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Final Fantasy X (US) - Aeon Stats FAQ - v1.1
===============================================================================

written by JungleJim - [email protected]

Final Fantasy X is (c) Square (c) Sony Entertainment of America

Permission to publish this FAQ is given to the following websites:
www.gamefaqs.com

For permission to publish elsewhere, send me email.

=================
TABLE OF CONTENTS
=================

1.0 - REVISION HISTORY
2.0 - INTRODUCTION
3.0 - YUNA'S STATS
3.1 - Modifier Tables
4.0 - BATTLE BONUSES
4.1 - Forced Battles
4.2 - Battle Bonus Tables
4.3 - Battle Bonus Formulas
5.0 - AEON'S SOUL
5.1 - Core Stat Formulas
5.2 - MP Table
5.3 - MP Formulas
5.4 - HP Table
5.5 - HP Formulas
6.0 - THANKS

======================
1.0 - REVISION HISTORY
======================

Version 1.1 01-28-03 Fixed some typos
Clarified MAX process

Version 1.0 01-23-03 Initial version

==================
2.0 - INTRODUCTION
==================

This FAQ describes the formulas that govern aeon stat increases. These stats
can increase in three ways:

-Raise Yuna's stats using the sphere grid
-Raise the aeons' stats directly by using the Aeon's Soul
-Fight a certain number of battles

For each stat, the formulas have this form:

stat = MAX(Y, B) + A

where

Y = the aeon's stat value if you'd only raised Yuna's stat
A = the aeon's stat value if you'd raised it directly using the Aeon's Soul
B = the aeon's stat value if you'd only fought battles
MAX is a function that returns the largest valued argument

The MAX function is applied for each type of stat. For example, the aeon's HP
is computed as if it were based only on the number of battles fought. Then the
aeon's HP is computed as if it were based only on Yuna's stats. The higher of
the two is taken to be the actual HP. The same process happens for each of the
other stats.

Section 3 shows how to calculate Y; Section 4 shows how to calculate B;
Section 5 shows how to calculate A.

==================
3.0 - YUNA'S STATS
==================

Raising Yuna's stats on the sphere grid is the most common and effective way to
increase the aeons' stats. The only problem is that there's a limit to how
much you can raise them this way. Yuna's core stats can't be raised beyond
255. Yuna's HP can go beyond 9999, but the aeons' stats will be unaffected
after that. Yuna's MP can go beyond 999, but the aeons' stats will be
unaffected after that.

First a note regarding Luck. The Luck stat is special for several reasons.
The only ways to raise it are to use the Aeon's Soul or to increase Yuna's
Luck. All of the aeons have a base Luck of 17, same as Yuna. If you never use
the Aeon's Soul, all of the aeons will have exactly the same value for Luck as
Yuna has while she travels around the sphere grid.

Everything else in this section applies to the other nine stats. Whenever Yuna
increases any one of these stats, it affects the corresponding stat of the
aeon, but it also affects each of the other eight stats to a lesser extent.

Now is a good time to mention that I got stuck while working on these formulas.
Terence showed me the light. The main problem was that I needed two floor
functions instead of one in the formula. Having only one caused my predicted
values to be off by one in a few places.

Terence suggested the following auxilliary stat, which he called the Aeon Power
Base:

PBase = [yHP/100] + [yMP/10] + yStr + yDef + yMag + yMdf + yAgl + yEv + yAcc

When a stat name is preceded by 'y', it's refering to the value of Yuna's stat.
[] represents the floor function, which basically rounds a decimal value down
to an integer.

Examples:

[5] = 5
[5.2] = 5
[5.9] = 5

Here's the formula for an aeon's stat based on Yuna's stat:

stat = [yStat * x] + [PBase * y]

Each aeon has different values for x and y for each stat. See Section 3.1 for
a list of the x and y values. Note that the aeons' stats have the same caps as
Yuna's stats (255 for core stats, 99999 for HP, 9999 for MP). Let's do some
examples.

First, using Yuna's base stats, we'll calculate Anima's base stats.

PBase = [475/100] + [84/10] + 5 + 5 + 20 + 20 + 10 + 30 + 3 = 105
HP = [475 * 120/100] + [105 * 8] = 1410
MP = [84 * 4/100] + [105 * 4/10] = 45
Str = [5 * 330/100] + [105 * 1/6] = 33
Def = [5 * 100/100] + [105 * 1/5] = 26
Mag = [20 * 70/100] + [105 * 1/12] = 22
Mdf = [20 * 100/100] + [105 * 1/30] = 23
Agl = [10 * 40/100] + [105 * 1/20] = 9
Luck = 17
Ev = [30 * 50/100] + [105 * 1/20] = 20
Acc = [3 * 200/100] + [105 * 1/20] = 11

Now let's see what Anima's stats are when Yuna is maxed.

