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2.4.1 - Influencing Individual Values
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In this section, we are going to cover all the possible things you can do to
improve your Pokémon's "Individual Values". This section is probably the
most rewarding as the difference between good and poor IVs can often mean
the difference between 0 and 31 free points in each of your statistics (at
Level 100) totalling a potential bonus of 186 stat points.
One of the problems with the game is that it doesn't tell you the IVs for
any particular Pokémon on the Summary screen, so at low levels it's very
difficult to discern if you received a quality Pokémon or not. Let's look
at 4 attempts to capture a quality Zigzagoon. All of these Pokémon were
Lv.3, so the only attribute that could haved possibly affected the
variation in stats would have been the Individual Values.
Attempt #: A1 A2 A3 A4
HP : 15 15 15 15
Attack : 7 6 7 7
Defense : 7 7 7 7
Sp. Attack : 6 7 7 7
Sp. Defense : 8 8 7 7
Speed : 8 8 9 8
----------------------------------
Total: : 51 51 52 51
As you can see, each of these captures yielded different stats and it appears
that attempt #3 was the best, but that doesn't tell us the entire story.
Since we are working with integers and not real numbers, it's not possible to
know if A1, A3 or A4 have the best IV for their Attack statistic due to the
problems with rounding integers (this means that the game will always round
down rather than use the .5 rule that you were taught in school). The only
real way to find out which value is truly better is to raise them all up a
few levels so we can see a larger difference between them. I did just that
and made them all level 12 (However, the more you level them up, the more
accurate values you will receive). Here is the chart:
Attempt #: A1 A2 A3 A4
HP : 32 33 33 32
Attack : 15 12 16 14
Defense : 14 16 15 15
Sp. Attack : 12 13 15 14
Sp. Defense : 17 17 16 15
Speed : 19 20 21 19
-----------------------------------
Total: : 109 111 116 109
Note: In order to save a great amount of time in this area, always keep
around 8-10 Rare Candies in your Bag. Whenever you need to check the
IVs for a newly aquired Pokémon, save your game, use the Rare Candies
to level-up the Pokémon to level 13-15 and then make the calculations.
Once you have the IVs, you can then reset your Gameboy Advance and
either decide to keep the Pokémon or try again. The real advantage to
this is that you will not gain any Effort Values while you level-up so
it makes the calculations as accurate as possible.
Now that they are all Lv.12 (using Gameshark, so it was impossible for
Effort Points to objectively affect the results), we can see that A3
continues to out-shine the others - it just has better genes. The second
thing we notice is that A1 is clearly better than A2 or A4. This was not so
obvious when observing the previous table since many of the stats had the
same values.
Now, you could be saying to yourself that a difference of 7 points isn't
much and you'd be correct in questioning it - I agree with you. I think
catching 5+ instances of the same species is probably a waste of time, let
alone a waste of money on the mass consumption of Pokéballs.
Breeding To Achieve Higher Stats
--------------------------------
Thus, the other way to help engineer high IVs is to breed your own Pokémon.
While this section isn't the complete guide to breeding (you should consult
a seperate FAQ to learn about these issues), it does shed some light on why
you should do it. First I'd like to say that breeding does in no way
guarentee incredible IVs. Even in this example in which we made 3 breeding
attempts, we received one egg that produced equivalent IVs to its wild
counterparts and a second that was just slightly better. Actually, only one
of them truely stood out and this could have taken us longer to achieve
given how random breeding can be (since no one has discovered how the
formulas really work yet).
For this test, I took one Lv. 13 Zigzagoon from the grass area outside the
Daycare Center (making sure it was a male) and bred it with my female
Lv. 46 Linoone (which is the evolved form of a Zigzagoon). I then passed
them along to the Daycare supervisor and after 3 attempts, this is what I
got when I raised each of them up to Lv.12.
B1 B2 B3
HP : 34 32 32
Attack : 15 14 13
Defense : 18 16 17
Sp. Attack : 15 13 13
Sp. Defense : 18 19 17
Speed : 23 23 20
----------------------------
Total: : 123 117 112
As you can see, the IVs for two of these Pokémon are better on average then
catching the 4 wild ones earlier. Now that we have B1, we can be assured
that this Pokémon will be much more powerful than any of the wild instances
we caught earlier since it has 7-14 more points at Lv.12.
Note: An interesting result is that the quality of the Pokémon decreased
after each egg. I originally thought that this was intended by the
developers, but I hadn't bred enough eggs to see the larger picture.
