Experience and Levels
For it is written that you will go out into the world and slay of the beasts therein, and in doing so become stronger and more shiny.
The cycle of combat and reward is a staple of gaming in general, and nowhere is it more apparent than among the workings of an RPG. Fighting monsters reaps tasty experience points, which in turn strengthen the party in order to face tougher foes. By analysing the steps of this numerical dance, it's possible to discover precisely how it works.
Note: This is an in-depth look into the mechanics behind the Final Fantasy IX experience system, with suitable mathematical content. It almost certainly won't help Zidane and company to know this, but is provided for the completists out there.
Summary
- All characters level up in the same way; None are better at improving certain attributes.
- Leveling up while wearing certain equipment permanently boosts stats; Don't waste levels.
Spoils
The first logical part of the cycle lies in gaining experience points (XP). Every creature is worth a certain amount of XP, though bosses are typically worth none. After a battle, the total XP for all slain creatures is added and divided equally among the fighters. Characters KOed, or suffering under Petrification, Virus, or Zombie, are not welcome to receive spoils. Thus, each of a party of four will gain much less experience than a lone fighter. AP, used to learn abilities, is not divided up, and all appropriate party members receive the full amount.
Levels
When a character earns so many XP, he will gain a level and become stronger. Extra points will count towards his next level, so none is wasted and it is possible to jump up two or three levels at once. The XP thresholds are given by the following formula:
XP required to reach level x: (x4 + 10x3 + 37x2 + 56x - 96) / 16
XP is cumulative, so reaching level 10 (1510XP) requires only 432XP after reaching level 9 (1078XP). A whopping table of experience points is available for those unable to evaluate quartics in their heads.
Attributes
Of course, levels are of little worth alone. More interesting is their effect on attributes, boosting vital statistics for combat. The formulae involved are quite simple, but contain an interestingly deceptive element which will be revealed later.
Every character has an immutable set of base attributes. These are their stats at level 1, and cannot change.
| Character | Speed | Strength | Magic | Spirit | Stones |
|---|---|---|---|---|---|
| Zidane | 23 | 21 | 18 | 23 | 18 |
From there, attributes are determined by adding on a multiple of the character's current level as given below:
| Attribute | Formula (round down) |
|---|---|
| Speed | 0.1 * Level |
| Strength | 0.3 * Level |
| Magic | 0.3 * Level |
| Spirit | 0.15 * Level |
| Stones | 0.4 * Level |
Thus, a level 17 Zidane will have (18 + 0.3 * 17) = 23 Magic, for example.
The catch
However, it's not quite as simple as that. Each attribute has an additional booster which grows over time based on current equipment. This bonus is applied on leveling up.
| Attribute | Additional points per level |
|---|---|
| Speed | 0 |
| Strength | 3/32 |
| Magic | 3/32 |
| Spirit | 1/32 |
| Stones | 5/32 |
If the character is wearing any attribute-boosting equipment when they level up, however, then its boosters are also added at a rate of 1/32 per point per level. As an example, consider the Glass Buckle, which temporarily adds 1 to Strength and Magic, and 2 to Spirit. If a character gains a level while wearing it, these boosters will "bleed" into their natural attributes.
| Attribute | Additional points per level while wearing Glass Buckle |
|---|---|
| Speed | 0 |
| Strength | 3/32 + 1/32 |
| Magic | 3/32 + 1/32 |
| Spirit | 1/32 + 2/32 |
| Stones | 5/32 |
Note that this only applies to the base attributes. Defence et al will not increase with levels.
An example
Perhaps the best way to see what's going on is to watch it in action. Consider Zidane, freshly landed in Evil Forest at level 1.
Level 1
| Attribute | Base | Level multiplier | Additional | Total |
|---|---|---|---|---|
| Speed | 23 | 0.1 * 1 => 0 | 0 | 23 |
| Strength | 21 | 0.3 * 1 => 0 | 0 | 21 |
| Magic | 18 | 0.3 * 1 => 0 | 0 | 18 |
| Spirit | 23 | 0.15 * 1 => 0 | 0 | 23 |
| Stones | 18 | 0.4 * 1 => 0 | 0 | 18 |
He ventures into the swamp, fights a few goblins, and levels up.