PBase = [9999/100] + [999/10] + 255 + 255 + 255 + 255 + 255 + 255 + 255 = 1983
HP = [9999 * 120/100] + [1983 * 8] = 27862
MP = [999 * 4/100] + [1983 * 4/10] = 832
Str = [255 * 330/100] + [1983 * 1/6] = 255
Def = [255 * 100/100] + [1983 * 1/5] = 255
Mag = [255 * 70/100] + [1983 * 1/12] = 255
Mdf = [255 * 100/100] + [1983 * 1/30] = 255
Agl = [255 * 40/100] + [1983 * 1/20] = 201
Luck = 255
Ev = [255 * 50/100] + [1983 * 1/20] = 255
Acc = [255 * 200/100] + [1983 * 1/20] = 255

---------------------
3.1 - Modifier Tables
---------------------

Terence provided the x and y values for HP, MP, and Str, and I figured out the
rest.

=-=-=
HP
=-=-=

Valefor: x = 20/100, y = 6
Ifrit: x = 70/100, y = 5
Ixion: x = 55/100, y = 6
Shiva: x = 40/100, y = 6
Bahamut: x = 100/100, y = 7
Anima: x = 120/100, y = 8
Yojimbo: x = 18/100, y = 9
Cindy: x = 240/100, y = 10
Sandy: x = 200/100, y = 8
Mindy: x = 150/100, y = 5

=-=-=
MP
=-=-=

Valefor: x = 4/100, y = 2/10
Ifrit: x = 3/100, y = 2/10
Ixion: x = 5/100, y = 2/10
Shiva: x = 7/100, y = 2/10
Bahamut: x = 5/100, y = 3/10
Anima: x = 4/100, y = 4/10
Yojimbo: x = 0/100, y = 0/10
Cindy: x = 18/100, y = 3/10
Sandy: x = 5/100, y = 3/10
Mindy: x = 20/100, y = 4/10

=-=-=-=-=-=
Strength
=-=-=-=-=-=

Valefor: x = 60/100, y = 1/7
Ifrit: x = 80/100, y = 1/7
Ixion: x = 100/100, y = 1/7
Shiva: x = 120/100, y = 1/8
Bahamut: x = 160/100, y = 1/7
Anima: x = 330/100, y = 1/6
Yojimbo: x = 240/100, y = 1/6
Cindy: x = 230/100, y = 1/6
Sandy: x = 550/100, y = 1/7
Mindy: x = 160/100, y = 1/7

=-=-=-=-=
Defense
=-=-=-=-=

Valefor: x = 50/100, y = 1/5
Ifrit: x = 170/100, y = 1/5
Ixion: x = 100/100, y = 1/5
Shiva: x = 40/100, y = 1/7
Bahamut: x = 200/100, y = 1/6
Anima: x = 100/100, y = 1/5
Yojimbo: x = 250/100, y = 1/8
Cindy: x = 300/100, y = 1/6
Sandy: x = 180/100, y = 1/6
Mindy: x = 140/100, y = 1/6

=-=-=-=
Magic
=-=-=-=

Valefor: x = 100/100, y = 1/70
Ifrit: x = 90/100, y = 1/33
Ixion: x = 90/100, y = 1/38
Shiva: x = 100/100, y = 1/28
Bahamut: x = 90/100, y = 1/250
Anima: x = 70/100, y = 1/12
Yojimbo: x = 60/100, y = 1/23
Cindy: x = 100/100, y = 1/60
Sandy: x = 110/100, y = 1/40
Mindy: x = 130/100, y = 1/40

=-=-=-=-=-=-=-=
Magic Defense
=-=-=-=-=-=-=-=

Valefor: x = 100/100, y = 1/30
Ifrit: x = 90/100, y = 1/34
Ixion: x = 130/100, y = 1/30
Shiva: x = 100/100, y = 1/25
Bahamut: x = 100/100, y = 1/12
Anima: x = 100/100, y = 1/30
Yojimbo: x = 100/100, y = 1/30
Cindy: x = 100/100, y = 1/12
Sandy: x = 100/100, y = 1/12
Mindy: x = 100/100, y = 1/12

=-=-=-=-=
Agility
=-=-=-=-=

Valefor: x = 50/100, y = 1/20
Ifrit: x = 40/100, y = 1/20
Ixion: x = 30/100, y = 1/20
Shiva: x = 100/100, y = 1/23
Bahamut: x = 50/100, y = 1/20
Anima: x = 40/100, y = 1/20
Yojimbo: x = 40/100, y = 1/20
Cindy: x = 50/100, y = 1/20
Sandy: x = 50/100, y = 1/20
Mindy: x = 70/100, y = 1/20

