Resilience
Resilience is a defensive stat that is generated when you are targeted by Black Ops during a war. It decreases the amount of damage taken from those Black Ops.
Generating Resilience and Formula
Resilience is generated only when you are successfully targeted by a Black Op. There are two kinds of Resilience: Spy and Wizard, each corresponding to the type of op that you took damage from. The amount of resilience gained depends on what you are targeted by. Spy resilience is generated at 8 resilience per successful op. Wizard resilience is generated at 11 resilience per successful op. These numbers are not modified by anything in the game, and always decay at the same rate: 8 resilience per tick elapsed. Additionally, if the op failed, i.e. the spies were caught or the spell was repelled, then no resilience is gained, nor do you gain any when you use Energy Mirror to reflect a spell back to sender. You also need to receive actual damage in order to gain resilience. Having your non-existent boats sabotaged gains no Spy resilience.
This resilience value is then put into a formula to determine the exact damage reduction acquired. The formula is as follows: 0.5 * (1 + erf(0.00226 * (RESILIENCE_VALUE - 770)))1. Additionally, at 0 resilience, there is never any damage reduction. Resilience itself is capped at 1000, leading to a 76.89% damage reduction in total. However, the damage decrease is not linear, and the first ops will see a barely noticeable decrease. If the barrage is kept up, however, then resilience starts decreasing more and more of the damage dealt. This allows the affected Dominion to start climbing out of the hole they have been thrown in and disincentivises other realms from dogpiling onto the target with the same type of Black Op.
Resilience Values and Damage Reduction
| Resilience Amount | Damage Reduction |
|---|---|
| 0 | 0% |
| 100 | 1.61% |
| 200 | 3.42% |
| 300 | 6.65% |
| 400 | 11.85% |
| 500 | 19.41% |
| 600 | 29.34% |
| 700 | 41.15% |
| 800 | 53.82% |
| 900 | 66.11% |
| 1000 | 76.89% |
This value is multiplicative with other decreases, such as the Towers Improvement.
Damage Reduction example
The following table shows the effect of resilience. It is a very simple set-up: if all ops are done in a single hour, what damage would be taken without resilience and with resilience? For this example, the Sabotage Boats op will be used: this normally sinks 2.25% of all boats that are not protected by Docks or the Harbour improvement. The third column shows what damage would have been done without resilience, whereas the fourth column shows the damage done with resilience in play.
| Amount of ops done | Resilience | Boats left w/o resilience | Boats left w/ resilience |
|---|---|---|---|
| 0 | 0 | 100% | 100% |
| 20 | 160 | 63.44% | 63.87% |
| 40 | 320 | 40.24% | 41.38% |
| 60 | 480 | 25.53% | 27.71% |
| 80 | 640 | 16.19% | 19.71% |
| 100 | 800 | 10.27% | 15.25% |
As you can see, the relative reduction of resilience only starts being a noticeable factor after the target has received a bunch of ops already. Resilience will not, and is not meant to, allow someone to run bad ratios and get away with it. It does, however, allow for faster recovery if the attacking realm tries to drive someone into the ground.
References
1 Erf is the Gauss Error function.