Why Does My Combat Power Calculation Differ from the Game?

[duirixuanyan]

Help me understand Combat Power calculation — my formula doesn't match the game

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**TL;DR:** I tried to reverse-engineer `Unit_CombatPower` for Byzantine Light Archers (got ~9) and Skoutatoi (got ~32). But the game shows different numbers. Can anyone point out my mistakes or give me the actual in-game values so I can work backwards?

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Hi everyone,

I've been trying to reverse-engineer the `Unit_CombatPower` function from `Unit.BSF` to understand how Combat Power is calculated. But my results don't match what the game shows. Can anyone help me figure out what I'm missing?

## The Formula (as I understand it)

From `Unit.BSF`:

```c
FUNCTION Unit_CombatPower(unitID)
{
attack = Unit_Attack(unitID) + (Unit_FlankingMod(unitID) / 2) + (Unit_AttackAssaultChange(unitID) / 2);
defense = Unit_Defense(unitID) + (Unit_DefenseAssaultChange(unitID) / 2);
range = Unit_RangedAttackValue(unitID) + Unit_RangedMaxEffecDamages(unitID);
xp = Unit_GetXPLevel(unitID);

base = (Unit_GetHits(unitID) * UNIT_CP_HIT_INCh) + (Unit_GetEffec(unitID) * UNIT_CP_EFF_INCh);
base += (attack * UNIT_CP_ATK_INCh) + (defense * UNIT_CP_DEF_INCh);
base += (range * UNIT_CP_RNG_INCh) + (xp * UNIT_CP_EXP_INCh);

mult = (Unit_GetHits(unitID) * UNIT_CP_HIT_PERC) + (Unit_GetEffec(unitID) * UNIT_CP_EFF_PERC);
mult += (attack * UNIT_CP_ATK_PERC) + (defense * UNIT_CP_DEF_PERC);
mult += (range * UNIT_CP_RNG_PERC) + (xp * UNIT_CP_EXP_PERC);

result = base * (100 + mult);
result = DivideAndRound(result, 10000);

result = Pow(result, UNIT_CP_NUMERATORh, UNIT_CP_DENOMINATORh) / 10; // ^1.66
result = Max(1, result);

if (Unit_TemplateKind(unitID) == KIND_NAV)
result /= 2;

return result;
}
```

With the constants (from the comments):

```
UNIT_CP_HIT_INCh = 100
UNIT_CP_EFF_INCh = 50
UNIT_CP_EXP_INCh = 35
UNIT_CP_ATK_INCh = 25
UNIT_CP_DEF_INCh = 25
UNIT_CP_RNG_INCh = 10

UNIT_CP_HIT_PERC = 8
UNIT_CP_EFF_PERC = 22
UNIT_CP_EXP_PERC = 18
UNIT_CP_ATK_PERC = 15
UNIT_CP_DEF_PERC = 15
UNIT_CP_RNG_PERC = 6
```

## Example 1: Byzantine Light Archers

| Stat | Value |
|---|---|
| Hits | 1 |
| Effectiveness | 3 |
| Attack | 3 |
| Defense | 3 |
| RangedAttack | 7 |
| RangedMaxDamages | 1 |
| FlankingModifier | 1 |
| AtkAssaultChg | 0 |
| DefAssaultChg | 1 |
| XP Level | 0 |

### My calculation

**Step 1 — Compute derived stats:**

```
attack = 3 + (1 / 2) + (0 / 2) = 3 + 0 + 0 = 3
defense = 3 + (1 / 2) = 3 + 0 = 3
range = 7 + 1 = 8
xp = 0
```

> Note: integer division, `1/2 = 0`.

**Step 2 — Base value:**

```
base = (1 × 100) + (3 × 50) = 100 + 150 = 250
base += (3 × 25) + (3 × 25) = 75 + 75 = 150
base += (8 × 10) + (0 × 35) = 80 + 0 = 80
base = 250 + 150 + 80 = 480
```

**Step 3 — Multiplier:**

```
mult = (1 × 8 ) + (3 × 22) = 8 + 66 = 74
mult += (3 × 15) + (3 × 15) = 45 + 45 = 90
mult += (8 × 6) + (0 × 18) = 48 + 0 = 48
mult = 74 + 90 + 48 = 212
```

**Step 4 — Combine:**

```
result = 480 × (100 + 212) = 480 × 312 = 149,760
result = 149,760 / 10,000 = 14.976
```

**Step 5 — Pow(1.66):**

```
14.976 ^ 1.66 ≈ ?
ln(14.976) ≈ 2.7063
1.66 × 2.7063 ≈ 4.4925
e^4.4925 ≈ 89.4
result = 89.4 / 10 = 8.94
```

**Step 6 — Final:**

```
result = max(1, 8.94) = 8.94 ≈ 9
```

**My result: ~9**

But the game shows 5. Can anyone tell me where the discrepancy comes from?

