Money formula on wild PKM

Kaminokage

Posted October 30, 2018

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Posted October 30, 2018 (edited)

SUMMARY

I. Introduction
II. How did i find and test this formula?
III. Money formula
IV. Money by level
V. Raw data
VI. References

I. Introduction

Hello PRO Community,

Since i started PRO, i notice it's possible to make a lot of money by killing wild PKM, but until now i didn't search what was the exact formula for money. After all, players don't really know if the money earned depends of the level of PKM, the areas, the evolved PKM, the IVs of the PKM, or any others you can imagine. So, i decided to look for it, to know what is the exact formula. Why? Because with the formula, we can make better decisions; know where to farm money, how much money we gain by killing PKM, know if there are some tricks, etc.

For real, after killing 1k PKM in different areas, i just look the data and it took me 3 minutes to imagine what was the possible formula, the rest of my time was used to test this theoretical formula. So, i think, just nobody before me tried to find it xD

In the begin of this guide, i will explain my theoretical formula, how i found it, and how i tested it. With that, you can criticize this theoretical formula, all the raw data are in the end of this post. If you don't care about it, just pass to the next part. (i tried to make easy and fast, so you can read it without knowledge in math, all is basic)

Warning: All you will read in that guide is just a theoretical formula, nothing official. Maybe, i didn't find all we have to know about it. You will see there is a random part in that formula, i have no idea how this random part is generated; maybe it depends of the IVs of the PKM, but in that case i can't test it, since i need to kill the PKM to see the money and i need to catch the PKM to see the IVs xD

This theoretical formula works very well with the data i found, maybe InGame it's not the exact same formula, or the formula is not the same at all but acts exactly the same.

II. How did i find and test this formula?

My first idea was the money earned depends of the PKM level, but not sure about it, i have to also try if it depends of the area or not.

A good area to check money earned is Cerulean Cave, the levels of the PKM are pretty huge, so the number will be less impacted by a rounded part in the formula.

Let's look what i find there :

In this data, we see the type of farming seems to not affect the money: Land and Surf give exactly the same range of amount for money. The type of PKM seems to not affect this range too, i got some Golbat with 6 pokedollars, some Golbat with 600, some Psyduck with 6, some Psyduck with 600, etc. It's a good point, make easier to find the formula. We see the range is not exactly the same depending of the level of the PKM, the max pokedollars with lv 60 is 600, max with 61 is 610, max with 62 is 620 and max with 63 is 630 (but the minimum is exactly the same: 6). So the money seems very correlated with the level. Until now, i don't know if it's linked to the area or not.

You might notice something very weird: in Cerulean Cave 1F, on the Bot Reborn we can see the level range is 60-64, but i got 0 PKM lv 64. It's normal, as i explained in that topic: https://pokemonrevolution.net/forum/topic/109273-url , the last level in a level range never spawn.

Edit : The bug of last level have been corrected since.

I admit here, the correlation with the level is not very impressive, so just to see it, here are my data in Resort Area :

Come back to Cerulean Cave, all my data are even number, it's normal, i didn't say it before but i farmed with MS, the MS bonus on money is +100% making double all the amount i find.

But something on Cerulean Cave give me a very good clue for the formula. Let's look the amount of money i found for level 60 (Land and Surf):

All this numbers are multiples of 6; the minimum is 6 and the max is 600, and all multiples of 6 are in that range. And from 6 to 600, there are a total of 100 multiples of 6. So i imagined first this formula:

Quote
Money earned= r * lvl / 20 * ms

r = random whole number generated between 1 and 100 (included)
lvl = level of the wild PKM
ms = 2 if membership is active; 1 otherwise

Because 6 is 60 divided by 10, so in the formula i have to divide 60 by 10. But there is the MS part making double money, without MS, it would be between 3 to 300, or 60 / 3 = 20. So it's lvl / 20 * 2 (for ms). And the random number between 1 to 100 to have the 100 different values.

This formula works well for lv 60-61-62-63 if i round the final result.

But, until now, i didn't test in others areas, and didn't check with others level. I know in advance, my formula is not over at all, but i feel it's a good start.

Let's check in Dragons Shrine, the level range is exactly the same, just for checking if the money range is the same :

I find exactly the same number than Cerulean Cave, it seems to not be linked to the area (still not sure), but my formula here seems to works. But i need to test with others level.

As i was lazy to move a lot, i started to collect data in Dragons Den:

As i expected, seems again correlated to level, good point, and the area seems to not affect the money. But let's try the formula with just one PKM:

I took the minimum value, so i can say "r" should be 1 in the formula.

