Representing unit damage and status

One of the challenges in miniature wargames (or really in any game) is how to record the game state. A game is in essence a manipulation of a lot of resources (tokens, cards, points, money, ...), and the state of the game at any given point should be unambiguously clear for the player who needs to access that information.

In a miniature wargame, we often play with units represented by a number of miniatures. The position of the unit on the battlefield is one part of the gamestate, and that is often recorded or made clear by putting the unit on its intended location. Another important aspect is the complete status (combat strength, morale, attributes, ...) of the unit, and this needs to be recorded as well.

In this post, I will not focus on the innate characteristics of a unit, but rather on its changing status during the course of the game as a result of being involved in combat and taking damage. How do we keep track of the unit's changing status, and are there elegant and less elegant ways to do it?

Figure removal

The oldest procedure of recording casualties as a result of combat is simply to remove the figures. This works well when you use individually-based figures. The number of figures in the unit indicates its strength, and when a unit takes a "hit", one figure is removed. 

The advantage of figure removal is that it's immediately visually obvious how "strong" a unit still is, or how much damage it can still sustain. On the other hand, the "footprint" of the unit (the actual area the unit occupies on the table) is gradually reduced. Sometimes this is a desired effect in the rules, sometimes it is not. Another disadvantage is that figures are removed from the table, which is a bit strange since we have spent so much time and money in painting and buying those figures.

Figure removal also requires a "holding space" next to the table so casualties can be put away. Depending on your table setup, this might or might not be very practical.

Grouping figures in stands (with a unit being multiple stands), and removing stands, is a variant of figure removal.

Recording hits and losses

Another method - also very old - is simply to record the losses on a piece of paper. Once a certain amount of losses is reached, the unit loses some abilities or is destroyed. Although this might seem trivial, it actually is a method with far-ranging consequences, since it decouples the visual representation of the unit with its current status, therefore allowing for more flexibility in combat resolution procedures.

In older wargaming books (e.g. How to Play with Toy Soldiers, Joe Morschauser) this system is sometimes referred to as the "roster system", the roster being a series of boxes that are ticked off as the unit takes hits. The recording can also be in numerical format, of course.

The original roster system described, in "How to Play with Toy Soldiers", by Joe Morschauser.

An advantage is that the entire unit can be kept on the table (visually very attractive), a disadvantage is that we have introduced a separate gaming procedure, and some bookkeeping. Depending on the level of detail, such bookkeeping can become cumbersome.

Markers

There are other numbers as well that needs to be tracked besides casualties or hits, such as morale, or other status indicators. Either we can record this on paper, or use some sort of markers

Markers come in all sorts of variants and sizes: markers containing text, numbers (or replace them with dice), dials, coloured beads, etc ...

In the figure below you see a number of markers I use for my own games. The exact type used in any particular game is dependent on the period and the visuals of the figures and terrain, since I feel that markers should not dominate the battlefield.

A selection of markers I use in my own games, often plundered from boardgames. Coloured glass beads are useful, as are dials. For some reason, the dials show an ugly gluemark in this photo, barely visible in reality ...

Useful markers: Coloured pawns and playpieces, and wooden chips.

Figure poses

A less well-known method is to use the poses of figures as an indication of various stats of the unit. In the photograph below the number of officers (2) indicate command rating, the number of men firing (4) indicate fire power, the number of men walking (5) indicate a movement characteristic, and the number of men advancing indicating morale (3). These figures are adjusted in numbers to reflect the changing status of the unit, and filler figures (men kneeling) are used to keep the total number of figures of the unit a constant.

A unit of the French Foreign Legion (Woodens flats).

The drawback is obvious: too much fiddling with figures, and a need for duplicate figures. Also, the number of figures needs to be linked directly to rule mechanisms, e.g. to roll a D6 vs a target number given by the numbers of figures in a certain pose.

On the other hand, the status of a unit can be read visually from the figures.

A more feasible variant is to use the pose of a figure in skirmish games. When an individual soldiers changes status, the figure is changed as well. I used this mechanic in our Marche ou Crève convention game, with the sequence of various status updates for a single figure shown below. Figures on the left got a "+1" on die rolls, the middle ones "+0" and if an individual found himself in the rightmost pose, he would get a "-1".

 

Flags

Figures can also be placed in various positions relative to the unit to indicate a change in status. In the photographs below, a banner or flag is placed either at the left, middle, or right position of the unit. The flag can also be placed in the front rank or 2nd rank, such that 6 different statuses can be indicated. Multiple flags can make this system more versatile, but again, practicality should be weighted against usefulness.

