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The Economics Behind the Pokeballs


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Introduction

 

I'm comming to this post to tell something i realised yesterday. I thinked "Maybe we pay too much for ultraballs". So i go to bulbapedia to see the capture mechanics in this game.

 

The third generation (Fire Red and Emerald) have a simple system of catch, based on three formulas. The calculus will be omited because I think nobody will like it (and i cant add gif's and png's at this forum).

 

Introduced these concepts (if you wanted to read) we will try simplificate this f*ck. To do you need have in mind this results are rounded.

 

The major simplification when i had is an adiction of one in the numbers like 2^k-1.

 

Now we will assume initials values for the variables, before do that  we will consider an hard capture pokemon (the lower catch rate in this game is 3).

 

First case: At the first case we will use to think in a poke sleeping with one point left on HP. Well, in this case the value of "a" will be, rounding, 6 times the ball value, and "b" will be 2^14 times the fouth root of a.

 

Second case:  For this case the poke have full HP and no status. Well, in this case the value of "a" will be same then the ball value, and "b" will be 2^14 times the fouth root of "ball".

 

The Probability of each shake

 

To find the probability we will find the how much possibles values of s our b beats. For this we have to divide b for maximum of s, 2^16. Probability will be the fouth root of a divided for 4

 

Test of Pokeballs

 

I will test the efectiveness of 4 kinds of pokeballs, the normal, great, ultra and repeat. They have 1x, 1.5x, 2x and 3x of efectiveness, respectively. The founded Value is for the first shake of the ball.

 

First Test: The probability for first shake will be:

 

Pokeball: p=39,13%

Greatball: p=43,3%

Ultraball: p=46,53%

Repeatball: p=51,49%

 

Second Test: The probability for first shake will be:

 

Pokeball: p=25%

Greatball: p=27,67%

Ultraball: p=29,73%

Repeatball: p=32,9%

 

Probability for capture: For capture we will need four shakes, the formula will be "a" divided for 4^4

 

First Test: The probability for capture will be:

 

Pokeball: p=2,34%

Greatball: p=3,51%

Ultraball: p=4,69%

Repeatball: p=7%

 

Second Test: The probability for capture will be:

 

Pokeball: p=0,39%

Greatball: p=0,59%

Ultraball: p=0,78%

Repeatball: p=1,17%

 

How many pokeballs we have to use for 90% of capture chance?

 

First Test:

 

Pokeball: 97 balls

Greatball: 65 balls

Ultraball:  48 balls

Repeatball: 32 balls

 

Second Test:

 

Pokeball: 588 balls

Greatball: 391 balls 

Ultraball: 294 balls

Repeatball: 195 balls

 

Final test: Capture Rate if You use same money for Pokeball and Other ball

 

Pokeball costs 200 pokeyens, Greatball 600, ultraball 1200 e repeatball 1500.

 

Greatball: In cash one greatball costs for three pokeballs.

 

First Case: 

  • Greatball have 3,51% of capture rate.
  • Three Pokeballs have 6,85%

Second Case:

  • Greatball have 0,59% of capture rate
  • Three Pokeballs have 1,16%

Ultraball: In cash one ultraball costs for six pokeballs.

 

First Case: 

  • Ultraball have 4,69% of capture rate.
  • Six Pokeballs have 13,24%

Second Case:

  • Ultraball have 0,78% of capture rate
  • Six Pokeballs have 2,31%

Repeatball: In cash one repeatball costs for seven and a half pokeballs.

 

First Case: 

  • Repeatball have 7% of capture rate.
  • Seven and a half Pokeballs have 16.27%

Second Case:

  • Repeatball have 1,17% of capture rate
  • Seven and a half Pokeballs have 2,88%

 

Conclusion: Even on the hardest case, Buy Pokeballs

Edited by TSReis
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Factor Time Vs Money

 

One Greatball costs 6 times one pokeball. When we calculate, for the probability for each ball, if x is greatball and y pokeball we can say, in time, x is 1,5 more efficient then y, but in money y is 3 times more efficient then x. So y is, approx, 2 times better then x.

 

One Ultraball costs 6 times one pokeball. When we calculate, for the probability for each ball, if x is ultraball and y pokeball we can say x is 2 more efficient then y, but (for money) we have y=6x, therefore, y is approx 3 times better then y...

 

Equal the anothers for repeatball y is 2.5 better then pokeball. (It's the only one is really worse).

Edited by TSReis
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Factor Time Vs Money

One Greatball costs 6 times one pokeball. When we calculate, for the probability for each ball, if x is greatball and y pokeball we can say, in time, x is 1,5 more efficient then y, but in money y is 3 times more efficient then x. So y is, approx, 2 times better then x.


One Ultraball costs 6 times one pokeball. When we calculate, for the probability for each ball, if x is ultraball and y pokeball we can say x is 2 more efficient then y, but (for money) we have y=6x, therefore, y is approx 3 times better then y...


Equal the anothers for repeatball y is 2.5 better then pokeball. (It's the only one is really worse).

The calculation you did doesn't factor in the value of the Pokemon. In order to maximize profits, one must catch Pokemon as fast as they can. As the value of the Pokemon that are being caught increases, the time that is spent trying to catch them becomes worth more. Certain rare Pokemon like Eevee, Bulbasaur, Charmander, etc go for 10-20k on the GTL with bad IVs, at the time of this post. Say that they are going for 20k for example. If I can catch them in one throw with an ultraball but two with a pokeball, I'm going to be making more money per hour by using ultra balls. And to put it simply mathematically, assuming catching a Pokemon worth 20k is 1x as fast with a pokeball, and 2x as fast with an ultraball (which I have observed is the case with Bulbasaur). If I use a pokeball I'll get (20,000-400)x1=19,600 units of money per unit of time, while if I use an ultraball I'll get (20,000-1,200)x2=37,600 units of money per unit of time. This example clearly proves that the ultraball, in certain cases, can yield more money per unit of time/hour than the pokeball when catching Pokemon. This is assuming that it takes 2 pokeballs per catch on average and one ultraball per catch on average, respectively. It also assumes that the unit of time=1, and that the value of the Pokemon is 20,000 units of money. Edited by Frublet
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I agree with you in almost your points. But you have to increase at you thought the necessary time for appear one of them... I didn't think completely about your point, its true, but you already spend so much time for find one of them.

But, in farming itens, the best shot is capture all.

 

So depends of how much time you can spend on that and the benefits rate...

 

Thank you

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Ok, but there's a catch(pun of the year).

Regarding two examples ultra balls seem superior

1)Loe-catch rate pokemons, mainly legendaries. Burning lots of turns in wasted pokéballs will eventually result in those guyz, depending of the moveset, either 1v6 your team or kill itself via struggle (even with sleeps, it might slowly but surely happen)

2) Catching a runaway pokemon (Like delibirds and heracrosses on gen II or roaming legendaries) If you don't feel like wasting your master ball here, time saving becomes WAY more important than money saving, so you want to maximize your rates of catching... or you get a arena trapper or another cheese to keep it on field. In the latter, it might become an "1)" case from there

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