Some Game Mechanics

I was actually planning on replaying this and digging up more than what's presented here, but since I won't be able to for a while, I thought I'd at least write down what I have.

Damage Formula

The damage primarily depends on the attack's power value, the Offense/Defense stats to some extent and what type the attack/enemy is.

Diff = (YourOffense - EnemyDefense)
PowerMod = Diff / 500 * Power + Power
Damage = PowerMod * TypeBonus / 30

Diff can't be lower than -500 and can't be higher than 500. E.g. even if you have 999 Offense and the enemy 0 Defense, it's still the same as having 500 Offense.
(for more accurate results, round down PowerMod and then Damage)

Now for the most complicated part, TypeBonus.
First, I'll present the type table:
http://pastebin.com/np7Nqie7

Each column stands for a digimon type (of the enemy) and each row stands for an attack type. To figure out the TypeBonus, look at the row corresponding to the attack's type and then look at the columns corresponding to the enemy's type. Add the values of the mentioned cells together.
If the enemy digimon has only two visible types, add 10
If the enemy digimon has only one visible type, add 20

Example: Your digimon uses Spit Fire against an enemy Agumon.
Spit Fire is of the type Fire, so only the first row is relevant.
Agumon is of the types Fire and Battle, so you're left with the following values: 10 and 15
Since Agumon only has two types, you add 10 to that.
The sum, and therefore TypeBonus is then 35.

Take-home summary of that: If you look at the table, only the values 2, 5, 10, 15 and 20 appear. You can describe them as following:
2: attack of type (row) is very weak against type (column)
5: attack of type (row) is weak against type (column)
10: attack of type (row) does normal damage against type (column)
15: attack of type (row) is strong against type (column)
20: attack of type (row) is very strong against type (column)
Example: Any Filth attack is very weak against Earth type digimon and very strong against Mech type digimon.

To sum this up: The most important thing is the Power value. That value is further increased or decreased based on the difference of the user's Offense value and the target's Defense value. E.g. if you have 50 more Offense than the enemy has Defense, your Power value is boosted by 10% and so on.

Digivolving Mechanics

Most of this was already discovered, but I'm adding a bit to that.
The process is split into several steps. First, a digimon reaches maturity, then the game looks if the conditions of a digimon it can digivolve to are met and finally, the game picks the "best" or "most fitting" digivolution.

Maturity
Maturity is measured in hours and resets upon digivolution. After a digimon reaches the necessary maturity, it will digivolve as soon as any conditions are met.

Baby 1 to Baby 2: 6 hours
Baby 2 to Rookie: 24 hours
Rookie to Champion: 72 hours (after 96 to Numemon)
Champion to Ultimate: 144 hours

Conditions
As you may know, there are three main conditions and several bonus conditions for any digimon.
The main conditions are:
Your stats need to be higher than or equal to the required stats. (This is different when digivolving to Rookies)
Your care mistakes must be below or above (depending on digimon) a specified value.
Your weight needs to be within +-5 of the required weight.

The bonus conditions are: everything else.

To be even able to digivolve, you need to meet 3 main conditions of a digimon or 2 main and 1 bonus condition.

Digivolution Fitness
More often than not, you'll fulfill the conditions of more than one digivolution (most famously: If your Agumon fulfills Greymon's conditions, it will automatically fulfill Centarumon's), so the game has a way of determining which digivolution 'fits' more.

The most important thing here are the stats for which there are requirements of the digimon you can digivolve to, but not the required values. That was a mouthful.
For example, Greymon requires certain values for Offense, Defense, Speed and Brains.
Centarumon only requires certain values for Brains, etc.

What you do with this is look at what the stats are, and then look at what values you have for these stats (Note: divide HP/MP by 10 and round down). Then, you calculate the average (and round down) and this is the fitness score. The digimon with the highest score wins and your partner will digivolve into that.

Example:
You have have an Agumon.
Stats: 800 HP, 600 MP, 102 Offense, 101 Defense, 102 Speed, 102 Brains
CM: 0 Care Mistakes
Weight: 30
Misc: 0 Battles

Looking at the conditions over at:
http://www.gamefaqs.com/ps/913684-digimon-world/faqs/64257

You'll see that you meet the conditions of: Greymon, Tyrannomon (CM, Weight, Battles) and Centarumon.

Greymon has requirements for Offense, Defense, Speed and Brains. Our values are 102, 101, 102 and 102. The average is (102+101+102+102)/4 = 101,75 and since we have to round down: 101
Tyrannomon has requirements for HP and Defense. Our values are 80 (remember: divide HP by 10) and 101. The average is 90
Centarumon has requirements only for Brains. Our value (and average) is 102

Centarumon has the highest score and will therefore be selected. If only Offense was 5 points higher*, we'd get Greymon.

*Strictly speaking, we only need Offense to be 1 points higher. With 103/101/102/102, Greymon would have a score of 102. The game checks the digimon in a certain order and for one digimon to beat another, it needs to have a higher score. Greymon is checked before Centarumon, so Centarumon'd lose.

Wow, cool info. Is the digivolution evolution order the same as in the Digimon Chart in the game if you have the same value for Greymon and Centarumon? First Digimon in Agumons chart is Greymon and last Centarumon.

For Agumon, the order is: Greymon, Meramon, Birdramon, Centarumon, Monochromon, Tyrannomon

I don't think this can be derived from anything in-game, can it?
But usually just a single session in the gym should be enough to avoid that tie-breaker rule, although you're not always near it.

ForteGSOmega posted...

For Agumon, the order is: Greymon, Meramon, Birdramon, Centarumon, Monochromon, Tyrannomon

I don't think this can be derived from anything in-game, can it?
But usually just a single session in the gym should be enough to avoid that tie-breaker rule, although you're not always near it.

I guess not then. In-game graphics don't have to match the code.
Yep, so it shouldn't be a problem.

I was gonna brag about how the info is old, but I noticed your deeper digging. Nice find. :p

This is really impressive info. Now I know how to exactly interpret the stat requirements for certain Champions I'd want. Aaaand I just want to be able to avoid a 3rd Centarumon LOL. XD

Hey, Mr FortisOmega, could you please hack the game to confirm which items the Treasure Hunt nets you? I'm mostly interested in the DV items.

BTW, I find it sooooo hard to win the DV items from Penguimon/Metalmamemon. I wich we could abuse the RNG for this.

Filth is strong against Mech? Interesting.

What about the random damage? Whith this damage formula an attack would deal the same damage everytime that it's used in a battle.

Thanks for sharing your work.