=-=-=-=-=
Evasion
=-=-=-=-=

Valefor: x = 50/100, y = 1/24
Ifrit: x = 30/100, y = 1/70
Ixion: x = 30/100, y = 1/47
Shiva: x = 100/100, y = 1/44
Bahamut: x = 50/100, y = 1/20
Anima: x = 50/100, y = 1/20
Yojimbo: x = 180/100, y = 1/20
Cindy: x = 50/100, y = 1/20
Sandy: x = 40/100, y = 1/20
Mindy: x = 60/100, y = 1/20

=-=-=-=-=-=
Accuracy
=-=-=-=-=-=

Valefor: x = 200/100, y = 1/20
Ifrit: x = 200/100, y = 1/20
Ixion: x = 250/100, y = 1/20
Shiva: x = 200/100, y = 1/20
Bahamut: x = 200/100, y = 1/20
Anima: x = 200/100, y = 1/20
Yojimbo: x = 300/100, y = 1/10
Cindy: x = 200/100, y = 1/20
Sandy: x = 270/100, y = 1/20
Mindy: x = 240/100, y = 1/20

====================
4.0 - BATTLE BONUSES
====================

Aeon stats will increase starting at 60 battles, then every 30 battles until
600 battles. All battles count, even before Yuna joins the party, and even if
you run away. Boss battles and arena battles count.

--------------------
4.1 - Forced Battles
--------------------

In one test, I used a cheat device to obtain all the aeons very early in the
game, in order to see what their base stats were. Masamune3 suggested another
test to back up those numbers. In order to verify the base stats of the aeons,
I used a cheat device to go through the game without having any random
encounters. This was necessary because in normal gameplay, it's not possible
to acquire all the aeons without passing 60 battles, the first point where the
stats increase. Below I've listed all the forced battles I encountered:

1 - Sinscales
2 - Sinscales
3 - Sinspawn Ammes
4 - Sahagin
5 - Geosgaeno
6 - Klikk
7 - Piranha
8 - Tros
9 - Dingo, Condor
10 - Water Flan
11 - Kimahri
12 - Garuda
13 - Garuda
14 - Condor, Dingo, Water Flan
15 - Sin, Sinscales
16 - Sinspawn Echuilles, Sinscales
17 - Ragora
18 - Sinspawn Geneaux
19 - Worker
20 - Worker
21 - Worker
22 - Oblitzerator
23 - Sahagin Chiefs
24 - Vouivre
25 - Garuda
26 - Raldo
27 - Chocobo Eater
28 - Sinspawn Gui
29 - Sinspawn Gui
30 - Extractor
31 - Treasure Chest, mole
32 - Spherimorph
33 - Crawler
34 - Seymour, Guado Guardians
35 - Guado Guardian
36 - Guado Guardian
37 - Wendigo, Guado Guardians
38 - Zuu
39 - Mech Guards
40 - Sandragora
41 - Guado Guardian, Bombs
42 - Guado Guardian, Dual Horns
43 - Guado Guardian, Chimeras
44 - Evrae
45 - Warrior Monks
46 - Warrior Monks, YKT-63
47 - Warrior Monks
48 - Warrior Monks, YKT-63
49 - Warrior Monks, YAT-99
50 - Grothia
51 - Pterya
52 - Spathi
53 - Evrae Altana
54 - Seymour Natus
55 - Defender X
56 - Yojimbo
57 - Biran Ronso, Yenke Ronso
58 - Seymour Flux
59 - Sanctuary Keeper

After Sanctuary Keeper, the first stat bonuses were applied, but I've only got
59 battles in the list. Either I missed one, or one of the other battles I
fought had a split and I counted it as one battle when it should have been
counted as two. After this, there are three more battles necessary to fight
before obtaining Anima and the Magus Sisters. These are Spectral Keeper,
Yunalesca, and Geosgaeno. Note that I didn't fight Belgemine at all because
I used a key items cheat in order to unseal the Magus Sisters.

The good news is that the 0-59 stats (or base stats) for Valefor through
Yojimbo are consistent with the base stats I observed from my other cheat game.
Also, the 60-99 stats are consistent for all aeons. From this I am reasonably
confident that the base stats I observed in my other cheat game are the true
base stats for all aeons.

-------------------------
4.2 - Battle Bonus Tables
-------------------------

The following tables show the stats of the aeons after each battle bonus is
applied. The 0-59 rows correspond to the base stats of each aeon. Notice that
Luck is unaffected by battles.

