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 Post subject: in the wake of a sale
PostPosted: Fri May 02, 2014 4:46 pm 

Joined: Mar 17, 2014
Posts: 17
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User avatarKaldor-Hicks & Co.
 
Have you ever wondered how your sales affect your market? Like what stats are affected, how large the effect is, and how long the effect of a sale lasts? That's what this post is about.

I should mention that Vaculus has already explored some of these questions in his retailing guide. (viewtopic.php?f=10&t=8995.) I just have a few points to add.

Also, fair warning--what follows is super nerdy. But I will not apologize.

In order to figure out how my sales affect the market, I did an experiment with digital watches in Abalesk. Essentially I dumped a tiny mountain of product on an empty market, just to see what would happen to the stats. Much like what Kim Jong Un does with his nukes when he's feeling frisky.

To be more precise, when I started the experiment on April 13, these were the critical market stats:

Saturation: 0
Daily sales: 0
Average qa: 0.01
Average price: 1357.43

Between the stat update on April 13, and the stat update on April 14, I sold 221,976 digital watches. I will call that 24-hour period "Day 0." The number I sold on Day 0 was exactly 4 times the SSC Threshold of 55,494. All of the watches I sold were qa 0, and I sold them for 0.01. I then recorded all the relevant stats for the next 18 days, ending with yesterday's stat update. I didn't sell any watches after April 14, and nor did anyone else (except Allmart of course).

The results were not entirely what I'd expected. These are the stats I'd like to talk about, particularly the first four columns after Day.

Image



Daily Sales TT

First of all, there are two stats in the game called Daily Sales, which is confusing because they don't mean the same thing. One of them is on the top ten list on the page with the pie graphs. I'll call that one Daily Sales TT. The other one is in the second column on the product detail listing page. That one I'll call Daily Sales PDL.

As you can see from the data, Daily Sales TT followed a pretty simple path. On Day 0, it was 0. On Day 1, it jumped to 31,710.8571, and remained there through Day 7. On Day 8, it jumped back to 0, and remained there for the duration. Here's a graph.


Image


One thing to note here is that the height of the plateau (31710.8571) is exactly one-seventh of the number of units I sold on Day 0 (221,976). In other words, Daily Sales TT was equal to my rolling seven-day average for the duration of the experiment. This is not particularly surprising, since it's well known that the rolling seven-day average plays a part in game mechanics.

There might be a practical lesson here though -- if you sell enough to make the top ten list, your name will probably be there for 7 days for everyone to see. And then it will disappear.


Daily Sales PDL

Of the two daily sales stats, Daily Sales PDL is more significant to game mechanics because it directly affects market saturation (a.k.a. market fullness or coverage). The formula is this: Saturation = Daily Sales PDL / SSC Threshold. And saturation, in turn, directly affects price, as the devs explained a while back. (viewtopic.php?f=8&t=5933)

So this is what Daily Sales PDL looks like:


Image


Right away you can see something weird here -- the stat increases substantially between Day 1 and Day 7. In other words, a sale you make today will have a greater effect 7 days from now than it will have tomorrow.

Also, the effect of a sale doesn't disappear in seven days -- it trails off over a surprisingly long period. Even after 18 days the stat has not returned to 0. Looks like it will get there in 4 or 5 days.

But even cooler than that is the formula for this curve. It's the following piecemeal function, where D equals the number of days since the sale, and UnitsSold is the number of units sold on Day 0:

If D <= 7, then

Image

If D >= 7 then

Image


So we have two interlocked exponential curves. All made out of 1's, 2's, and 7's. It's kind of...magical.

Also, the second half of the function implies that sales never truly disappear from the market. Each day after Day 7, Daily Sales PDL gets halfway closer to 0, never quite reaching it. For example, even if no one sells digital watches in Abalesk for the next year, Daily Sales PDL will be approximately 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000020442 this time next May, all because I sold some watches three weeks ago. By the same token, today's Daily Sales PDL stat reflects, in some small way, every sale that was ever made in the Abalesk digital watch market, going all the way back to the beginning of the game. It's the entire history of the market encapsulated in a single number. A living fossil.