Money earned= r * lvl / 20 * ms

Money earned= 1 * 51 / 20 * 2

Money earned= 5,1

Even with a round down, i should expect to find 5 pokedollars, but i found 4. It means there is a round down before the MS.

Money earned= ⌊ r * lvl / 20 ⌋ * ms

Money earned= ⌊ 1 * 51 / 20 ⌋ * 2

Money earned= ⌊ 2,55 ⌋ * 2

Money earned= 2 * 2

Money earned= 4

It's a good start this round down, but nothing sure about it. So i looked with all the data i got in this area (and the previous area), and it seems to work.

I had a very good feeling about it at this point. So let's go for this formula:

And look what would be the amount of money for all r and all level:

Yes i know, it burns eyes. But something funny appears. We notice for some level, the distribution of each amount of money is not exactly the same if this formula is correct. And specially with low level like 1-2-3, we can even test in practice this distribution :

It means, for example, for level 1, the amount of money i will find will be 0, 2, 4, 6, 8 or 10; the amount 10 will appear way less than the others amounts. Sadly, there is no area to farm easily some PKM lv 1. But, i found a nice area: Route 101 with only PKM lv 2 and 3. If there is a difference in the distribution, i should find it.

Let's see my data :

As expected by my formula, the distribution is not an equal-distribution for all amount of money, for lv 2 the amount 20 appears less than others, same for lv 3 and the amount 30. My sample seems low, but it's enough to notice it's not an equal-distribution.

At this point, i am pretty confident on my formula, if it's able to predict this distribution of amounts and the amounts, it seems pretty correct.

I did just an other test for my own fun, for lv 19, it's possible to find 0 pokedollar. For this, i went to Ice Path B1F, with only PKM lv 18 and 19.

After 152 PKM lv 18-19 killed, i finally found it:

Nice, as i expected a lv 19 giving 0 pokedollar. I was happy to find it :3

But it's not enough yet, my data don't take all possible level, and for distribution of level i don't have a lot of data to check. I started looking for an area with high level PKM, and i discovered Resort Area:

An area with PKM lv 1 to lv 100 :o

In fact, like i said before, the last level in a level range seems to never spawn, so i will not find PKM lv 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100. But it's still a very good area to test my formula.

As i posted before, here are my results:

We see very well here the link between money and level. A good test for my theoretical formula is : the formula is supposed to predict some specifics amounts of money i am supposed to earn. If i find just ONE amount different from what my formula predict, it means my formula is not correct.

So let's see:

Yes i like burning eyes :3

On 5000 magikarp killed, all the amounts of money i found are all in the list of amounts i am supposed to find with the formula. Just one would be enough to say the formula is not correct!

So, i know my formula is able to predict the min value, the max value and all the values inside. Now, i will look how to check if it's able to predict the distribution. A good way is look the average money i am supposed to find.

Since i have a theoretical distribution of level, i am able to calculate an theoretical average by level, and in the end a global average:

With this theoretical global average, i am supposed to find in average 251,62 pokedollars per PKM in this area.

Let's look what i really found:

Hum... 251 to 221, it's a huge gap. I missed something.

And this thing is this "bug" : https://pokemonrevolution.net/forum/topic/110291-url

To resume : the distribution of level is not an equal-distribution, the lower level spawn more than the others.

So, my global average can't be correct if i don't take into account the distribution of level. I don't have the exact percentage for the distribution. So, i decided to use the number of PKM by level i got to calculate my global average :

With this global weighted average theoretical, i am supposed to find 220,09 pokedollars per PKM. In my data, i find 221,03; very close :)

It means my formula is able to predict the average money, so the distribution of amounts of money.

Let's check in others data the average too, i will use only Cerulean Cave and Dragons Shrine, because it's there i got the most data. And also, because both areas are lv 60-63 so i can add the data to each others because the area doesn't matter (i deleted the Kadabra, because it's not the same level and i don't have a lot of data).

So, i am supposed to find 309,27 pokedollars per PKM; and i find in practice 309,07.

In final, i pretty confident about this formula, be able to predict all the amounts possible, the distribution of this amounts, the average money in areas, the average money by level, the min value, the max value. I think i got the right formula.

But, like i said in the introduction, i don't know how the random number is generated, and i don't know if it's coded like this formula. In practice, whatever the real formula or how it's coded, my theoretical formula acts exactly the same.

III. Money formula

IV. Money by level

With MS

Without MS

If you want to use this average, don't forget: the distribution for level is not an equal-distribution, so the best area for farming can not be the one you expect ;) And the last level in a level range seems to never spawn.

V. Raw data

Cerulean Cave 1F Land

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