# Eve Math

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
 This article should be cleaned up or improved. The reason is: This page needs to be merged into pages dealing with each concept separately.

This page teaches basic understanding of some important calculations in EVE and how they affect you.

## Ship Fitting

In EVE, there are two types of modifiers.

1. Flat modifiers are added directly to whatever stat they affect. For example, 1600mm Steel Plates I increases armor by 3500.
2. Percent modifiers multiply the stat they affect. For example, Hull Upgrades IV gives a 20% bonus to armor (or, more precisely, multiplies armor by 1.2).

### Basic Bonuses

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.

When percent modifiers combine, they multiply by each other. For example, Hull Upgrades IV gives +20% armor and a Layered Plating II module gives +8% armor. This doesn't give +28% armor, but instead:

20% + 8% + (20% of 8%) = 29.6%

As noted above, percentages are really just multipliers. For example, +20% is a 1.2 multiplier, and +8% is a 1.08 multiplier. This changes the above formula into:

1.2 × 1.08 = 1.296

As an example, lets take a look at the Harbinger with a 1600mm Steel Plates I, Hull Upgrades IV and a Layered Plating II. The base armor for the Harbinger is 5250. The plate gives 3500 more armor and, as we saw above, Hull Upgrades IV gives a 1.2 multiplier and layered plating a 1.08 multiplier.

Total Armor = (5250 + 3500) × 1.2 × 1.08 = 8750 × 1.296 = 11340

So the Harbinger will end up with 11,340 HP of armor.

### Basic Reductions

Some reductions are actually bonuses. Two 25% reductions make a 44% reduction. Two 50% reductions make a 75% reduction. One big reduction is better than lots of small ones.

Again, like bonuses, reductions are best thought of as multipliers. For example, a 25% reduction is a 0.75 multiplier.

### Stacking Penalties

Main article: Stacking penalties

Stacking Penalties, also known as diminishing returns, keeps players from applying many bonuses to the same stat. Stacking penalties apply only to modules and rigs. Skills and Ship Bonuses/Penalties always have full effect.

The biggest modifier from a module always gives its full effect to a stat; the next-biggest modifier has a somewhat reduced effect; the third-biggest modifier has a greatly reduced effect, and so on:

• 1st = Fully effective (100%)
• 2nd ≈ 87% effectiveness
• 3rd ≈ 57% effectiveness
• 4th ≈ 28% effectiveness
• 5th ≈ 10% effectiveness
• 6th ≈ 3% effectiveness

These are described by the following function, where n is 1 for the first module, 2 for the second module, etc.:

Effectiveness = 0.5(0.45(n−1))2

This effect means that it usually doesn't make sense to fit more than three modules which improve any one attribute. For example, a Ballistic Control System I increases missile damage by 7%. The first module fit to a ship gives the full bonus, but the second will only give an additional 7% × 87% = 6.1% bonus, and the third 7% × 57% = 2.8%.

As the biggest modifiers take the smallest stacking penalties, 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.

Almost all modules that boost or penalize a stat affected by stacking penalties will say so in their description: "Penalty: Using more than one type of this module, or similar modules that affect the same..."

Stacking penalties 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 penalties 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 incoming damage by 25%. If the ship has 20% thermal resistance already, then you need to multiply the penalties 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 penalty. The stacking penalty 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, an EM Ward Field I, a Thermal Dissipation Field I, and a Damage Control I would have the following.

EM: (base) 1.0 × (DCU) 0.925 × (EM Ward Field) 0.5 × (Adaptive Invulnerability Field (diminished)) (1 − 0.25 × 0.8691) = 0.361, or 64%
Thermal: (base) 0.8 × (DCU) 0.925 × (Thermal 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.