Combat Balance Formula

Thanks 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%!