Unit analysis and expected combat results
Unit analysis and expected combat results
Deciding on what units to have is a major decision for most players and therefore it is critical to thoroughly analyse the units available. Unit evaluation is quite an interesting subject so this will be quite a long section.
The first and most important consideration is to understand how your units will behave in combat. We have the description of the combat algorithms in the early part of the FAQ but we need to understand how this is affected by unit choice.
The major consideration is the average combat score we expect to achieve with a unit and the implications of the various minor adjustments. This is important for deciding what the unit properties actual mean. If we consider a “vanilla” combat with no leaders or terrain effects we see that our average attack strength is the unit score plus an average dice roll of 4.5; this means a unit attack score of zero is not the ineffective no attack that it sounds like. If you check back to the formula the main run has a “score-1” in the formula and then a linear progression. This gives an interesting basis for comparison of units.
A zero factor unit against another zero factor unit will, on average, inflict (4.5-1)x3.5xtech casualty rate on the enemy. This gives a 3.5 (ie 4.5-1) base effective score expectation for a unit. Each extra point of attack adds onto this so that, for example, achieving a +1 advantage over the enemy defence will increase their casualties by 1 part in 3.5 or about a 28.6% increase in casualties.
To create a general evaluation of a unit in combat we need to consider the effect that all of its scores will have. Each +1 of attack increases enemy casualties by an amount proportional to our unit’s tech modifier. Each point of defence decreases our casualties by an amount proportional to the
enemy unit’s tech modifier. This has the interesting consequence that evaluating a unit is
very dependent on who you are fighting based on unit class, unit type and tech level. Many players have suggested that preferred regiment selection is a no-brainer. This is
not true.
Late game Latin Unit List
If we consider that the average casualties we inflict are proportional to our attack score minus the enemy defence score plus modifiers plus average 3.5 contribution from the dice roll times our tech modifier then this leads us to some evaluation formulae.
Using F for friendly, E for enemy, A for attack score, D for defence score, M for current multiplier and L for losses we get the following
EL = (FA-ED+3.5) x FM
FL = (EA-FD+3.5) x EM
These equations can be applied to all types of combat – shock, fire and morale. This leads to the possibility of calculating the value of a given unit in the context of fighting a particular enemy. It also highlights the fact that you cannot evaluate a unit without considering what you are going to fight with it.
The evaluation formula (using words to make it understandable) goes as follows
A unit’s value in combat assuming it is fighting an enemy unit of similar class (ie inf/cav) and the same tech level is
Sum of (Attack+Defence)xMultiplier for each of fire, shock for casualty causing plus
Sum of (Morale Attack + Defence) x (Fire+Shock multipliers) for morale combat
This basic formula is relatively easy to evaluate but reveals a few interesting things straight off. For a start morale scores are as significant as the other scores put together because they get used on both fire and shock days. Next, defence is just as important as attack – this is interesting to look at, a unit with attack 10 defence 8 (henceforth abbreviated as 10/8) against an 8/10 unit will find both units achieve exactly the same results because 8-8 is the same as 10-10. The difference between attack and defence comes out when we look at different tech levels and unit classes.
A further conclusion is that the actual balance between shock and fire days is of some significance to evaluating units. It is very unusual for there to be the same number of fire days as shock days because of the way that combat works. A we assume battles have random lengths (which they don’t)then , on average, we will have 2.5 days more shock than fire. With battle length not being random this becomes harder to evaluate but the key conclusion is that the shorter battles are the higher the ratio of shock to fire. This has consequences because the technology trends through the game have an influence on battle length. It also has implications for how important maximum morale is for units as higher morale increases the relative number of fire days by making the battle longer.
An example: Blue Coat Infantry – 7/6 7/6 9/9 – multipliers 1.3/1.25
Its value is
13 x 1.3 + 13 x 1.25 for casualties
18 x 2.55 for morale
Compared to Red Coat Infantry – 6/6 6/8 8/10
12 x 1.3 + 14 x 1.25 for casualties
18 x 2.55 for morale
With the slightly higher shock modifier the Blue Coat infantry comes out very slightly on top and the units do not become fully equal until shock and fire multipliers are the same. Fire doesn’t overtake until tech 50 by which time new units are available.
