Determining IVs without use of IV Battles or IV Calculators.

[Princess Emily]

OK guys, I guess some of us really wanted to know if the IVs of a particular stat of our Pokemon is really at MAX, or 31.
Because as we all know, the IVs, or Individual Values of a Pokemon, really do make a difference, in addition to EVs or Effort Values.

Sometimes many of us only have to rely on the slow and unsteady IV Battle as the only way to accurately determine the IVs.

But there are ways to determine manually and accurately if the IV of a stat is really 31 or not, especially if your Pokemon are the products of breeding. One way is through manual computation, using the given formula to determine the stat value, given the IVs, Level, and EVs, and using Rare Candies and Vitamins.
I guess all of us are familiar to this formula:

Stat Value = {[(Base Stat*2+IV+EV/4)*Level/100]+5}*Nature

Nature is the value of either 0.9 or 1.1 if the nature of your Pokemon hinder or boost the particular stat of your Pokemon, respectively. It is just 1 if that nature do nothing to that stat.


For example, I'll consider Gible

, the one I've been breeding months ago, and I want to find out if its Attack and Speed IVs are both at MAX.
Gible's Base Attack is 70, while its Base Speed is 42.

1.) Let's consider its Attack, which has a base value of 70.
I'll use one segment of the formula which is (Base Stat*2+IV+EV/4) to start computing for it...
And assume the IV is 31, and 30 on the other.
70*2+31 = 171 (31 IVs)
70*2+30 = 170 (30 IVs)

And I'll give the hatched Gible only 3 Proteins...
70*2+31+3*10/4 = 171+30/4 = 171+7.5 = 171+7 = 178 (31 IV)
70*2+30+3*10/4 = 177 (30 IV)

Using the next part of the formula, the difference will show up at level 9...
178*9/100 = 16.02 = 16 (31 IV)
177*9/100 = 15.93 = 15 (30 IV)

Using the final part of the formula...
16+5=21
15+5=20

So if your Gible has a nature neutral to Attack, then it must have an Attack stat of 21, after feeding it only 3 Proteins and leveling it up to Level 9, in order for it to have 31 Attack IVs. If it's not 21, then it certainly is not 31 IV.

BTW if its Adamant then it must have an Attack stat of 23 at Level 9 and 3 Protein feedings.
21*1.1 = 23.1 = 23

2.) For the Speed, with a base stat of 42...

42*2+31 = 115 (31 IVs)
42*2+30 = 114 (30 IVs)

Using my math skills, the difference will show up at level 7, without feeding it some Carbos.

115*7/100 = 8.05 = 8 (31 IVs)
114*7/100 = 7.98 = 7 (30 IVs)

Then add 5, according to the formula...
8+5 = 13 (31 IVs)
7+5 = 12 (30 IVs)

If you level up your Gible (don't feed any Carbos) to level 7, it must have a Speed stat of 13 if the nature is speed-neutral or 14 if speed-beneficial...for it to have 31 IV.
13*1.1 = 14.3 = 14

I guess this is my way of doing it, and it's not just on one Pokemon.
I can do lots of computations, each for different Pokemon, but because I'm a bit busy in school then I can only post a little for the meantime.

By the way, there are times where we need 30 IVs instead of 31, especially for the purposes of Hidden Power.
All you need to do is to determine if the IV is at least 30, then make sure it's NOT 31.

Actually it's more on the base stat that I'll consider, because there are 2 different Pokemon with the same base stat for the same stat...such as Pinsir and Heracross having 85 in Speed and 125 in Attack. And I also try to find the fastest way of doing the computations...

For example, it would be tedious if I'll level up the said Gible to level 17 just to determine if its Attack IV is 31.

70*2+31 = 171
171*17/100 = 29.07 = 29
29+5=34
34 if Jolly, 37 (34*1.1 = 37.4 = 37) if Adamant, etc...

That's why I also use vitamins to help me with the computing and to cut down item usage (in this case it's 11 {8 from using Rare Candies to level up to level 9 and 3 from feeding Proteins}, instead of 16 {leveling up to level 17})

Hopefully I could make more links for this one in the future for different Pokemon/Base Stats, if possible. And I'll probably add detailed tables and/or charts for each Pokemon, including Uber or non-Uber legends, considering each of its IVs, etc...

 

[swampie]

This project is quite interesting. But it's only necessary when you want to know the value of a stat lower then 31. If the stat is 31 you could better talk to the IV guy in Emerald.

 

[mingot]

... or the IV guy in Platinum, for that matter.

This is interesting, though.