=-=-=-=-=
Valefor
=-=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 725 24 18 23 21 23 10 17 19 11
60- 89 785 27 19 25 24 26 10 17 20 11
90-119 885 29 20 28 27 27 12 17 21 12
120-149 955 30 21 29 27 30 12 17 21 12
150-179 1003 31 22 30 30 33 12 17 21 12
180-209 1127 35 24 33 31 37 15 17 24 13
210-239 1169 36 25 34 34 41 15 17 24 13
240-269 1229 39 27 36 38 41 18 17 25 14
270-299 1341 43 28 39 42 42 19 17 27 15
300-329 1465 46 30 44 42 46 21 17 28 15
330-359 1525 49 32 46 46 46 22 17 30 16
360-389 1573 50 33 47 47 51 24 17 30 16
390-419 1685 53 35 50 51 55 25 17 31 17
420-449 1785 55 36 52 51 55 27 17 33 17
450-479 1845 58 38 54 55 60 28 17 34 18
480-509 1917 60 39 58 55 60 30 17 36 18
510-539 2005 63 40 60 59 60 31 17 37 19
540-569 2053 64 42 61 59 65 31 17 39 19
570-599 2177 69 44 64 64 65 34 17 39 20
600+ 2225 71 45 66 64 69 34 17 42 20

=-=-=-=
Ifrit
=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 857 23 19 29 21 21 9 17 10 11
60- 89 907 26 20 31 23 23 9 17 10 11
90-119 1097 28 21 36 26 23 11 17 10 12
120-149 1262 29 22 37 26 26 11 17 10 12
150-179 1302 30 23 38 30 30 11 17 10 12
180-209 1512 34 25 41 30 32 13 17 12 13
210-239 1547 35 26 42 32 36 13 17 12 13
240-269 1597 37 28 44 37 36 16 17 12 14
270-299 1797 41 29 47 41 37 17 17 14 15
300-329 2007 44 31 57 41 41 18 17 14 15
330-359 2057 47 33 59 45 42 19 17 15 16
360-389 2097 48 34 60 45 45 21 17 16 16
390-419 2297 51 36 63 49 49 22 17 16 17
420-449 2487 53 37 65 50 49 23 17 17 17
450-479 2537 56 39 67 53 53 24 17 17 18
480-509 2597 58 40 76 53 53 26 17 18 18
510-539 2777 60 41 78 58 53 27 17 18 19
540-569 2817 61 43 79 58 58 27 17 19 19
570-599 3027 66 45 82 62 58 30 17 20 20
600+ 3067 68 46 84 62 62 30 17 22 20

=-=-=-=
Ixion
=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 891 25 20 26 20 29 8 17 11 12
60- 89 951 28 21 28 23 32 8 17 11 12
90-119 1121 30 22 32 26 33 9 17 11 13
120-149 1261 31 23 33 26 37 9 17 11 13
150-179 1309 33 24 34 29 41 9 17 11 13
180-209 1503 37 26 37 30 46 11 17 13 14
210-239 1545 38 27 38 32 51 11 17 13 14
240-269 1605 41 29 40 36 51 14 17 13 15
270-299 1787 45 30 43 40 52 15 17 15 16
300-329 1981 48 32 50 41 58 16 17 16 16
330-359 2041 51 34 52 44 58 17 17 17 17
360-389 2089 52 35 53 44 64 18 17 17 17
390-419 2271 56 37 56 48 69 19 17 17 18
420-449 2441 58 38 58 49 69 20 17 19 18
450-479 2501 61 40 60 52 75 21 17 19 19
480-509 2573 63 41 66 52 75 22 17 20 19
510-539 2731 66 42 68 56 75 23 17 20 20
540-569 2779 67 44 69 57 81 23 17 21 20
570-599 2973 72 46 72 61 81 26 17 22 21
600+ 3021 74 47 74 61 87 26 17 24 21

=-=-=-=
Shiva
=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 820 26 19 17 23 24 14 17 32 11
60- 89 880 30 20 18 27 27 15 17 34 11
90-119 1020 32 21 19 30 28 18 17 34 12
120-149 1130 33 22 20 30 31 18 17 34 12
150-179 1178 35 23 21 33 34 19 17 35 12
180-209 1342 40 25 23 34 38 22 17 39 13
210-239 1384 41 25 24 37 42 22 17 39 13
240-269 1444 44 27 26 42 42 27 17 39 14
270-299 1596 48 28 27 46 43 27 17 44 15
300-329 1760 51 30 31 46 47 32 17 44 15
330-359 1820 55 31 33 51 48 32 17 48 16
360-389 1868 56 32 34 51 52 37 17 48 16
390-419 2020 60 34 36 56 57 37 17 49 17
420-449 2160 62 35 37 56 57 42 17 53 17
450-479 2220 66 36 39 60 61 42 17 53 18
480-509 2292 68 38 42 61 62 47 17 57 18
510-539 2420 71 39 43 65 62 47 17 58 19
540-569 2468 72 40 45 65 66 47 17 62 19
570-599 2632 78 41 47 70 67 52 17 62 20
600+ 2680 80 42 48 70 71 52 17 66 20

