Mechanics

Level / Experience

CHAR_EXP = LVL ^ (PI())
RANK_EXP = LVL ^ (1.5 * PI())

      | Character EXP   | Rank EXP	
Level | Total   | Diff  | Total	  | Diff
------------------------------------------
0     | 0       | 0	| 0	  | 0
1     | 1	| 1	| 1	  | 1
2     | 9	| 8	| 26	  | 25
3     | 32	| 23	| 177	  | 151
4     | 78	| 46	| 687	  | 510
5     | 157	| 79	| 1967	  | 1280
6     | 278	| 121	| 4645	  | 2678
7     | 452	| 173	| 9604	  | 4959
8     | 687	| 235	| 18018	  | 8415
9     | 995	| 308	| 31388	  | 13370
10    | 1385	| 390	| 51569	  | 20181
11    | 1869	| 484	| 80807	  | 29238
12    | 2457	| 588	| 121765  | 40958
13    | 3159	| 702	| 177556  | 55791
14    | 3987	| 828	| 251768  | 74213
15    | 4952	| 965	| 348497  | 96729
16    | 6065	| 1113	| 472369  | 123872
17    | 7338	| 1273	| 628570  | 156201
18    | 8781	| 1443	| 822872  | 194302
19    | 10407	| 1626	| 1061657 | 238785
20    | 12227	| 1820	| 1351946 | 290289
.     | .               | .
------------------------------------------
TOTAL:| 65316		| 5435890	
------------------------------------------

Damage Calculation

The calculation of the damage should be close to exponential but disallow small incremental changes from a single source to make a large impact to the overall changes.

To accomplish that, we multiply the effective attribute value of the character to its equipments.

(ATTACKER_ATK * ATTACKER_EQUIPMENT_ATK)
 -------------------------------------   * (SUM_OF_MODIFIERS)
(DEFENDER_DEF * DEFENDER_EQUIPMENT_DEF)

Instead of taking the square value of the sum of attack, this ensures that the character's damage doesn't also grow exponentially from just a small change either from the equipment or the character's own attributes.

EX: character's attack: 100, equipment's attack: 50

# taking the sum
(100 + 50)^2 = 22,500
(100 + 51)^2 = 22,801 (301 higher, or 1.3%)
(105 + 50)^2 = 24,025 (1,525 higher, or 6.7%)
(120 + 50)^2 = 28,900 (6,400 higher, or 28.4%)

# multiplying each other
(100 * 50) = 5,000
(100 * 51) = 5,100 (100 higher, or 2%)
(105 * 50) = 5,250 (250 higher, or 5%)
(120 * 50) = 6,000 (1,000 higher, or 20%)

The example should look the same for the defence value as well.