# Shield and armor as a partial protection

This proposal aims at making the dual shield and armor tanking viable, while also reducing the effectiveness of one-layer tanks and allow to hull tank.

Basically, no defensive layer (armor, shield) protects the hull from 100% damage. The bigger the layer the more damage is absorbed, and the bigger the incoming damage, the lower the part of damage is absorbed.

There are two models : a base one that is more complicated, but maybe more fair, and a simplified one. In the simplified one, shield does not protect armor ; in the complicated one, shield protect hull and armor, armor protects hull only.

## Base model

### Formula

Considering a damage ds of a given type (does not matter which) reaches the shield of a ship with shield s, shield resonnance rs ; with armor point a, armor resonance rr ; with hull resonnance rh ; then

- the shield absorbs ds × s / (ds+s) damage, then reduced by its resonance ; the rest, that is da = ds × ds / (ds+s) passes through the shield towards the armor
- the armor absorbs da × a /(da+a) damage, then reduced by its resonance ; the rest, that is dh = da × da / (da + a) passes through the armor towards the hull
- the hull takes dh , then reduced by its resonance.

### Example

Considering a ship with 1000 points in shield, armor, hull, and 0.5 resonance (-50% to all resists).

considering an incoming shot of 100 damage.

- the shield absorbs 100×1000 / 1100 = 90.9 damage, which are then reduced by resonance so the shield loss is 45.45 , 9.1 go through
- the armor absorbs 9.1×1000 / 1009.1 = 9.02 damage, again reduced by resonance so armor loss is 4.51
- the hull take the remaining 0.092 damage, reduced by resonance so hull damage is 0.046

Second damage instance of the group

- the shield absorbs 100×954 / 1054 = 90.5 damage, which are then reduced by resonance so the shield loss is 45.25, 9.5 go through
- the armor absorbs 9.5×995.5 / 1005 = 9.4 damage, again reduced by resonance so armor loss is 4.7
- the hull take the remaining 0.1 damage, reduced by resonance so hull damage is 0.05

## Simplified model

This simplifies the damage application as all the computations are made in a single pass. However more damage is redirected to the hull.

### Formula

Each part of damage absorbed by a layer is equal to layer_hp/(damage+shield+armor).

- shield loses d ×s / (d+s+a) × rs
- armor loses d ×a / (d+s+a) × ra
- hull loses d ×d / (d+s+a) × rh

We can factor the d / (d+s+a) as *shared*, then layers take *shared* × hp × resonance as damage, hull takes *shared* ×d×resonance…

### Example

incoming 100 damage, 1000 hp shield/armor, 0.5 resonance everywhere

- first hit removes 100×1000/(100+1000+1000)×0.5 = 23.81 hp to shield and armor, 100×100 / /(100+1000+1000)×0.5 = 2.38 damage to hull.

Google sheet helps makes the simulation

#### 8 shots of 100 damage

That’s basically what happens when a 8-guns ships shoots at that target.

hit | 1.00 | 2.00 | 3.00 | 4.00 | 5.00 | 6.00 | 7.00 | 8.00 | |
---|---|---|---|---|---|---|---|---|---|

incoming damage | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | |

shield hp | 1000.00 | 976.19 | 952.41 | 928.66 | 904.93 | 881.24 | 857.58 | 833.96 | 810.38 |

armor hp | 1000.00 | 976.19 | 952.41 | 928.66 | 904.93 | 881.24 | 857.58 | 833.96 | 810.38 |

hull hp | 1000.00 | 997.62 | 995.18 | 992.69 | 990.13 | 987.52 | 984.83 | 982.08 | 979.25 |

shared | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.06 | 0.06 | |

shield damage | 23.81 | 23.78 | 23.75 | 23.72 | 23.69 | 23.66 | 23.62 | 23.59 | |

armor damage | 23.81 | 23.78 | 23.75 | 23.72 | 23.69 | 23.66 | 23.62 | 23.59 | |

hull damage | 2.38 | 2.44 | 2.49 | 2.55 | 2.62 | 2.68 | 2.75 | 2.83 |

Most of the damage (379 / 400 ) is soaked by the two defense layers

#### 2 shots of 400 damage

hit | 1.00 | 2.00 | |
---|---|---|---|

incoming damage | 400.00 | 400.00 | |

shield hp | 1000.00 | 916.67 | 834.58 |

armor hp | 1000.00 | 916.67 | 834.58 |

hull hp | 1000.00 | 966.67 | 930.85 |

shared | 0.17 | 0.18 | |

shield damage | 83.33 | 82.09 | |

armor damage | 83.33 | 82.09 | |

hull damage | 33.33 | 35.82 |

Here 330 out of 400 damage is into layers.

#### 1 shot of 800 damage

hit | 1.00 | |
---|---|---|

incoming damage | 800.00 | |

shield hp | 1000.00 | 857.14 |

armor hp | 1000.00 | 857.14 |

hull hp | 1000.00 | 885.71 |

shared | 0.29 | |

shield damage | 142.86 | |

armor damage | 142.86 | |

hull damage | 114.29 |

Here 285 / 400 damage are absorbed by layers.

#### Analyzis

The more shots used to apply the same damage, the less % is applied ot the hull. Is it good or bad ? We can always make up justifications later, that what rational means.

What it means is that a high variance makes it more possible to do good damage to the hull.

#### One shot

If a target is one-shot (by a single damage instance) it means that the damage applied to hull and multiplied by resonance, equals the hull hitpoints h :

d × d / (a+s+d) × r = h

=> d² -hd/r -h(a+s)/r=0

The solution is d = h/2r + sqrt( (h/2r)² + h(a+s)/r ). With 0 shield and 0 armor it becomes d= h/2r + h/2r = h/r = hull EHP. With e = h/r this becomes d = e/2 + sqrt( (e/2)² + e×(a+s) ) = e/2 + sqrt( e×(e/4 + a+s) )

## Layer regen

Since it’s not possible to fully protect one’s hull, it needs to gain some regen. I propose a constant armor and hull recharge rate, that is layer_max/recharge_time, with an armor recharge time of 240s for s, 360s for m, 540s for L, 810s for XL ; and triple that for hull recharge time.

This is mere number. Remember that the base value for shield is divided by 2.5 and then again reduced by skills.

### Stability

Assuming a layer takes ONE hit with ONE damage type every second, with resonance r, it remains stable if the damage taken by that layer is equals to the regen in one second. regen is then d× h / (d+h+other_layer_hp) × r .