=-=-=-=-=
Bahamut
=-=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 1210 35 23 27 18 28 10 17 20 11
60- 89 1280 39 24 29 20 32 10 17 21 11
90-119 1550 42 25 34 23 33 12 17 22 12
120-149 1785 44 26 35 23 36 12 17 22 12
150-179 1841 47 27 37 26 40 12 17 22 12
180-209 2139 52 29 39 26 44 15 17 25 13
210-239 2188 54 30 40 28 49 15 17 25 13
240-269 2258 58 32 42 32 50 18 17 26 14
270-299 2542 63 33 44 36 51 19 17 29 15
300-329 2840 67 35 54 36 56 21 17 29 15
330-359 2910 71 37 56 39 57 22 17 32 16
360-389 2966 73 38 57 39 61 24 17 32 16
390-419 3250 78 40 59 43 66 25 17 33 17
420-449 3520 81 41 61 43 67 27 17 35 17
450-479 3590 85 43 62 46 72 28 17 36 18
480-509 3674 89 44 72 47 73 30 17 38 18
510-539 3930 92 45 74 51 74 31 17 39 19
540-569 3986 94 47 75 51 78 31 17 41 19
570-599 4284 101 49 77 55 79 34 17 42 20
600+ 4340 103 50 79 55 84 34 17 44 20

=-=-=-=
Anima
=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 1410 45 33 26 22 23 9 17 20 11
60- 89 1490 50 35 28 25 26 9 17 21 11
90-119 1810 54 36 32 28 27 11 17 22 12
120-149 2090 56 37 33 28 30 11 17 22 12
150-179 2154 59 39 34 31 33 11 17 22 12
180-209 2506 65 41 37 32 37 13 17 25 13
210-239 2562 68 42 38 35 41 13 17 25 13
240-269 2642 73 44 40 39 41 16 17 26 14
270-299 2978 79 46 43 43 42 17 17 29 15
300-329 3330 85 48 50 44 46 18 17 29 15
330-359 3410 90 50 52 47 46 19 17 32 16
360-389 3474 93 51 53 47 51 21 17 32 16
390-419 3810 98 53 56 51 55 22 17 33 17
420-449 4130 102 55 58 52 55 23 17 35 17
450-479 4210 107 56 60 56 60 24 17 36 18
480-509 4306 111 58 66 57 60 26 17 38 18
510-539 4610 116 60 68 61 60 27 17 39 19
540-569 4674 119 61 69 61 65 27 17 41 19
570-599 5026 126 63 72 65 65 30 17 42 20
600+ 5090 130 65 74 66 69 30 17 44 20

=-=-=-=-=
Yojimbo
=-=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 1030 0 29 25 16 23 9 17 59 19
60- 89 1120 0 31 26 18 26 9 17 62 20
90-119 1246 0 32 32 20 27 11 17 63 21
120-149 1327 0 33 33 20 30 11 17 63 22
150-179 1399 0 35 34 23 33 11 17 63 22
180-209 1561 0 37 36 23 37 13 17 71 24
210-239 1624 0 38 36 25 41 13 17 71 24
240-269 1714 0 40 38 28 41 16 17 72 25
270-299 1858 0 42 39 31 42 17 17 81 27
300-329 2020 0 44 51 32 46 18 17 81 28
330-359 2110 0 46 52 34 46 19 17 89 29
360-389 2182 0 47 53 35 51 21 17 89 30
390-419 2326 0 49 55 37 55 22 17 90 31
420-449 2452 0 51 56 38 55 23 17 97 32
450-479 2542 0 52 57 41 60 24 17 98 33
480-509 2650 0 54 69 42 60 26 17 105 34
510-539 2758 0 56 70 44 60 27 17 106 35
540-569 2830 0 57 71 44 65 27 17 113 36
570-599 2992 0 59 72 48 65 30 17 114 37
600+ 3064 0 61 73 48 69 30 17 122 38