This just goes to illustrate that breeding does not provide you with
amazing IVs all the time - you really have to work at it and have some
luck.
Note: Although I am using a higher level Zigzagoon, the actual level of your
male or female has no effect on the IVs passed down to the child (while
the IVs of the parents does have some effect on the child). We'll get
more into this in the breeding section of the guide, as this sort of
talk is better discussed there.
Although some people might believe this extra time and effort in hatching
multiple eggs may or may not be worth these extra points, keep in mind that
this is only the first step in achieving powerful stats. Also keep in mind
that as you gain more levels, your IVs will continue to be an asset as they
are multiplied by your current level. Thus, the higher your current level is
and the higher your IVs, the higher your stats will be. Since this Pokémon
is only level 12, we still have (potentially) another 88 more levels to go!
Calculating IVs
---------------
Now that you have some examples of stats at various levels, it's actually
possible to calculate your IVs. While the formula is correct (since we are
working with the game's rounded numbers), our values can only be estimates
to the actual values stored within the game. However, for our purposes,
this should be sufficient enough since all we can do is compare them to
others using the same methods anyway.
First off, you need to know the formula for calculating your IV given the
base stat, the actual value of the statistic, the effort value and the
personality value (for non-HP stats). For your convenience, I derived the
new formula by rearranging the variables using basic algebra. All you have
to do is plug in the values.
IV = (( Math.Ceiling( Stat/P ) - 5 ) * 100/Level ) - 2 * BaseStat - EV/4
Note: It is *very* important that you round-up "Stat/P" or the formula will
produce smaller, inaccurate values. In most cases this isn't a
problem, but if your Pokémon have low or non-existant IVs, this
formula will produce negative values. Thus, make sure you always
round-up this 'sub-result' before you compute the rest of the formula.
Note: Since the input values to this formula come from the game, you have to
keep in mind that they are not accuarate. Many people have complained
that this formula produces negative values or different values
depending on the input. When you put in "23" into the "Stat" variable,
the value could have actually been 23.111111 or 23.999999 - there is
no way to tell. Thus, the best way to ensure accurate results is
use higher level Pokémon - preferably level 12 or higher. Anything
lower, and your values will be completely inaccurate.
Note: Some moves like Hidden Power rely on a Pokémon's IVs, so if you want
to calculate its exact power, you need to heed the advice given in the
warning above.
Now, to calculate the IVs for our Zigzagoon, we need to first find out our
base stats. I have looked these up at the following website:
http://user.yagb.de/meowth346/index.php?data=stats/stats_rs_pokemon.php
For convenience, I have shown the base stats here along side the actual
statistics of B1 (our first attempt at breeding a Lv.12 Zigzagoon).
Base Stats B1's Actual Stats
---------------- -----------------
HP : 38 HP : 34
Attack : 30 Attack : 15
Defense : 41 Defense : 18
Sp. Attack : 30 Sp. Attack : 15
Sp. Defense : 41 Sp. Defense : 18
Speed : 60 Speed : 23
Now that we have the base stats, finding the IVs is a simple matter of using
the formula shown above and applying the techniques of basic algebra. By
assuming that,
Level = 12; and
Effort Value = 0; and
Personality = 1 (for 100%, let's assume to make it simple),
we can begin to calculate the IV for each stat given our Summary information
from within the game. Let's find out our Attack and Sp. Attack IVs. Some of
you might be able to calculate this in fewer steps, but I wanted to show
each step for clarity.
IV = (( Math.Ceiling( Stat/P ) - 5 ) * 100/Level ) - 2 * BaseStat - EV/4
IV = (( Math.Ceiling( 15/1 ) - 5 ) * 100/12 ) - 2 * 30 - 0/4
IV = (( 15 - 5 ) * 100/12 ) - 60
IV = ( 10 * 100/12 ) - 60
IV = 1000/12 - 60
IV = ~23
So by using the formula and solving for IV, we managed to figure out that
our Attack IV and Sp. Attack IV are both 23, which is two-thirds of the
maximum value of 31 - Not bad. Let's calculate our Defense and Sp. Defense
IVs next.
IV = (( Math.Ceiling( Stat/P ) - 5 ) * 100/Level ) - 2 * BaseStat - EV/4
IV = (( Math.Ceiling( 18/1 ) - 5 ) * 100/12 ) - 2 * 41 - 0/4
IV = (( 18 - 5 ) * 100/12 ) - 82
IV = ( 13 * 100/12 ) - 82
IV = 1300/12 - 82
IV = ~26
Now Speed.