Level 2
| Attribute | Base | Level multiplier | Additional | Total |
|---|---|---|---|---|
| Speed | 23 | 0.1 * 2 => 0 | 0 | 23 |
| Strength | 21 | 0.3 * 2 => 0 | 3/32 => 0 | 21 |
| Magic | 18 | 0.3 * 2 => 0 | 3/32 => 0 | 18 |
| Spirit | 23 | 0.15 * 2 => 0 | 1/32 => 0 | 23 |
| Stones | 18 | 0.4 * 2 => 0 | 5/32 => 0 | 18 |
By the time he reaches Dali, he has fought his way to level 5 and is beginning to show signs of improvement.
Level 5
| Attribute | Base | Level multiplier | Additional | Total |
|---|---|---|---|---|
| Speed | 23 | 0.1 * 5 => 0 | 0 | 23 |
| Strength | 21 | 0.3 * 5 => 1 | 15/32 => 0 | 22 |
| Magic | 18 | 0.3 * 5 => 1 | 15/32 => 0 | 19 |
| Spirit | 23 | 0.15 * 5 => 0 | 5/32 => 0 | 23 |
| Stones | 18 | 0.4 * 5 => 2 | 25/32 => 0 | 20 |
Much later, he reaches level 10, still without using any special equipment.
Level 10
| Attribute | Base | Level multiplier | Additional | Total |
|---|---|---|---|---|
| Speed | 23 | 0.1 * 10 => 1 | 0 | 24 |
| Strength | 21 | 0.3 * 10 => 3 | 27/32 => 0 | 24 |
| Magic | 18 | 0.3 * 10 => 3 | 27/32 => 0 | 21 |
| Spirit | 23 | 0.15 * 10 => 1 | 9/32 => 0 | 24 |
| Stones | 18 | 0.4 * 10 => 4 | 45/32 => 1 | 23 |
Here he acquires a Glass Buckle. The future path now depends on whether he equips it as he levels up:
Level 20
| Attribute | Base | Level multiplier | Additional (Standard) Gained 19 levels | Total | Additional (With Glass Buckle) Gained 19 levels, 10 with Glass Buckle | Total |
|---|---|---|---|---|---|---|
| Speed | 23 | 0.1 * 20 => 2 | 0 | 25 | 0 | 25 |
| Strength | 21 | 0.3 * 20 => 6 | 57/32 => 1 | 28 | 57/32+10/32 => 2 | 29 |
| Magic | 18 | 0.3 * 20 => 6 | 57/32 => 1 | 25 | 57/32+10/32 => 2 | 26 |
| Spirit | 23 | 0.15 * 20 => 3 | 19/32 => 0 | 26 | 19/32+20/32 => 1 | 27 |
| Stones | 18 | 0.4 * 20 => 8 | 95/32 => 2 | 28 | 95/32 => 2 | 28 |
By wearing the Buckle for a few hours, Zidane has "absorbed" some of its power and permanently boosted his natural attributes. Of course, wearing the Buckle also adds a temporary attribute boost which isn't included in the above table.
Yes, yes, but what about the important things? You haven't mentioned HP or MP yet
Busted. HP and MP don't follow this formula, nor do they have a easy calculation. Instead, HP and MP are a function of Level and Strength or Magic. After all level multipliers and additionals are added, as in the tables above, HP is worked out by multiplying Strength by a special number which changes for each level. MP is similarly linked to Magic.
The level 20 HP multiplier is around 34.67, so in the above example "standard" Zidane would have (34.67 * 28) = 971HP, while the Buckled Zidane would enjoy (34.67 * 29) = 1005HP.
Multipliers increase almost linearly with level, up to approximately level 40. There they begin to level out, becoming almost constant by the time they reach level 50.