## Example 2: Skoutatoi

| Stat | Value |
|---|---|
| Hits | 3 |
| Effectiveness | 3 |
| Attack | 6 |
| Defense | 8 |
| RangedAttack | 0 |
| RangedMaxDamages | 0 |
| FlankingModifier | 1 |
| AtkAssaultChg | 1 |
| DefAssaultChg | 0 |
| XP Level | 0|

### My calculation

**Step 1 — Derived stats:**

```
attack = 6 + (1 / 2) + (1 / 2) = 6 + 0 + 0 = 6
defense = 8 + (0 / 2) = 8 + 0 = 8
range = 0 + 0 = 0
xp = 0
```

**Step 2 — Base value:**

```
base = (3 × 100) + (3 × 50) = 300 + 150 = 450
base += (6 × 25) + (8 × 25) = 150 + 200 = 350
base += (0 × 10) + (0 × 35) = 0 + 0 = 0
base = 450 + 350 + 0 = 800
```

**Step 3 — Multiplier:**

```
mult = (3 × 8 ) + (3 × 22) = 24 + 66 = 90
mult += (6 × 15) + (8 × 15) = 90 + 120 = 210
mult += (0 × 6) + (0 × 18) = 0 + 0 = 0
mult = 90 + 210 + 0 = 300
```

**Step 4 — Combine:**

```
result = 800 × (100 + 300) = 800 × 400 = 320,000
result = 320,000 / 10,000 = 32.0
```

**Step 5 — Pow(1.66):**

```
32 ^ 1.66 ≈ ?
ln(32) ≈ 3.4657
1.66 × 3.4657 ≈ 5.7531
e^5.7531 ≈ 315.4
result = 315.4 / 10 = 31.54
```

**Step 6 — Final:**

```
result = max(1, 31.54) = 31.54 ≈ 32
```

**My result: ~32**

But the game shows 12.

## My Questions

1. **Are my constants correct?** I got them from comments in `Unit.BSF`.

2. **Integer division truncation:** In `attack = Unit_Attack + (Flanking / 2) + (AtkAssaultChg / 2)`, does `1 / 2` become 0 (integer) or 0.5 (float)?

Thanks for any help!

[Surt]

Won't the result of step 4 be 15 as its divide and round?
There should be a file where the real numbers are.

[duirixuanyan]

Thanks for replying.

Yes, the result of step 4 should be 15. However, the number still doesn't match which is confusing.

[Surt]

Thanks for replying.

Yes, the result of step 4 should be 15. However, the number still doesn't match which is confusing.

Comments gets outdated so you need to find the file where the values are actually set.

[duirixuanyan]

Comments gets outdated so you need to find the file where the values are actually set.

Thank you. You are right. The real values are in MapGlobals.BSF as follows. And the numbers finally match with the game.

Code: Select all

// Units, cbt power estimate
// see Unit_CombatPower for the details
#define UNIT_CP_HIT_INCh 75 
#define UNIT_CP_HIT_PERC 10
#define UNIT_CP_EFF_INCh 50
#define UNIT_CP_EFF_PERC 20
#define UNIT_CP_EXP_INCh 25
#define UNIT_CP_EXP_PERC 18
#define UNIT_CP_ATK_INCh 15
#define UNIT_CP_ATK_PERC 8
#define UNIT_CP_DEF_INCh 15
#define UNIT_CP_DEF_PERC 8
#define UNIT_CP_RNG_INCh 10
#define UNIT_CP_RNG_PERC 6
#define UNIT_CP_NUMERATORh 200
#define UNIT_CP_DENOMINATORh 120

The lesson is that comments are sometimes unreliable.

[duirixuanyan]

Code: Select all

case 1

attack  = Attack + FlankingMod/2 + AtkAssaultChg/2
        = 3 + 1/2 + 0/2
        = 3 + 0 + 0          （Truncating division，1/2 = 0）
        = 3

defense = Defense + DefAssaultChg/2
        = 3 + 1/2
        = 3 + 0
        = 3

range   = RangedAttack + RangedMaxDamages
        = 7 + 1
        = 8

xp      = 0

Code: Select all

case 2

attack  = Attack + FlankingMod/2 + AtkAssaultChg/2
        = 6 + 1/2 + 1/2
        = 6 + 0 + 0          （Truncating division，1/2 = 0）
        = 6

defense = Defense + DefAssaultChg/2
        = 8 + 0/2
        = 8

range   = RangedAttack + RangedMaxDamages
        = 0 + 0
        = 0

xp      = 0

The problem is that truncating division makes 1 FlankingMod and AtkAssaultChg useless in combat power, especially in case 2.

[Surt]

Hmm yeah the values should be multiplied by x and then only at the end rounded. There x could be 2 as that is the only divisor.