However, the gain is also determined by the number of wounds (the bigger the wounds, the bigger the gain).
So I did some work to see how these stats manipulate the battle shock result, to get a good understanding of what makes a good defensive unit, or a poor one.
Battle shock test
We can break this test down to the following formula.
models fleeing = models lost + roll - bravery
Based on this, we work out how much damage is required to make 1 model flee.
1 flee = damage/wounds + roll - bravery
Expressed in terms of wounds
wounds = (damage/wounds + roll - bravery) * wounds
wounds = damage + roll * wounds - bravery * wounds
damage = (bravery - roll + 1) * wounds
This expression tells us how much damage we need to do (or can handle) until we start losing models. A unit with 2 wounds per model, bravery 4 and a shock roll of 3 loses a model after 4 wounds have been dealt.
The value of bravery and wounds
Now we can check the value of our attributes, using partial derivation:
value_bravery = wounds
value_wounds = bravery - roll + 1
We notice that bravery is as valuable as the number of wounds. Indeed, if we continue our example, the same unit (2 wounds, shock roll of 3) with 5 bravery would need an additional 2 wounds taken before it loses a model in the test. And for a roll of 3, bravery of 4, the unit with 3 wounds instead of 2 would require 4-3+1=2 more damage to lose a model in the test.
While this all seems trivial, this gives us two very important factors.
Bravery * wounds = defense score
Imagine for a moment, that we wouldn't have to roll in the battle shock phase. We'd have the following formula:
models fleeing = models lost - bravery
Or:
damage = (bravery + 1) * wounds
And:
value_bravery = wounds
value_wounds = bravery + 1
This shows that for every point in wounds, the value of bravery increases by 1 point and the other way around. As is apparent in the damage formula: bravery and wounds are being multiplied. This is a common sight in game mechanics, and it has an important effect: they multiply each other's value which dramatically increases their power when combined.
It's worth keep an eye out for that.
For example, the damage required to make a model flee on a roll of 3 in a unit with 4 bravery and 4 wounds is:
damage
= (4-3+1) * 4
= 8
A unit with 6 wounds and 6 bravery, can take a whole lot more:
damage
= (6-3+1) * 6
= 24
While the attributes have only increased by 2 on each side, there is a spectacular increase in resilience: we needed 3 times the damage for 1 model to flee with the same flee roll.
Of course there are fineries to the formula. The point I'm trying to make is to look at the combination (multiplication) of these two stats, and not just their values individually.
Roll vs wounds
We take another look at the value of the wound attribute:
value_wounds = bravery - roll + 1
We can see that the roll can affect the value of wounds negatively. The flee result counts the number of models that run away, not the number of additional wounds. A model with a higher wound count is a bigger loss than a model with a lower wound count, in terms of damage dealing or defense anyway. This probably jumped to many people's mind when they read the battle shock rule: it makes you lose models, which could be handy against multiwound models.
This expression above formalizes that and the benefit of getting such a unit to test increases with every wound the models have.
Conclusion: wounds are powerful multipliers of a unit's resilience, but they introduce a weakness to the roll of a battle shock.
Instability! High wounds, low bravery
We already concluded that the multiplication of bravery and wounds can ramp up the damage a unit has to take before losing additional models. But we also indicated that wounds increase a weakness to the battle shock (well.. it increases the benefit of making a unit fail its test). Bravery is the shield against that roll but once the test goes foul the unit could be losing a lot of wounds very quickly.
What we seem to get is instability for models with high wound counts and low bravery. Without the bravery to protect them against the roll, once a model goes down it could lead to a disastrous effect.
They key trick is then to tackle that bravery and get them to test. The test could be aided by either a combat buff, or simply by damaging one model with magic and shooting before jumping in.
It looks like this is the new form of instability that can pop a unit quickly.
A few examples
The formula we need:
damage = (bravery - roll + 1) * wounds
- Trolls, 5 bravery, 4 wounds, 3+ roll: 12 wounds required.
- Trolls, 5 bravery, 4 wounds, 4+ roll: 8 wounds required.
- Trolls, 5 bravery, 4 wounds, 5+ roll: 4 wounds required. (see the instablity?)
- Night Goblin, 4 bravery, 1 wounds, 2+ roll: 3 wounds required.
- Night Goblin, 4 bravery, 1 wounds, 3+ roll: 2 wounds required.
- Night Goblin, 4 bravery, 1 wounds, 4+ roll: 1 wounds required.
- Liberators or Dark Riders, 6 bravery, 2 wounds, 3+ roll: 8 wounds required.
- Liberators or Dark Riders, 6 bravery, 2 wounds, 4+ roll: 6 wounds required.
- Liberators or Dark Riders, 6 bravery, 2 wounds, 5+ roll: 4 wounds required.
- Cold One Chariots, 7 bravery, 6 wounds, 3+ roll: 30 wounds required.
- Cold One Chariots, 7 bravery, 6 wounds, 4+ roll: 24 wounds required.
- Cold One Chariots, 7 bravery, 6 wounds, 5+ roll: 18 wounds required. Notice the strong increase in required wounds.
Countering high wounds, damage in advance
According to the rules, right now, it's possible to damage a unit with a spell or shooting before charging in that unit in the same round. This could be used as a mechanic to make a single model die quickly.
On high wound models, this could significantly improve your odds of damaging the unit through battle shock. Though... my numbers show this is only very effective against units with a lower bravery.
Round up of conclusions
Based on this theory hammering, I think it's important to look at the wounds and bravery together. They show a synergy in the resilience of a unit against the battle shock testing.
- Bravery is the shield to survive the test roll.
- Wounds makes it harder to modify that roll
- Wounds also create a "desire" to score wounds through battle shock
- A low bravery and high wound count can make a unit unstable.
- When trying to get an indication of a unit's resilience to battle shock know that wounds and bravery don't add up but multiply instead.
- A rule of thumb for a unit's resilience to battle shock: (bravery - 3) * wounds, which is more or less 50% chance to pop one model.
- Models with high bravery and a notable number of wounds are incredibly resilient to battle shock.
More number munching!