References

1. How to Play with Toy Soldiers, Joe Morschauser, 1962
2. Visual Display Units, James Oliver, Wargames Illustrated 74 (November 1993)
3. Flagging spirits, Arthur Harman, MiniatureWargames w Battlegames, 385 (May 2015)

A reroll, or a modifier?

Wargaming rules often use die roll modifiers, usually in the context of a die roll needing to hit some target number. Alternatively, some rules allow a reroll when the first roll fails.

Many rulesets these days are designed around the idea of giving special abilities to troop types. Some troops receive a +1 on their attack roll, e.g. in a bucket of dice mechanisms, while other troops are allowed rerolls. These sound like fun variations, and there might be reasons why on one case a special ability gives a +1, an in another case calls for a reroll, but does it also makes a difference from a statistical point of view?

Rerolls

For the sake of simplicity, let us assume we only roll D6s.

One mechanism might call for a roll, needing a 5+ to succeed. It's fairly obvious the probability for succeeding is 1 in 3 (33.33%). If you get a +1 on your roll, the die would only need a 4 or higher, and the probability increases to 1 in 2 (50%). In general, every +1 on a D6 increases the probability for success by 16.67%, irrespective of the original target number.

How does that change when doing a reroll for a failed first roll? Let's assume our die meets the target number with x (x between 0 and 1) probability. We have to consider 3 cases:

1. The original die roll succeeds: probability x
2. The original die roll fails, but the reroll succeeds: probability (1-x), followed by x, or total probability of (1-x)*x
3. The original die roll fails and the reroll fails: total probability (1-x)*(1-x).

So we score a success with a total probability of x+(1-x)*x = x*(1+1-x) = x*(2-x).

We can continue this calculation by now allowing for another reroll: take the probability for success after 1 reroll, and add the probability of failure multiplied by another basic success, and so on. We could do that type of calculation very easily in a spreadsheet, and this gives us the following table or probabilities. for a D6:

Target number	Basic roll	1 reroll	2 rerolls	3 rerolls
1+	1.00	1.00	1.00	1.00
2+	0.83	0.97	1.00	1.00
3+	0.67	0.89	0.96	0.99
4+	0.50	0.75	0.88	0.94
5+	0.33	0.56	0.70	0.80
6+	0.17	0.31	0.42	0.52

 

It is interesting to realize that these are also the same probabilities for taking the maximum score of a number of dice. Allowing for 2 rerolls is the same as taking the maximum roll of 3 D6’s. After all, it doesn’t matter whether we roll the 3 dice simultaneously, or only after the first one failed etc.

Plotted in a graph, this gives us the following probabilities for reaching a target number (graph made with anydice.com):

 

We can do a calculation for a D10 including several rerolls as well, and this gives us:

Modifiers

The standard +1, +2, +3 modifier are well-known in wargaming. Computing the probability vs a target number is easy enough, we simply shift the probabilities towards higher numbers, as shown in the table below:

Target number	no modifier	+1	+2	+3
1+	1.00	1.00	1.00	1.00
2+	0.83	1.00	1.00	1.00
3+	0.67	0.83	1.00	1.00
4+	0.50	0.67	0.83	1.00
5+	0.33	0.50	0.67	0.83
6+	0.17	0.33	0.50	0.67

In graph format:

Reroll vs Modifier

So we can ask the question whether it does really matter whether we apply a reroll, or rather a modifier. Let’s assume we only allow a single reroll (the most common case). By plotting the reroll probability vs various modifiers, we see that a D6 with a single reroll produces almost the same probability result as a D6+1. Of course, there are some deviations, but overall, the fit is very close.

We can do the same exercise for a D10, and see that a D10+2 fits closest to a D10 with a single reroll.

This is of course not terribly surprising. The real question is whether rerolls or better, or modifiers are better in a wargames?

This heavily depends on the rest of the rules, of course. A single die mechanic is always part of a larger rules framework. Personally, I don’t mind rerolls, and I don’t mind modifiers. But I do mind if both of them are used throughout the same ruleset without any real consistency. Hence, I prefer either modifiers in a ruleset, or rerolls, but not both. I understand modifiers and rerolls are used in the same game to add some “variety”, but probability-wise, this is often not necessary.

Happy wargaming!