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

written by JungleJim - junglejimgf@yahoo.com

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