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 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 10 resilience per successful op. Wizard resilience is generated at 12 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.
The amount of resilience is then put into a formula to determine the exact damage reduction. The formula is as follows: 0.5 * (1 + erf(0.0019 * (RESILIENCE_VALUE - 700)))1, and 0 resilience means no damage reduction. Resilience itself is capped at 1000, leading to a maximum reduction of 78.99%. The damage decrease is not linear with the amount of resilience. The first ops will see a barely noticeable decrease, but as resilience increases, the decrease becomes larger and larger. 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 in a very simple set-up. All ops in this example are done in a single hour, and the Sabotage Boats op is used. This normally sinks 2.4% of all boats that are not protected by Docks or the Harbour improvement, and because it's a Spy Black Op, every success adds 8 resilience. The third column shows what damage would have been done without resilience, whereas the fourth column shows the damage done with resilience damage reduction applied.
| Amount of successful ops | Resilience | Unprotected boats left w/o resilience | Unprotected 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% |
The relative reduction of resilience only starts being a noticeable factor after the target has been hit by 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.