56:  994 
57: 1002 58: 1011 59: 1019 60: 1027 61: 1035 62: 1043 63: 1051 64: 1059

 

[rygD]

I find this conversation extremely boring. Unfortunately, it is somewhat on topic.

 

[comradekingu]

I'm not afraid of zombies, i'm afraid of this. Everyone like that, imagine.

 

[rygD]

I'm not afraid of zombies, i'm afraid of this. Everyone like that, imagine.

Which this? Which that? I don't understand.

 

[Djoga'Ro]

Everyone into statistics like that.

 

[FBnil]

I find this conversation extremely boring. Unfortunately, it is somewhat on topic.

It's MATH, man! Jumping up and down, screaming like a math man...

Ok, how about: We will have Debian. Debian has this nice laptop-mode-tools It allows you to do things like:

NTP daemon runs while on AC, but not when the battery is used.

Now, predict what we all would use it for? (sinds version 1.68 it has systemd integration)


@Caine: LOL, you know, 57 days, is like, 2 Months? (could be 60, if we use 1024)


Talking about predictions, here are some excerpts I could translate from the book of the Dragon (as there is some overlap with the book of Pyra, I could extrapolate a few words):

And then, after these 57 days, there will be three days of darkness, where the Evil Dragon will not utter a word on the [forum]. But after these three days, he-who-wont-be-named will not have power over the device, and behold! A new device will be assembled and be send out through the air [unreadable]. This device, seeding the hope that it that brings freedom as a beacon of light in a darkening world. For the new device was disguised as a black device, but the insides were bright. And the usurper stood powerless, while the angel Michael coordinated it all. God looked upon it, and saw it was good.

From the book of the Dragon, chapter 3:3

Thou shall stand for 10 hours, and then shall you feed. But then [unreadable] came, and made that 11 hours. But the world did not rejoice. For the device was not for this world, but for a few, as only a few were willing to pay the price. These few now could stand fast at the 11th hour.

From the book of the Dragon, chapter 1:8

Then God warned: A [EMP] storm is coming. Thou shall make a metal cage, such like are called Faraday cage, and put the device in there. For 40 hours thou shalt wait, if you fail to heed my command, the device will be destroyed. Some did not listen, and they used their device, and the earth [magnetic] shielding was weak, but the storm was strong, and their devices were destroyed. And these could not be repaired, for there were no [materials] available. So the disobedient ones fell on the ground and weeped, such was their pain.

From the book of the Dragon, chapter 12:1


...Then The king of the east prepared a golem, it looked like the device, but it was not the device. And the people of the earth liked this device. Then others came, until everybody had a device. Then the world plunged into darkness again....

From the book of the Dragon, chapter 11:9

 

[Caine]

: LOL, you know, 57 days, is like, 2 Months? (could be 60, if we use 1024)

Now that you mention it I think the prediction is a tad on the optimistic side though. It will probably take longer.

 

[iArnold]

Prices mentioned on the statistic would be nice.
But only 13 orders for 2GB. Looks like those are best cancelled ;-)

 

[levi]

But only 13 orders for 2GB. Looks like those are best cancelled ;-)

Oi!

 

[Hồng Thất Công]

Prices mentioned on the statistic would be nice.
But only 13 orders for 2GB. Looks like those are best cancelled ;-)

Why cancel those? They are still money to help Ed. What Ed can do is secretly upgrade those to the 4GB versions and don't tell nobody here or even to those who preordered those 13. Let them find out once they received their units.