Saturday 26 December 2015

The Count

Most people do it. They do it in private, of course, although the results are often blazoned in public across the internet. It is a very personal thing. Perhaps we should keep it quiet, but part of being human is to make the private public. Otherwise, there would not be so many salacious stories eagerly snapped up by a public that just cannot get enough of private stories.

This is, it seems, as good a time as any to go public. The dark and storm of winter (unless you are in the southern hemisphere, of course) lends itself to introspection, to doing things in private that would not be dreamt of in summer.

I refer, of course, to the phenomenon we observe on many wargame blogs to counting what we have painted during the previous year. One problem I face is that I cannot really remember, but, ignoring that fact with dignity, here is the count.

I think I started the year with these. I vaguely remember painting more pike men than I believed possible, so it must be them. A total of 29 bases, by my reckoning, of which 12 are pike. 192 pike men, 60 heavy cavalry, 16 Galatians, 12 light cavalry and four elephants. An opening total of 284 figures.

I found a couple of hoplite strips lurking, and, as I had just run out of hoplites for a campaign battle, painted them. Two bases, sixteen figures. A total of 31 bases and 300 figures.

I also ran out of officer markers during the battle, and so painted another boxful. Twelve figures, twelve bases, giving a running total of 43 bases and 312 figures. I also needed some new sorts of markers, and, after an appeal to the collective wisdom of the blog, made 8 bases thereof, so a total of 51 bases, but I won’t claim any figures for that.

The campaign is looking like it will need a Thracian army. Now I have Thracians as components of other armies, but I needed to create a few more, so nine bases, eight as dense and one as light peltasts, so 68 figures on nine bases. 380 figures and 60 bases.

Strange as it might seem, I do not have a painted army of Moors. I have had the figure for ages and ages, but not painted them. This is now being rectified. So far, 23 bases have been painted (but the basing is incomplete). 43 light cavalry, 48 light infantry on 23 bases so far. I realise that the numbers do not work, one of the cavalry bases is waiting for an extra figure from the next batch to make up the numbers.

So work in progress is some more Moors, but the total so far is 471 figures on 83 bases. That is quite a lot more than I would have thought. Mind you, there are a lot of pike men there.

On the downside, of course, as wargamers we cannot help but obtain more figures. I have not done too badly for that this year, having only acquired 45 cavalry, 96 infantry and two extra elephants. These are all for the Moorish armies, as the Moors will be the first army which has been immediately doubled. That is a  total of 143 figures, leaving me with a net gain of 328 figures over my lead pile.

Mind you, that lead pile is still fairly substantial, consisting in a few odds and ends, plus Spanish, Parthian, Sarmatian and Pontic armies demanding to be doubled, a pile of early Persians claiming to be part of the doubling of them, and doubtless a few other things needing painting.

Plus, of course, my buildings project, which has acquired another 5 building to its unpainted pile and I’m not sure that I painted any this year, so that is not looking good. And finally is that fact that Santa has delivered 150 ancient galleys. Now I need to work out what I am going to do with them….

And a very happy thingumabob to you.

Saturday 5 December 2015

Events and Probabilities

Insofar as there is ever a theme in blog posts, there has been a bit of a trundle around ways of conceptualising, or at least considering, the shape of rules. Firstly, I noted perturbation theory, the rather pretentious name I assigned to the idea that units, in battle, are slowly reduced in capacity until they run away. Secondly, I considered a crisis sort of rule, in that a unit can crumble immediately a threat is perceived.

As has been observed in some of the comments, the outcome for a unit is more than a function of simply shooting and being shot at, and the ratio between the two. While casualties may have some impact, perhaps more important is command and control within the unit, and this includes the ability of lesser commanders, or even ordinary soldiers, to take control at a point of crisis.

The modern wargame rule set, however, tends to focus on the unit as a whole.  The argument is that a general would not know that the Grenadiers have just had their colonel wounded and that the major is taking over command. He might note that the unit is hesitating, slowing in its advance or whatever, but the cause would be opaque to him. He might just mutter ‘Tell the Grenadiers to get on with it’ to an ADC and then turn to other matters.

This sort of approach leads us to consider much more widely the statistics of battles, and here we hit a snag. There are many reasons why a unit might hesitate. A disruption to the chain of command is just one of them. So far as the general is concerned, a unit hesitating in its advance is an event, and that event might be replicated in many other units across the army. The cause of the event, on this model, is irrelevant and unknown by the observer.

However, if we focus in more closely on the unit and what is happening to it in detail, we can say that the event of the colonel being wounded is a specific thing. On this, more detailed, look, the chance of the poor chap being hit would be, at least to some extent, more calculable. We could consider the colonel in his recognisable uniform, and ponder the efficacy of skirmishers sniping. We could classify the density of shooting incoming to the unit, and calculate the chance of any individual being hit. And so on. I am not suggesting that we could, in fact, do this calculation, but we could possibly come up with something plausible.

If we stick with the more global view, however, we have to simply try to work out the probability of a unit hesitating, whatever the root cause might be. Here, we have a problem, because we simply do not have the data required. An event is an event. Its cause is a unique set of circumstances, hidden to us as observers.

In theory (if not in practice) we can calculate the portability of an event happening. We could do this by observing how often a unit in an army does hesitate, and work from there. I have, of course, no idea what the outcome of that might be, but suppose we come up with a number that states that one fifth of the units in an army will hesitate once in a four hour battle. Or, put another way, one twentieth of the units will hesitate per hour.

Now, there are two problems, at least, jumping out here. The first is the difference between the set of events and the ideal probabilities I have just stated. If the process is statistical, then there will be fluctuations away from the ideal probabilities. The only way to try to cure this is by increasing the number of tests. We know that the ideal probability of tails in a coin toss is ½. Even if we make 5,000 such coin tosses, we will not land up with exactly 2,500 tails. If we were seeking to define the ideal probability from the empirical results, we would land up with strange probabilities.

Of course, we are not so naïve. We can work out the possibilities and proceed from there. But in a battle, or even in all the battles in history, there are not, I suspect sufficient unit histories to define a probability of hesitation. We might be able to say that units seem to hesitate with a probability of one in twenty per hour, but that is not necessarily helpful. Along the same lines, we might be able to say that infantry squares were broken twice in the Napoleonic wars, but that is rather hamstrung by the issue that we do not know how many times squares were charged. We have no idea how frequently squares were charged, and so can make no stab at the probability of the square collapsing. In short, we cannot approach the ideal probability, because we do not have sufficient evidence.

Ideally, of course, we would work out the ideal frequency and use that, with suitable fluctuations, in wargame rules. If we could suggest that ‘a unit under fire will hesitate one time in twenty’ then we can roll a die and get on with it. The sort of calculation made tends towards the unrealistic, in that firing a musket one hundred times at a battalion sized sheet might give us some interesting data of ‘accuracy’, but it takes little account of the (average) battlefield conditions, where what is important to most people is not getting hit yourself. While these sorts of experiment might provide a useful upper limit, it is only that – no more than (say) eighty per cent efficacy.

So statistical ideas are necessary to wargame rules, but their application is by no means as simple as we would like. We can, only to some extent, monitor events. We can try to classify events, although, of course, that classification depends on what we are doing and the level of detail we are interested in. but we do not seem to be able to access the ideal probabilities, unless we persuade the world to have a lot more battles and that is almost certainly a bad idea.