=-=-=-=
Cindy
=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 2190 46 28 32 21 28 10 17 20 11
60- 89 2290 52 30 34 24 32 10 17 21 11
90-119 2870 55 31 41 28 33 12 17 22 12
120-149 3400 57 32 42 28 36 12 17 22 12
150-179 3480 63 34 44 31 40 12 17 22 12
180-209 4100 70 36 46 31 44 15 17 25 13
210-239 4170 72 37 47 34 49 15 17 25 13
240-269 4270 79 39 49 38 50 18 17 26 14
270-299 4870 87 41 51 43 51 19 17 29 15
300-329 5490 91 43 65 43 56 21 17 29 15
330-359 5590 97 45 67 47 57 22 17 32 16
360-389 5670 99 46 68 47 61 24 17 32 16
390-419 6270 107 48 70 51 66 25 17 33 17
420-449 6850 110 50 72 51 67 27 17 35 17
450-479 6950 116 51 73 56 72 28 17 36 18
480-509 7070 120 53 87 56 73 30 17 38 18
510-539 7630 126 55 89 60 74 31 17 39 19
540-569 7710 128 56 90 60 78 31 17 41 19
570-599 8330 140 58 92 64 79 34 17 42 20
600+ 8410 142 60 94 64 84 34 17 44 20

=-=-=-=
Sandy
=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 1790 35 42 26 24 28 10 17 17 13
60- 89 1870 39 43 28 27 32 10 17 17 13
90-119 2350 42 44 32 31 33 12 17 18 14
120-149 2790 44 45 33 31 36 12 17 18 14
150-179 2854 47 46 35 34 40 12 17 18 14
180-209 3366 52 48 37 34 44 15 17 21 15
210-239 3422 54 49 38 38 49 15 17 21 15
240-269 3502 58 51 40 43 50 18 17 22 16
270-299 3998 63 52 42 48 51 19 17 25 17
300-329 4510 67 54 51 48 56 21 17 25 17
330-359 4590 71 56 53 53 57 22 17 27 18
360-389 4654 73 57 54 53 61 24 17 27 18
390-419 5150 78 59 56 57 66 25 17 28 19
420-449 5630 81 60 58 57 67 27 17 30 19
450-479 5710 85 62 59 63 72 28 17 31 20
480-509 5806 89 63 69 63 73 30 17 32 20
510-539 6270 92 64 71 67 74 31 17 33 21
540-569 6334 94 66 72 67 78 31 17 35 21
570-599 6846 101 68 74 73 79 34 17 36 22
600+ 6910 103 69 76 73 84 34 17 38 22

=-=-=-=
Mindy
=-=-=-=

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 1237 58 23 24 28 28 12 17 23 12
60- 89 1287 66 24 26 31 32 12 17 24 12
90-119 1637 70 25 29 36 33 15 17 25 13
120-149 1962 72 26 30 36 36 15 17 25 13
150-179 2002 79 27 32 40 40 15 17 25 13
180-209 2372 88 29 34 40 44 18 17 28 14
210-239 2407 91 30 35 44 49 18 17 28 14
240-269 2457 99 32 37 50 50 22 17 29 15
270-299 2817 108 33 39 56 51 23 17 33 16
300-329 3187 114 35 47 56 56 25 17 33 16
330-359 3237 122 37 49 62 57 26 17 36 17
360-389 3277 125 38 50 62 61 29 17 36 17
390-419 3637 134 40 52 67 66 30 17 37 18
420-449 3987 138 41 54 67 67 33 17 39 18
450-479 4037 146 43 55 73 72 34 17 40 19
480-509 4097 150 44 63 73 73 37 17 43 19
510-539 4437 158 45 65 78 74 38 17 44 20
540-569 4477 161 47 66 78 78 38 17 46 20
570-599 4847 174 49 68 85 79 42 17 47 21
600+ 4887 178 50 70 85 84 42 17 50 21

---------------------------
4.3 - Battle Bonus Formulas
---------------------------

Terence also figured out this one. The above tables can be generated with the
same formulas presented in Section 3.0, but using some "fake stats" for Yuna
instead of her real stats. The following table lists the fake stats:

Battles HP MP STR DEF MAG MDF AGL LK EV ACC
------------------------------------------------------------
0- 59 475 84 5 5 20 20 10 17 30 3
60- 89 475 104 5 5 23 23 10 17 32 3
90-119 675 104 5 7 26 23 13 17 32 3
120-149 875 104 5 7 26 26 13 17 32 3
150-179 875 124 5 7 29 29 13 17 32 3
180-209 1075 144 5 7 29 32 16 17 36 3
210-239 1075 144 5 7 32 36 16 17 36 3
240-269 1075 164 5 7 36 36 20 17 36 3
270-299 1275 184 5 7 40 36 20 17 40 3
300-329 1475 184 5 11 40 40 24 17 40 3
330-359 1475 204 5 11 44 40 24 17 44 3
360-389 1475 204 5 11 44 44 28 17 44 3
390-419 1675 224 5 11 48 48 28 17 44 3
420-449 1875 224 5 11 48 48 32 17 48 3
450-479 1875 244 5 11 52 52 32 17 48 3
480-509 1875 244 5 15 52 52 36 17 52 3
510-539 2075 264 5 15 56 52 36 17 52 3
540-569 2075 264 5 15 56 56 36 17 56 3
570-599 2275 304 5 15 60 56 40 17 56 3
600+ 2275 304 5 15 60 60 40 17 60 3

Terence also noticed that these fake stats almost exactly mirror Yuna's natural
Sphere Grid path if you activated every node along the way and didn't open any
Locks.