 

[Xia]

I'm just going through and picking out all the instances where numbers should be spelled out and some small grammar things (it's just habitual by this time ;]).

OK guys, I guess some of us really wanted to know if the IVs of a particular stat of our Pokemon is really at MAX, or 31.
Because as we all know, the IVs, or Individual Values of a Pokemon, really do make a difference, in addition to EVs or Effort Values.

Sometimes many of us only have to rely on the slow and unsteady IV Battle as the only way to accurately determine the IVs.

But there are ways to determine manually and accurately if the IV of a stat is really 31 or not, especially if your Pokemon are the products of breeding. One way is through manual computation, using the given formula to determine the stat value, given the IVs, Level, and EVs, and using Rare Candies and Vitamins.
I guess all of us are familiar to this formula:

Stat Value = {[(Base Stat*2+IV+EV/4)*Level/100]+5}*Nature

Nature is the value of either 0.9 or 1.1 if the nature of your Pokemon hinder or boost the particular stat of your Pokemon, respectively. It is just 1 if that nature do nothing to that stat.


For example, I'll consider Gible

, the one I've been breeding months ago, and I want to find out if its Attack and Speed IVs are both at MAX.
Gible's Base Attack is 70, while its Base Speed is 42.

1.) Let's consider its Attack, which has a base value of 70.
I'll use one segment of the formula which is (Base Stat*2+IV+EV/4) to start computing for it...
And assume the IV is 31, and 30 on the other.
70*2+31 = 171 (31 IVs)
70*2+30 = 170 (30 IVs)

And I'll give the hatched Gible only three Proteins...
70*2+31+3*10/4 = 171+30/4 = 171+7.5 = 171+7 = 178 (31 IV)
70*2+30+3*10/4 = 177 (30 IV)

Using the next part of the formula, the difference will show up at level 9...
178*9/100 = 16.02 = 16 (31 IV)
177*9/100 = 15.93 = 15 (30 IV)

Using the final part of the formula...
16+5=21
15+5=20

So if your Gible has a nature neutral to Attack, then it must have an Attack stat of 21, after feeding it only three Proteins and leveling it up to Level 9, in order for it to have 31 Attack IVs. If it's not 21, then it certainly is not 31 IV.

By the way, if it's Adamant then it must have an Attack stat of 23 at Level 9 and 3 Protein feedings.
21*1.1 = 23.1 = 23

2.) For the Speed, with a Base Stat of 42...

42*2+31 = 115 (31 IVs)
42*2+30 = 114 (30 IVs)

Using my math skills, the difference will show up at level 7, without feeding it some Carbos.

115*7/100 = 8.05 = 8 (31 IVs)
114*7/100 = 7.98 = 7 (30 IVs)

Then add five, according to the formula...
8+5 = 13 (31 IVs)
7+5 = 12 (30 IVs)

If you level up your Gible (don't feed any Carbos) to level 7, it must have a Speed stat of 13 if the nature is Speed-neutral or 14 if Speed-beneficial...for it to have 31 IV.
13*1.1 = 14.3 = 14

I guess this is my way of doing it, and it's not just on one Pokemon.
I can do lots of computations, each for different Pokemon, but because I'm a bit busy in school then I can only post a little for the meantime.

By the way, there are times where we need 30 IVs instead of 31, especially for the purposes of Hidden Power.
All you need to do is to determine if the IV is at least 30, then make sure it's NOT 31.

Actually it's more on the base stat that I'll consider, because there are two different Pokemon with the same Base Stat for the same stat, such as Pinsir and Heracross, having 85 in Speed and 125 in Attack. And I also try to find the fastest way of doing the computations...

For example, it would be tedious if I'll level up the said Gible to level 17 just to determine if its Attack IV is 31.

70*2+31 = 171
171*17/100 = 29.07 = 29
29+5=34
34 if Jolly, 37 (34*1.1 = 37.4 = 37) if Adamant, etc...

That's why I also use vitamins to help me with the computing and to cut down item usage (in this case it's 11 {eight from using Rare Candies to level up to level 9 and three from feeding Proteins}, instead of 16 {leveling up to level 17})

Hopefully I could make more links for this one in the future for different Pokemon/Base Stats, if possible. And I'll probably add detailed tables and/or charts for each Pokemon, including Uber or non-Uber legends, considering each of its IVs, etc...

And it may not be universal, but I was always taught that you had to use the term before using the abbreviation.

To determine your Individual Values (IVs), you have to take into consideration your Effort Values (EVs).

Unless other people back me/you up, though, it's your call as to how you introduce the abbreviation.

