Erfworld 139 The Battle for Gobwin Knob, Page 126

[Tubercular Ox]

We have no idea how the combat stats determine combat or how bonuses affects those stats, as the authors haven't given us any real details in that area. We don't know if the bonuses add strength to the unit, multiply existing strength, or something like adding a bonus to the "dice rolls" or some wierd combination...

Actually, we know more than you think. Enough to create a scale:

1. Doombats.
2. Basic infantry.
3. Advanced infantry.
4. Heavy infantry.

The absolute values between these four ranks can be as whacked as Moh's Hardness, but the conclusions we can draw are the same. Just to drive this point home, just look at that scale: 1-3 are linear, but 4 is weaker than you would expect, which is okay because 5 is more than you would expect. 5-7 is linear, but at a smaller slope than 1-3, and 7-10 suddenly turns exponential.

So we don't know what exactly leadership bonuses do, but at least two of us feel like they seem additive. Let's go ahead and make them additive on the Erf's Hardness scale above. Even if the jump from 1-4 is exponential, we can pretend we're taking the logarithm and consider the bonuses additive anyways. So Warlord bonus is +1a, Chief Warlord bonus is +1b, and in-stack bonus is +1c. We're calling them all +1 even if the actual values are different; it doesn't matter for the demonstration.

Now, apply this to one bat and it is simply additive. Apply it to 100 bats and it is multiplicative, like the Magic the Gathering bonus above. In fact, if all you have is one soldier and a pile of additive bonuses to that soldier, suddenly more soldiers start to look multiplicative in the same way bonuses look multiplicative when all you have are a bunch of soldiers. As I suggested above, power is a function of "area," and area is additive troops x additive bonuses. Even if levels of troop strength is exponential; even if (because of the stack bonus) number of troops is exponential. Even if level of troop strength is logarithmic, even if number of troops is logarithmic! In the extreme example of one curve being exponential and the other curve being logarithmic, there is still an optimal point between the two scales that makes increasing the length and breadth together more attractive than increasing either one individually. It just makes the calculus more exciting. The area will always advance faster than the length of the two sides. THAT is the multiplicative bonus. The rest is semantics.

As long as Ansom relies solely on massive numbers of troops and does not consider bonuses, he is falling behind. Yes, Parson is trying to stack multiple bonuses onto his troops, but through Uncroaking, he is planning to add to his troop numbers as well.

Personally I think troop strength is a logarithmic scale, or at least capped. As Ansom's fight on the walls shows, there's a limit to the number of troops that can attack at once... if all 1000 uncroaked piled into a super stack had a shot at Ansom, he'd be a goner. But certainly more than the one uncroaked the flying Ansom has chosen to engage can attack, so Ansom is attacking a stack as a whole. The first 8 troops in a stack are the steep end of the logarithmic scale, and every troop after that is the gentle end of the curve, up to the cap of the max number of troops that can attack at once, past which more troops only serve to increase the stack's ability to soak losses.

The strength curve per unit? Clueless, totally clueless. Although Parson's excitement at the "multiplicative" nature suggests a power curve or even an exponential curve.

In fact, this alone may explain the preference for multiple stacks. Number of stacks may be a third dimension orthogonal to unit strength and unit count, adding another balancing factor where there is a point that adding a second stack is more powerful than just one huge stack, even if the huge stack would theoretically have a higher length and breadth. Number of stacks would let your strength go up with the cube, whereas the super stack only goes up in strength with the square.