"I say 'almost exactly' because of 600+. At 600+, the 'fake stats' gain 4 MDef
and 4 Eva. However, the final leg of Yuna's Sphere Grid path (ending at Holy)
has two +4 Eva nodes, and no MDef node. Which is, in fact, *very* interesting,
in my opinion. A design change at the last second? They followed the path so
*well* up until then...." -Terence

=================
5.0 - Aeon's Soul
=================

------------------------
5.1 - Core Stat Formulas
------------------------

The following formula applies to Str, Def, Mag, Mdf, Agl, Luck, Ev, and Acc:

ns = MIN(99, [stat / 2])

where
ns: number of spheres needed to raise the core stat by 1
MIN: the minimum function, returns the lowest valued argument
stat: the current value of the stat to be raised
[]: round down to an integer value (aka floor function)

--------------
5.2 - MP Table
--------------

In the following table, the first column is the range of current MP values, the
second column is the number of spheres required to raise MP by 10 for the given
range of current MP, and the third column is the number of values in the given
range of MP.
Examples:

Current MP = 15
12 Mana Spheres are needed
New MP = 25

Current MP = 1500
35 Mana Spheres are needed
New MP = 1510

I've listed the third column so that you can see the pattern. The number of
values in the MP range increases by 3 and 6 alternately.

An interesting side note: If you wanted to increase Yojimbo's MP from 0 to 9999
MP, you would need 53,905 Mana Spheres. That should give you an idea of how
much time it would take to max out the MP of all your aeons.

0- 2 10 3
3- 8 11 6
9- 20 12 12
21- 35 13 15
36- 56 14 21
57- 80 15 24
81- 110 16 30
111- 143 17 33
144- 182 18 39
183- 224 19 42
225- 272 20 48
273- 323 21 51
324- 380 22 57
381- 440 23 60
441- 506 24 66
507- 575 25 69
576- 650 26 75
651- 728 27 78
729- 812 28 84
813- 899 29 87
900- 992 30 93
993-1088 31 96
1089-1190 32 102
1191-1295 33 105
1296-1406 34 111
1407-1520 35 114
1521-1640 36 120
1641-1763 37 123
1764-1892 38 129
1893-2024 39 132
2025-2162 40 138
2163-2303 41 141
2304-2450 42 147
2451-2600 43 150
2601-2756 44 156
2757-2915 45 159
2916-3080 46 165
3081-3248 47 168
3249-3422 48 174
3423-3599 49 177
3600-3782 50 183
3783-3968 51 186
3969-4160 52 192
4161-4355 53 195
4356-4556 54 201
4557-4760 55 204
4761-4970 56 210
4971-5183 57 213
5184-5402 58 219
5403-5624 59 222
5625-5852 60 228
5853-6083 61 231
6084-6320 62 237
6321-6560 63 240
6561-6806 64 246
6807-7055 65 249
7056-7310 66 255
7311-7568 67 258
7569-7832 68 264
7833-8099 69 267
8100-8372 70 273
8373-8648 71 276
8649-8930 72 282
8931-9215 73 285
9216-9506 74 291
9507-9800 75 294
9801-9998 76 300

-----------------
5.3 - MP Formulas
-----------------

Xharas contributed the following closed-form expressions which will generate my
table.

mp: aeon's current MP
ms: number of mana spheres needed to raise MP by 10
SQRT: square root function
[]: round down to an integer value (aka floor function)
base: MP level base (corresponding to the first number in the first column of
my table)
span: the number of MP values in that level (corresponding to the third column
of my table)

Find ms given mp:

ms = [SQRT(mp / 2.25) + 10]