 

[Princess Emily]

Actually I can be a tutor for you guys to calculate IVs, whether if its 31, 30, or something below it.

But it does need a lot of mental calculations...
Especially memorizing the patterns of fractions, decimals, and how many numbers they repeat...

Example, any integer divided by 7 except those divisible by 7 itself always gives a decimal with the pattern 142857 and back...
(you should confirm this on your calculator)
sub-example: 11/7 = 1.571428571428...

Such as what I've written on my first post above, 42*2+31 = 115 (42 being Gible's Base Speed)
And that the last 2 digits of the answer (which is 15) is exactly one more than one of the 2 consecutive numbers from the decimal pattern of dividing 7 (given above, the 14 from 142857...)

And like what I've written above...
42*2+30=114
42*2+31=115
114*7/100=7.98=7
115*7/100=8.05=8
7+5=12
8+5=13

And if the Speed stat of Gible (if speed-neutral nature) is 13 at level 7 then the minimum IV is 31 (but there's nothing bigger than 31 IV, so the IV is exactly 31)
If it's 12, then it doesn't mean the minimum IV is 30, but 16
(12-5=7, 7*100/7=100, 100-[42*2]=16)

Second example:
Beldum has 30 Base Speed

Dividing by 11 (except those divisible by it) always gives decimal patterns of:
09090909...
18181818...
27272727...
36363636...
45454545...

And Beldum's Base speed stat*2+31=91
And 91, the last 2 digit (nothing else) is exactly one more than 90, one of the segment from the decimal patterns of dividing 11 (090909...)

And using the formula, Beldum's Speed stat must be 15 (speed-neutral nature) if levelled up to level 11 to have 31 Speed IVs...

Forgive me of giving examples of assuming IVs to be 31...
But I already know about the IV men from Emerald/Platinum...
Although there might be times where they kept on repeating on the same stat (especially 3 or more 31 IVs)

I'll post soon about the patterns of dividing by certain integers (might be limited up to 20 or 25)...

 

[Objection]

... or the IV guy in Platinum, for that matter.

Speaking of which, is there a list of the things that he says and what they mean in terms of IVs? I know there's one for the guy in Emerald.

 

[Solefuge]

WARNING: Algebra ahead. Skip to the end, once its finished, if you are innumerate.
(And for the numerate, I apologize for the messy notation and logic I use. This was pretty much written as I thought of it, feel free to notify me of extraneous steps and the like so I can remove or correct them.)

It seems the basic problem (in the sense of 'question', not in the sense of 'hindrance') is to, for any base stat, find the lowest possible number of items that are needed to determine any IV, with highest priority given to 30, 31, and 0 (for gyro ball users, etc.). Looking at the formula...

Stat Value = {[(Base Stat*2+IV+EV/4)*Level/100]+5}*Nature

we are given Base Stat and Nature (henceforth abbreviated as B and N) and we control Level and EV (L and E). To make things simpler, lets call V the number of vitamins fed to the pokemon, and say E = 10*V (also, lets call R the number of rare candies used, though I doubt we'll see it for awhile). To check if we have some particular IV (call it I), we want to find some combination of L and V such that:

1. ((B*2 + (I - 1) + 10*V/4)*L/100+5)*N < ((B*2 + I + 10*V/4)*L/100+5)*N < ((B*2 + (I + 1) + 10*V/4)*L/100+5)*N, removing the last conditional if I = 31 and the first if I = 0, and
2. R + V is as low as possible.

Now, since we don't get a fractional value for a stat but instead have it rounded down, we need to be more specific with our first condition:

[((B*2 + (I - 1) + 10*V/4)*L/100+5)*N] + 1 = [((B*2 + I + 10*V/4)*L/100+5)*N] = [((B*2 + (I + 1) + 10*V/4)*L/100+5)*N] - 1

(Note; I am pretending that [ ] means 'floor', or 'round down')

Anything with floors in it is a real pain to simplify, but there are still a few things we can figure out. For a start, I'm just going to simplify this thing into a bunch of polynomials:

[((B*2 + I + 10*V/4)*L/100+5)*N] =
[5*N + L*N*(B*2 + I + 10*V/4)/100] =
[5*N + L*N*B/50 + L*N*I/100 + L*N*V/40]

now, considering just the case where N is one, some things can be easily pulled out of this hideous thing:

(Case N=1): [5*N + L*N*B/50 + L*N*I/100 + L*N*V/40] =
[5 + L*B/50 + L*I/100 + L*V/40] =
5 + [L*B/50 + L*I/100 + L*V/40]

so we can now reduce the earlier equation, somewhat:
[L*B/50 + L*(I - 1)/100 + L*V/40] + 1 = [L*B/50 + L*I/100 + L*V/40] = [L*B/50 + L*(I + 1)/100 + L*V/40] - 1

This still isn't a big help; but we do know a few more useful things to lower the possibilities further: first off, we can consider the last term to be unimportant until proven otherwise, as we have complete control over L and V and 40 always equals 40. So calling it 0 for the time being, we see that:

Stat - 5 = L*B/50 + I*L/100

and (pretending '{}' means truncate) that the fractional part of Stat is:

{Stat} = {L*(B*.02 + I*.01)} = {L*((2*B + I)*.01)}

and adding one vitamin is an effective stat increase of:

L*1/40 = .025*L

Now what we want to find is a low L such that, for our I, there exists some V less than or equal to ten for which:

{L*((2*B + I)*.01)} + .025*V*L > 1
and
{L*((2*B + I - 1)*.01)} + .025*V*L < 1

Calling (2*B + I) X for the moment, for simplicity's sake, the relevant quantities are

{{L*X*.01} + .025*V*L}

and

{{L*.01*(X - 1)} + .025*V*L}

We see that
{L*X*.01} + .025*V*L must be greater than one and
{L*.01*(X - 1)} + .025*V*L less than one.
setting up an inequality:

{L*X*.01} + .025*V*L > 1 > {L*.01*(X - 1)} + .025*V*L

{L*X*.01} > 1 - .025*V*L > {L*.01*(X - 1)}

Now, we also have control over L, and its time to exercise it. Now, we will finally use R for something.
Each increase in R effectively increases L by one, increasing the stat by B/50 + I*/100 or X/100.
Remember, we know what X is (the IV we are checking times plus twice the base stat) and so we know what this increase is, even though we don't know it; we also know L, the level we are starting this whole thing at, so the real 'unknowns' here are V and R, both of which we have control over.
The complete inequality is:

{L*X*.01} > 1 - .025*V*L - R*X/100 > {L*.01*(X - 1)}

where each of the right and left sides is a known quantity and the middle is an unknown containing V and R. 'Simplifying' it further (the simplification is only apparent if you use real numbers instead of variables):

100 - 100{L*X*.01} < (2.5*L)*V + (X)*R < 100 - 100{L*.01*(X - 1)}

you now have a simple first order inequality set of the form:

A < B*V + C*R
B*V + C*R < D
V > -1
V < 11
R > -1
R < 101 - L

where values of A, B, C, D are assigned as 100 - 100{L*X*.01}, (2.5*L), (X), and 100 - 100{L*.01*(X - 1)}.
You can simplify this further by saying

V > A/B - C*R/B
V < D/B - C*R/B

and graph this to find what integer combinations of V and R are available. It's hard to explain how to do this without a graph, so I'll try to get one up here as soon as I can. Unfortunately, this is almost impossible to figure out in the general case; you have to actually plug in numbers to get any real answers (namely B I and L). I will give an example of the most common case (for me) below: L = 1 and I = 31.
Plugging these numbers in gives us:

X = (2B - 31)
V > (100 - 100{1*(2B - 31)*.01})/(2.5*1) - (2B - 31)*R/(2.5*1)
V > 40 - 40{.02*B - .31} - (.8*B - 12.4)*R
V < 40 - 40{.02*B - .30} - (.8*B - 12.4)*R

{.02*B - .30} and {.02*B - .31}, unless B is less than .15, are both positive, and depending on how big B is they are either equal to:

(B < 65): .02*B - .30 and .02*B - .31
(64 < B < 130): .02*B - 1.30 and .02*B - 1.31
(129 < B < 185): .02*B - 2.30 and .02*B - 2.31

(note: I may have slightly messed up these numbers. If you notice that I did, please tell me so I can fix it.)

Lets pretend for example that the base stat is Gible's attack, in the first example, so we have the second case.

V > 40 - 40{.02*70 - .31} - (.8*70 - 12.4)*R
V < 40 - 40{.02*70 - .30} - (.8*70 - 12.4)*R

V > 40 - 40{1.09} - (52.6)*R
V < 40 - 40{1.1} - (43.6)*R

V > 40 - 40*.09 - (52.6)*R
V < 40 - 40*1.1 - (43.6)*R

V > 4 - (52.6)*R
V < -4 - (43.6)*R

unfortunately, this seems to result in only negative Vs, so long as R is positive. I will try to find the error in my calculations and correct it.