IV = (( Math.Ceiling( Stat/P ) - 5 ) * 100/Level ) - 2 * BaseStat - EV/4
IV = (( Math.Ceiling( 23/1 ) - 5 ) * 100/12 ) - 2 * 60 - 0/4
IV = (( 23 - 5 ) * 100/12 ) - 120
IV = ( 18 * 100/12 ) - 120
IV = 1800/12 - 120
IV = 30
Since the HP statistic uses a different formula, we need to come up with a
new formula for calculating the HP IV as well. This formula was derived
in the same way as the others, but simply rearranging the variables in order
to solve for IV. Here is the formula:
IV = (( Stat - Level - 10 ) * 100/Level ) - 2 * BaseStat - EV/4
Using this formula, we can now calculate the HP IV for our Zigzagoon.
IV = (( Stat - Level - 10 ) * 100/Level ) - 2 * BaseStat - EV/4
IV = (( 34 - 12 - 10 ) * 100/12 ) - 2 * 38 - 0
IV = ( 12 * 100/12 ) - 76
IV = 100 - 76
IV = 24
When we receive numbers like 23, 26, 30 and 24 for Individual Values, we can
clearly see that wild Pokémon produce poor IVs in comparison to ones hatched
in the breeding process. In the breeding section of this guide, I'll talk
more about how to get quality IVs.
When using these formulas for all our main stats, we can now fully list our
set of IVs for this Lv.12 Zigzagoon:
HP IV : 24
Attack IV : 23
Defense IV : 26
Sp. Attack IV : 23
Sp. Defense IV : 26
Speed IV : 30
-------------------
Average :~25
As you can see, we made out pretty good with B1 with an efficiency rating of
81% (since we received an average of 25 out of a possible 31). If you use
these steps followed in this section of the guide, you can now be absolutely
certain that your breeding is working correctly. Now that you have the
actual values for the IVs, you can also re-input them with various EVs and
level values to calculate your projected stats at later points in the game.
Note: Although we demonstrated that breeding has provided us with some more
favourable results, IVs are generated by the game randomly when both
catching Pokémon from the wild and hatching eggs, thus making it
possible to receive a 'super' Pokémon. Since IVs range from 0-31 and
there are 6 stats, there is a 1 in 1,073,741,824 chance of receiving a
perfect set of IVs (or equally a set of all 0's as well).
When considering these terrible odds, as long as you receive a total
of 144 or more points in your all of your IVs (i.e. 75% of the
maximum), you should consider jumping up and down for joy and start
working on your EVs next.
Looking back to the Pichu example shown earlier in this guide, I realized
that I was unlucky and received a Pichu that had poor IVs (or at least ones
that compared with the wild Pikachu at best). If I had known that from the
beginning, I would not have wasted so much time leveling it up to Lv. 50.
After reading this section, I'm certain you won't make the same mistake.
A Common Problem People Have
----------------------------
If you have had some problems with the formulas, you should really read this
section. Otherwise, you can go on to section, "2.4.2 - Influencing Effort
Values".
A person named John had just emailed me stating that he was having some
problems with the formulas outlined in this guide. While he wasn't the
first to have issues, he was the first person to actually provide me with
adequate information that illustrated the main problem. In this section,
I'm going to show you his email that illustrates the problem and the
explanation I gave him that shed some light on the subject.
Here is the email sent to me on April 09, 2003:
Hello. I read your Advanced Trainer Guide from Gamefaqs last night and
sought out to breed and raise a Vulpix with decent IVs across the board,
using your formula to calculate the values from the ones that I've bred
and hatched. The problem I'm having is in the consistency of the
solutions for various levels. I would assume that rather I did the
calculations at level 5 or level 50, they should come out the same,
assuming that I have not attained any EVs (which I haven't), and that
I'm actually doing the math correctly. Here's what I did, and perhaps
you can see what I'm doing wrong.
I took a newly hatched Vulpix, used a Fire Stone to evolve it to a
Ninetails (I did this because the Base Stat Guide that I look at only had
the bases for Ninetails), and then did my calculations from there. The
Pokemon did not fight in any battles whatsoever, and no EV altering items
were used. I could only go as high as level 17, as I have only received
12 rare candies thus far in my travels. I got the base figures using the
material that was recommended within your guide. All numbers under each
corresponding level are respective in the order that I've listed the
Bases.