Saturation

Saturation is the stat you can see inside a store when you do a price check. It's given as a percentage called % of target supply met. As I already mentioned, it equals Daily Sales PDL / SSC Threshold. And since SSC Threshold doesn't change very much on a day-to-day basis (see data above) , the saturation graph looks a lot like the Daily Sales PDL graph. The vertical axis is a percentage.

Image


Average Price

Finally, the thing we really care about, retail price. Here's the graph.


Image


You should recognize this -- it's the Daily Sales PDL / Saturation curve turned upside down. So a sale below average price will force down the average retail price, with the effect reaching its maximum 7 days after the sale. On Day 8, it will start to return to its original level.

Notice that the average price in the experiment never quite made it back to the original average price of 1357.43. And in fact it started declining a little bit around Day 14. But this is probably because the retail spending index in Abalesk dropped steadily over the course of the experiment (see data above), and not because of lingering effects of the sale. I strongly suspect that if the retail price index had remained constant, average price would have returned to its original level on the same day that Daily Sales PDL returned (or rather, will return) to its original level.

So that's it. If you made it this far, thanks for reading.

Kaldor

Scientific Entrepreneur
Member of Synergy


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PostPosted: Fri May 02, 2014 7:10 pm 

Joined: Apr 23, 2014
Posts: 360
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User avatarKvothe
Cleaning Up the Competition: 1st Place
This was a good read with my breakfast:)

_________________
I am known by many names and titles. If you ask the patrons in my bar, they shall tell you I am Kote. If you ask my student here, he will tell you I am Reshi. I have traveled the world and gathered such names as Maedre, Dulator, Shadicar, Lightfinger, Sixstring, Kvothe the Bloodless, Kvothe the Arcane, and Kvothe the kingslayer. All of them are true. All of them are hard earned.

Which name will you see?


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PostPosted: Fri May 02, 2014 9:36 pm 

Joined: Mar 25, 2013
Posts: 1019
Offline
User avatarHatuey Enterprise
 
Kaldor wrote:
Have you ever wondered how your sales affect your market? Like what stats are affected, how large the effect is, and how long the effect of a sale lasts? That's what this post is about.

I should mention that Vaculus has already explored some of these questions in his retailing guide. (viewtopic.php?f=10&t=8995.) I just have a few points to add.

Also, fair warning--what follows is super nerdy. But I will not apologize.

In order to figure out how my sales affect the market, I did an experiment with digital watches in Abalesk. Essentially I dumped a tiny mountain of product on an empty market, just to see what would happen to the stats. Much like what Kim Jong Un does with his nukes when he's feeling frisky.

To be more precise, when I started the experiment on April 13, these were the critical market stats:

Saturation: 0
Daily sales: 0
Average qa: 0.01
Average price: 1357.43

Between the stat update on April 13, and the stat update on April 14, I sold 221,976 digital watches. I will call that 24-hour period "Day 0." The number I sold on Day 0 was exactly 4 times the SSC Threshold of 55,494. All of the watches I sold were qa 0, and I sold them for 0.01. I then recorded all the relevant stats for the next 18 days, ending with yesterday's stat update. I didn't sell any watches after April 14, and nor did anyone else (except Allmart of course).

The results were not entirely what I'd expected. These are the stats I'd like to talk about, particularly the first four columns after Day.

Image



Daily Sales TT

First of all, there are two stats in the game called Daily Sales, which is confusing because they don't mean the same thing. One of them is on the top ten list on the page with the pie graphs. I'll call that one Daily Sales TT. The other one is in the second column on the product detail listing page. That one I'll call Daily Sales PDL.

As you can see from the data, Daily Sales TT followed a pretty simple path. On Day 0, it was 0. On Day 1, it jumped to 31,710.8571, and remained there through Day 7. On Day 8, it jumped back to 0, and remained there for the duration. Here's a graph.


Image


One thing to note here is that the height of the plateau (31710.8571) is exactly one-seventh of the number of units I sold on Day 0 (221,976). In other words, Daily Sales TT was equal to my rolling seven-day average for the duration of the experiment. This is not particularly surprising, since it's well known that the rolling seven-day average plays a part in game mechanics.

