I have often mentioned that what
we have in a set of wargame rules is a set of models. These cover such things
as movement, ranged combat, close combat and morale. Each of these models can
be well founded, based on empirical data and so on. I am sure I have commented
on what exactly that might mean in the past, and how, in fact, fudge factors
have to be introduced because, for example, men under fire take longer to
spread out into a line, or do not, themselves, fire as accurately (or even, at
all) as those who are not, or who are in parade ground situations.

Perhaps the interesting thing is
how the models interact, however. The situation being modelled is not that of a
specific model but of a set thereof. A model of movement, for example, can be
modified by a model of firing. If the soldiers moving come under fire, then we
expect that, in some sense, that will affect how the movement is carried out,
potentially at least.

In practice, of course, we have modifiers
and reaction tests. If a unit is moving and come under fire, we might apply a
reaction test to it. We sum up the various external and internal factors such
as surprise, cohesion, and training, cover and so on, roll dice and reach some
sort of conclusion. The firing model has interacted with the movement one. As
another example, many rule sets state that some troops can move half a full
move and fire. Again, one model has changed another. Similarly, we might assess
the damage from combat as being more than one man per figure (I think that was
a Tercio thing) and make a forced morale check on that basis. In that case the
combat model and the morale model have interacted and modified each other. It
can work the other way around, as well. A morale failure can mean that a unit
recoils and hence, if reengaged by their opponents, then fights at a
disadvantage.

I think that there is a little
bit of a problem for the unwary rule writer here, however. Our models can conflict,
and hence we can arrive at odd situations. I am sure we have all seen them on
the table. A rather shaky D class regiment of new recruits sees off two
regiments of superb cavalry in short order. We shake our heads and mutter ‘these
things happen’ and get on with winning the battle by other means. What has
happened is that a combination of a morale model and a combat model has given
some low probability event; somehow the models have conspired against the
normal course of events.

In a sense this is not a problem.
I dare say we could find examples all over history where unreliable troops have
performed well above expectations. But it is as well to be aware of what is
happening here. The models are throwing up low probability events. It is a bit
like the interminable arguments over breaking squares in Napoleonic wargames. It
did happen, but not very often, and our models probably make it too probable.

One way of looking at how models
interact is using perturbation theory. This is a quintessential physics
viewpoint. It arises when we want to model something a bit more complex than
the normal. We can solve, for example, the quantum mechanical equations for a
particle in a box, or a hydrogen atom in a vacuum. That we, we can write down a
mathematical equation for the electron in a potential well produced by a
proton, and solve it. The solution gives us a set of waves, of states in which
the electron can exist.

We would like to solve more
complex problems, however; for example, a hydrogen atom in an electric field.
Unfortunately, we cannot write down the Schrodinger equation for this and solve
it. The mathematics does not work out easily. So what we can do is treat the
electric field as a small correction to the already known solutions for the
atom in a vacuum. This is fine, so long as the electric field is fairly weak.

I won’t bore you with all the
mathematical bits of how this is solved, but the upshot of it is that the extra
bit, the perturbing field, mixes the solutions we found before. That is, instead
of being in a pure state, say state 1, as a given solution, the electron in the
hydrogen atom is in a mixed state, a bit of state 1 plus a bit of state 2.
Given that normalisation is upheld in this (that is, the electron has to be
somewhere) we can see that the application of the electric field could force
the electron to shift from state 1 to state 2; the probability of this is given
by the ratio of the ‘bits’ of each state the perturbed electron has access to.

Thus the electron can jump from
one state to another by the application of an electric field. Classically, we
would say that it gained energy from the field (or lost it, it can go the other
way), but quantum mechanically, I hope you can see that it is a bit more complex
than that. Nevertheless, its application to wargame rules is, I hope, fairly
clear. The models perturb each other, and we need to be specific as to how that
happens, and clear as to which models can modify which other models.

The thing is, I think, that if we
do not do this modification clearly, we can end up with situations where one
model tells us something (for example the combat model says ‘run away’) while
another model tells us something else (for example ‘stand firm’). We need to be
clear as to which model takes precedence. In Polemos: SPQR it is the combat
model. In older rule sets, as I recall, it was the morale model.

I am not saying that one is
better or worse than another, but we do need to be clear as to which model is
the perturber, and which the basis. And of course, what we have here is weak
interaction of the models. This leads to a slow evolution of the states of our
units. Another approach is via catastrophe, but that is another story.

Pertubation theory and wargame design; marvelous!

ReplyDeleteRather than physics, my own thoughts on this topic stem from statistics and forecasting where the model(s) contain a fixed (or deterministic) component and a random (or unexplained) component. The random component must adhere to a strict set of assumptions. Violate these assumptions and the model loses its ability to forecast reasonably. Mis-specify the model and the relatively small random component can dominate the deterministic component and the tail can wag the dog. Not a desired outcome for a wargame in my mind so care must be taken to properly specify any model.

I think that the perturbation model of a wargame system is not incompatible with a statistical approach, because the perturbing field can be 'random', and its effects determined by probability. One step at a time, though, I think.

Deletethe other impact is of chance and necessity: stuff happens necessarily (I let go of my pen and it falls to the ground) but chance is contained within a envelope of possibility. I think I mentioned before that we started Polemos using 10 sided die. the results were exactly as you describe - wild. So we reverted to 6 sided die and a degree of sanity was restored.