Species : Ninetails
Personality : Quirky
Base Hp : 73
Base Attack : 76
Base Defense : 75
Base Speed : 100
Base Sp. Attack : 81
Base Sp. Defense : 100
Lv.5 IV Lv.10 IV Lv.11 IV Lv.17 IV
--------- ---------- ---------- ----------
HP: 23 14 37 24 40 26 57 30
Attack: 11 32? 19 12 21 7 31 1
Defense: 13 10 22 20 24 22 34 20
Speed: 15 0 25 0 27 0 39 0
Sp. Attack: 13 2 22 8 24 10 34 8
Sp. Defense: 16 20 27 20 29 18 42 17
I also did the same with a standard Vulpix (after I found the base
stats), but posting those would probably be irrelevant as they aren't as
"detailed" as what I have above, however I will note that I got the same
end result as I have above. The last one I did was of a Pichu, and those
results were even more insane looking than those of the Vulpix and
Ninetails.
I'm sure many people have had a similar situation, so I wanted to let you
know why this is happening and I also wanted to ease your mind that there is
nothing wrong with the formulas directly.
If you compare the results from the Level 5 Ninetails to the Level 17
instance, you can clearly see the results are completely different. The
reason for this is that these formulas do not work very well at low levels
(such as Level 5). The main reason for this is due to fact that the final
stat doesn't change much if the IV is "0" or "31". At Level 5, you'll be
lucky to see more than a 5 point difference. The more levels you gain,
however, the more accurate the formulas will become. That is why I
recommend that you raise the Pokémon in question to level 12 or higher, as
stated earlier in this guide. If you have more Rare Candies or a Gameshark,
feel free to level the Pokémon up as high as possible to receive the most
accurate results (for data collection purposes only).
John's assumption that the formulas should provide the same IV results for
level 5 to level 50 is actually incorrect. While that statement might be
true while doing algebra or calculus equations, you have to remember that
we usually work with real numbers in those equations and make an effort to
avoid rounding down. However in these equations, your input is already
incorrect - it's been rounded by the game. Thus, you can't really trust
the actual stat values being provided on the Summary screen. While at level
5, it might show you 23 for your HP stat, it may actually be anywhere
between "23.000001" or "23.999999". If you plug that information into the
IV formula, you will receive two totally different IVs even though they
produce the same integer value.
Therefore, the best way to 'estimate' your IVs is to level up your
Pokémon as much as possible so that the actual stat value is closer to the
real value rather than the inaccurate integer that has been rounded by the
game.
Now, there is another interesting observation that I would like to point
out. When you look at the calculated IVs for Level 11 and 17, you should
be able to see that the IVs do not differ all that much - they are
relatively close together. In fact, you had calculated the IVs for higher
levels, you would start to get the impression that the values are stablizing
to their correct value. This is clearly different when you look at the
difference between the Level 5 and 11 values - the degree of seperation is
huge (in fact, they are opposites in some cases).
What does all this mean? John's Level 17 results are probably fairly
accurate, and if they aren't, they are at most 1 point off from the actual
value stored from within the game. Thus, if you plotted a graph of all the
IV values for levels 5 through 100 with the correct stat values, you'll
probably start to see it flatten out after level 12. This means that
anything before level 12 is nonsense.
Where's the proof of this? Well, let's take a look at the Defense and Speed
values, as this clearly shows that IVs are influencing the final values.
You'll see that the Defense value is "34" and the Speed value is "39".
If you look closely however, the Speed Base stat for Ninetails is 100 -
that's 25 more points than the Defense Base stat. Then how can the actual
stats be so close? If you look at the IVs, this particular Ninetails has a
very good Defense IV of 20 while the Speed IV is 0. This is how its Defense
stat was only a few points behind its Speed - truely not the norm for most
Ninetails Pokémon.
Now, I know many people probably don't like these uncertainties, especially
when mathematics is supposed to be an exact science. If the game provided
you with real numbers, these formulas would work perfectly no matter what
level you used. Since the inputs are inaccurate to begin with, you can't
expect your answers to be perfect either. There isn't much you can do unless
you can find a way to hack into the game and find the real numbers stored in
the console or emulator's memory, and I'm sure many of you aren't prepared
to do that.
So remember everyone, the results of using these formulas are only
"estimates". All you should be interested in is comparing your estimates
with others. If you need the exact IVs later on, you'll probably have to do
some more digging, but I can't see many practical uses for that anyway. All
you really need to care about is getting the best IVs possible (as your
estimates indicate) and then get max EVs (which we will discuss in the next
section of this guide). That's all there is to it folks and that's really
the best you can hope to accomplish.