Example:
mp = 323
ms = [SQRT(323 / 2.25) + 10] = [21.981...] = 21

Find base and span given ms (when ms is even):

base = 2.25 * (ms - 10) * (ms - 10)

span = 4.5 * (ms - 10) + 3

Example:
ms = 22
base = 2.25 * (22 - 10) * (22 - 10) = 324
span = 4.5 * (22 - 10) + 3 = 57

base of next level = 324 + 57 = 381
range of current level = 324-380

Find base and span given ms (when ms is odd):

base = 2.25 * (ms - 10) * (ms - 10) + 0.75

span = 4.5 * (ms - 10) + 1.5

Example:
ms = 21
base = 2.25 * (21 - 10) * (21 - 10) + 0.75 = 273
span = 4.5 * (21 - 10) + 1.5 = 51

base of next level = 273 + 51 = 324
range of current level = 273-323

--------------
5.4 - HP Table
--------------

In the following table, the first column is the range of current HP values, the
second column is the number of spheres required to raise HP by 100 for the
given range of current HP, and the third column is the number of values in the
given range of HP.
Examples:

Current HP = 725
22 Power Spheres are needed
New HP = 825

Current HP = 31000
60 Power Spheres are needed
New HP = 31100

I've listed the third column so that you can see the pattern. The number of
values in the HP range increases by 32 each time.

An interesting side note: If you wanted to increase an aeon's HP from 0 (if it
were possible to have an aeon's HP that low) to 99999 HP, you would need 68,171
Power Spheres. That should give you an idea of how much time it would take to
max out the HP of all your aeons.

0- 15 16 16
16- 63 17 48
64- 143 18 80
144- 255 19 112
256- 399 20 144
400- 575 21 176
576- 783 22 208
784- 1023 23 240
1024- 1295 24 272
1296- 1599 25 304
1600- 1935 26 336
1936- 2303 27 368
2304- 2703 28 400
2704- 3135 29 432
3136- 3599 30 464
3600- 4095 31 496
4096- 4623 32 528
4624- 5183 33 560
5184- 5775 34 592
5776- 6399 35 624
6400- 7055 36 656
7056- 7743 37 688
7744- 8463 38 720
8464- 9215 39 752
9216- 9999 40 784
10000-10815 41 816
10816-11663 42 848
11664-12543 43 880
12544-13455 44 912
13456-14399 45 944
14400-15375 46 976
15376-16383 47 1008
16384-17423 48 1040
17424-18495 49 1072
18496-19599 50 1104
19600-20735 51 1136
20736-21903 52 1168
21904-23103 53 1200
23104-24335 54 1232
24336-25599 55 1264
25600-26895 56 1296
26896-28223 57 1328
28224-29583 58 1360
29584-30975 59 1392
30976-32399 60 1424
32400-33855 61 1456
33856-35343 62 1488
35344-36863 63 1520
36864-38415 64 1552
38416-39999 65 1584
40000-41615 66 1616
41616-43263 67 1648
43264-44943 68 1680
44944-46655 69 1712
46656-48399 70 1744
48400-50175 71 1776
50176-51983 72 1808
51984-53823 73 1840
53824-55695 74 1872
55696-57599 75 1904
57600-59535 76 1936
59536-61503 77 1968
61504-63503 78 2000
63504-65535 79 2032
65536-67599 80 2064
67600-69695 81 2096
69696-71823 82 2128
71824-73983 83 2160
73984-76175 84 2192
76176-78399 85 2224
78400-80655 86 2256
80656-82943 87 2288
82944-85263 88 2320
85264-87615 89 2352
87616-89999 90 2384
90000-92415 91 2416
92416-94863 92 2448
94864-97343 93 2480
97344-99855 94 2512
99856-99999 95 2544

-----------------
5.5 - HP Formulas
-----------------

Xharas submitted the following closed-form expressions which can generate my
table. Much nicer than the iterative expressions I used before.

hp: aeon's current HP
ps: number of power spheres needed to raise HP by 100
SQRT: square root function
[]: round down to an integer value (aka floor function)
base: HP level base (corresponding to the first number in the first column of
my table)
span: the number of HP values in that level (corresponding to the third column
of my table)

Find ps given hp:

ps = [SQRT(hp / 16) + 16]

Example:
hp = 3533
ps = [SQRT(3533 / 16) + 16] = [30.859...] = 30

Find base and span given ps:

base = 16 * (ps - 16) * (ps - 16)

span = 32 * (ps - 15.5)

Example:
ps = 30
base = 16 * (30 - 16) * (30 - 16) = 3136
span = 32 * (30 - 15.5) = 464

base of next level = 3136 + 464 = 3600
range of current level = 3136-3599

============
6.0 - THANKS
============

-Gamefaqs for hosting this and all my other faqs

-Masamune3 for suggesting a helpful test

-Xharas for providing formulas for the HP/MP Aeon's Soul tables

-Terence for providing the PBase formulas, HP/MP/Str modifiers, and battle
bonus formulas

-Also thanks to all those who showed interest in this topic on the message
board