There might be a practical lesson here though -- if you sell enough to make the top ten list, your name will probably be there for 7 days for everyone to see. And then it will disappear.


Daily Sales PDL

Of the two daily sales stats, Daily Sales PDL is more significant to game mechanics because it directly affects market saturation (a.k.a. market fullness or coverage). The formula is this: Saturation = Daily Sales PDL / SSC Threshold. And saturation, in turn, directly affects price, as the devs explained a while back. (viewtopic.php?f=8&t=5933)

So this is what Daily Sales PDL looks like:


Image


Right away you can see something weird here -- the stat increases substantially between Day 1 and Day 7. In other words, a sale you make today will have a greater effect 7 days from now than it will have tomorrow.

Also, the effect of a sale doesn't disappear in seven days -- it trails off over a surprisingly long period. Even after 18 days the stat has not returned to 0. Looks like it will get there in 4 or 5 days.

But even cooler than that is the formula for this curve. It's the following piecemeal function, where D equals the number of days since the sale, and UnitsSold is the number of units sold on Day 0:

If D <= 7, then

Image

If D >= 7 then

Image


So we have two interlocked exponential curves. All made out of 1's, 2's, and 7's. It's kind of...magical.

Also, the second half of the function implies that sales never truly disappear from the market. Each day after Day 7, Daily Sales PDL gets halfway closer to 0, never quite reaching it. For example, even if no one sells digital watches in Abalesk for the next year, Daily Sales PDL will be approximately 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000020442 this time next May, all because I sold some watches three weeks ago. By the same token, today's Daily Sales PDL stat reflects, in some small way, every sale that was ever made in the Abalesk digital watch market, going all the way back to the beginning of the game. It's the entire history of the market encapsulated in a single number. A living fossil.


Saturation

Saturation is the stat you can see inside a store when you do a price check. It's given as a percentage called % of target supply met. As I already mentioned, it equals Daily Sales PDL / SSC Threshold. And since SSC Threshold doesn't change very much on a day-to-day basis (see data above) , the saturation graph looks a lot like the Daily Sales PDL graph. The vertical axis is a percentage.

Image


Average Price

Finally, the thing we really care about, retail price. Here's the graph.


Image


You should recognize this -- it's the Daily Sales PDL / Saturation curve turned upside down. So a sale below average price will force down the average retail price, with the effect reaching its maximum 7 days after the sale. On Day 8, it will start to return to its original level.

Notice that the average price in the experiment never quite made it back to the original average price of 1357.43. And in fact it started declining a little bit around Day 14. But this is probably because the retail spending index in Abalesk dropped steadily over the course of the experiment (see data above), and not because of lingering effects of the sale. I strongly suspect that if the retail price index had remained constant, average price would have returned to its original level on the same day that Daily Sales PDL returned (or rather, will return) to its original level.

So that's it. If you made it this far, thanks for reading.

Kaldor

Scientific Entrepreneur
Member of Synergy


Selling a lot of product for a little price = Retail spending decreases, Product average decreases, and Fullness increases.

Try the opposite and see your cash grow along with the city and the competition :grin: .

_________________
Just an old player passing by
[b]I was gone for years, but had too many good memories and felt compelled to check the game and its community once more.


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PostPosted: Sat Jun 21, 2014 5:30 pm 

Joined: Apr 5, 2014
Posts: 11
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User avatarTechnoTek
 
Amazing math!


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PostPosted: Wed Jun 25, 2014 3:28 pm 

Joined: Mar 5, 2011
Posts: 1017
Location: Vienna
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User avatarHulesch+Quenzel
Brainstormer
To make the math a bit more easy:
(Daily Sales PDL today) = (Daily Sales PDL yesterday) / 2 + (Daily Sales TT) / 2

And I am not sure what the Saturation should be for, as the average price is ((Your qty * your price)+(Allmarts qty *allmarts price)) / (Your qty + allmarts qty)

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For the Snark was a Boojum, you see.
(Lewis Carroll)


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PostPosted: Sun Jun 29, 2014 3:54 pm 

Joined: Jun 29, 2014
Posts: 1
Location: OHIO
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User avatarM&B INC.
ooo yeah?


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