# Combat Balance Formula

Th*anks to RJC9000 for providing the formula. I have not verified it, but I have no plan on verifying it soon, so I will provide it as is.*

The Combat Balance formula uses the Coefficient of Variation of Awareness, Critical Avoidance and Deflect. If all values are equal then it provides the full amount of 10% damage reduction or given as a multiplier: a coefficient of 0.9.

The exact formula is calculated by:

$$
Mean = (Awareness + Critical Avoidance + Deflect) / 3
$$

$$
Stdev = Standard Deviation(Awareness; Critical Avoidance; Deflect)\\
\= \sqrt{((Awareness-Mean)²+(Critical Avoidance-Mean)²+(Deflect-Mean)²)/3}
$$

$$
CV    = Coefficient~~of~~Variance = Standard\~Deviation/Mean
$$

$$
Combat\~Balance =0.9 + Min(CV/10;0.1)
$$

## Examples:

### Example ‘All close together’:

* Awareness = 50000, Critical Avoidance =47000, Deflect = 48500
* Mean = (50000 + 47000 + 47000) / 3 = 48500
* Stdev = SquareRoot(((50000-48500)²+(47000-48500)²+(48500-48500)²)/3) \~ 1225
* CV \~ 1225 / 48500 \~ 0.025258
* Combat Balance =0.9 + Min(0.025258/10;0.1) \~ 0.90253

The damage reduction of 9.747% is still very close to 10%. There is no need to overtune stats because of that feat! The 0.25% loss on the coefficient barely matters. Big hits shall still be taken with the shield!

### Example ‘Deflect ignored’:

* Awareness = 50000, Critical Avoidance =49000, Deflect = 34500
* Mean = 44500
* Stdev \~ 7083
* CV \~ 7083 / 44500 \~ 0.159
* Combat Balance =0.9 + Min(0.159/10;0.1) \~ 0.9159

The damage reduction of 8.4% on a build ignoring Deflect is still very high.

### Example ‘Messed up build’:

* Awareness = 70000, Critical Avoidance =31000, Deflect = 31000
* Combat Balance =0.9 + Min(0.418/10;0.1) \~ 0.418

The damage reduction of 5.2% is still higher than 5%! One has to try hard to bring the coefficient below 5%!


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