Eve math

From UniWiki

In eve bonuses and penalties are calculated in a multiplicative fashion, not just added. This page will hopefully give a basic understanding of the way different bonus and penalties are calculated.

Contents 1 Basic Bonuses 2 Basic Reductions 3 Stacking Penalties 4 Resistances

Basic Bonuses

tl;dr version: two 25% bonus give a 56% bonus. Two 50% bonuses give a 125% bonus. More bonuses are generally better than one big bonus. Best is lots of big bonuses.

Bonuses in eve come in two different forms: flat bonuses and multipliers. A bonus would be something like armor plates, they add some amount to the armor of the ship. A multiplier is something that the attribute is multiplied by. For example, Hull upgrades[1] or the Regenerative Plating II[2] mod. Both of these give a percent bonus to armor.

It is simple so far. The tricky part is that two multiplicative bonuses effect each other. Say you have Hull Upgrades IV and a Regenerative Plating II mod fitted to your ship. That is a 20% bonus and an 8% bonus. This does not give a 28% bonus, but rather: 20%+8%+20% of 8% = 29.6%

Here the eve devs have done you a disservice in giving the bonuses in percent, they are much easier to think of as multipliers, a 20% bonus is the same as a 1.2 multiplier, and 8% is a 1.08 multiplier. This changes the mess above into the simple formula: 1.2*1.08=1.296

As an example, lets take a look at the Harbinger[3] with a 1600mm Reinforced Rolled Tungsten Plate,[4] Hull Upgrades IV and a Regenerative Plating II. The base armor for the Harbinger is 5,469. The plate gives 4200 more armor and, as we saw above, Hull upgrades IV gives a 1.2 multiplier and regenerative plating a 1.08 multiplier.

Total Armor = (5469+4200)*1.2*1.08 = 9669*1.296 = 12531.02 That is then truncated to 12531.

Basic Reductions

tl;dr version: Some reductions are actually bonuses. Two 25% reductions are the same as a 44% penalty. Two 50% reductions is the same as a 75% penalty. One big reduction is better than lots of small ones.

Again, like bonuses, reductions are best thought of as multipliers. A 25% reduction would be a .75 multiplier.

Stacking Penalties

Stacking Penelties, also known as diminishing returns, is a function created to prevent the stacking of the same modifier from compounding on itself to unfair proportions. It can be determined by checking how much a module boosts effectiveness by compared to how much it should. The data points are:

1st = 1

2nd = 0.8691

3rd = 0.5706

4th = 0.2830

and fitting a function to this curve gives us:

e^(-0.140274*(n-1)^2)

The module with the highest boost for a given stat is affected the least by stacking penelties, followed by the second highest, and so on. This means that even if a large number of people have a Remote Sensor Booster I on a target, if someone turns on a Remote Sensor Booster II, they will see at least the 5% difference between the Sensor Booster I and II, plus any gains seen by the addition of a single sensor booster at the highest diminishing returns.

Any module that boosts or penelises a stat affected by stacking penelties will say so in their description: "Penalty: Using more than one type of this module, or similar modules that affect the same..."

Stacking penelties also affect some remote modules such as the Remote Sensor Booster, Sensor Dampener, Tracking Disruptor and the like. These can come from many different sources, and can interact with modules fitted on the ship. Stacking penelties are cumulative for all sources, local or remote.

Resistances

Resistances are best thought of as reductions to incoming damage. Each mod affects one or all of the four resistances for each layer of defence. It's easy to see that the -25% EM Damage Resistance Bonus of the Adaptive Invulnerability Field I on a ship with 0% EM resistance would reduce incoiming damage by 25%. If the ship has 20% thermal resistance already, then you need to multiply the penelties to incoming damage together:

20% base resistance (1 - 0.2) = 0.8

25% Adaptive Invulnerability Field (1 - 0.25) = 0.75

0.8 * 0.75 = 0.6

(1 - 0.6) = 0.4 or 40% resistance.

Besides the base resistances of the ship and the Damage Control module, all resistance rigs/modules suffer a stacking penelty. The stacking penelty is ordered highest to lowest per resistance, not per rig/module, which means the highest resistance module for that resistance is calculated first, even though that may not be the highest resist module for another resist.

For example, a ship with base shield resistances, an Adaptive Invulnerability Field I, a Photon Scattering Field I, a Heat Dissipation Field I, and a Damage Control I would have the following.

EM

(base) 1.0 * (DCU) 0.925 * (Photon Scattering Field) 0.5 * (Adaptive Invulnerability Field (diminished)) (1 - 0.25 * 0.8691) = 0.361 or 64%

Thermal

(base) 0.8 * (DCU) 0.925 * (Heat Dissipation Field I) 0.5 * (Adaptive Invulnerability Field (diminished)) (1 - 0.25 * 0.8691) = 0.289 or 71%

Kinetic

0.6 * 0.925 * 0.75 = 0.416 or 58%

Explosive

65%

Three Adaptive Invulnerability Fields, due to diminishing returns would provide much lower EM and Thermal (38% and 50%) with only a 63% kinetic resistance.