Frederickian Infantry 5/4 8/7 10/8
9 x 1.3 + 15 x 1.25
18 x 2.55
Slightly weaker again simply because of poor shock values.
Note that in the comparison shock dominates over fire and since this matches the bias in combat type days in a battle they reinforce each other. If a unit were better due to a fire advantage then the actual balance between shock and fire in a battle would be critical. A unit with a fire advantage would lose it when at low morale since it could only sustain short shock dominated battles.
As you can see this is getting complicated and I have hardly started just yet. The next thing to do is to look at unit evaluation in the context of fighting units from a different class. This results in a change to the evaluation formula. The basic difference is that our attack values are scaled by our multiplier whilst the defence values are scaled by the enemies multiplier. This is best demonstrated with an example. Going back to our tech 35 western infantry we get
Blue Coat 7/6 7/6 9/9 multipliers 1.3/1.25 versus Cavalry – multipliers 4.2/0.05
(7 x 1.3) + (7 x 1.25) + (6 x 4.2) + (6 x0.05) = 43.35
The telling point in this analysis is that shock defence is now by far the most valuable characteristic and fire defence is almost irrelevant. This suddenly causes Austrian white coat infantry, which we ignored earlier, to pop into prominence since they can offer an 8 point shock defence
White Coat 6/8 5/5 8/9
(6 x 1.3) + (5 x 1.25) + (8 x 4.2) + (5 x0.05) = 47.9
These have 3 points less of basic scores compared with our previous infantry units but with the new scaling on shock defence they compare quite favourably. Thus we find that different enemies create different preferred units. In the case of cavalry we get a preference for high shock defence and indifference to fire defence. This means that we need to understand what we will be fighting against before deciding on what unit is best.
Similar arguments can be used for adjusting the preferred unit for fighting lower technology or higher technology enemies creating a complex decision making process.
To further complicate this the analysis is also fatally flawed since it is being used to calculate average casualties based on the casualty graph being linear which it is not. Below scores of 2 it is non-linear and this has not been allowed for at all. Sadly the only truly effective path to comparing units is to produce some modelling software and examine the average results. Rather than do this I will simply map out some “rules of thumb” that do a good job of selecting units.
Before that it is worth a quick look at the implications of the way infantry and cavalry scores increase over time. In the above we have seen infantry units with scores around the 6+ mark. Contemporary cavalry has slightly lower scores. The cavalry choice around tech 35 is easy as Swedish Arme Blanche is an easy winner. They have the best shock values and still have good fire defence so they are good against both cavalry and infantry. However, there shock attack is only 5 so against white coats (defence 8) they will get a –3 combat modifier. This means they need a score of significantly over 5 before they really start causing casualties. This trend means that cavalry develop a much wider spread of possible combat results later in the game and it compensates to a large degree for the better cavalry multipliers. What we get is cavalry being really effective with high scores and infantry being medium effective but over a wider range of scores. Again modelling is the only way forward.
Rules of thumb
1) Concentrate on shock factors for all units until tech 50 and even after this they are just as good as fire
2) Ignore fire attack on cavalry, it is permanently worthless
3) Look at defence values based on the abilities of other units not your own. Ie. Cavalry fire defence counts.
4) Artillery will never be good in battle unless they can survive 5 shock days which they can’t
5) Fire factors are only effective when operating with good morale levels
Sometimes the choice of units is obvious but often it is not.
Some definite choices
Latin knights -> Caracolle -> Galoop -> Arme Blanche
Medieval Infantry -> Men at Arms -> Galloglaigh -> varies depending on whether fighting cavalry or infantry
The final conclusion has to be that we need a modelling program to inform us what unit is best for particular circumstances. Usually it will be the best unit for like against like but if you are up against an army that is all cavalry then the best infantry choice may be quite different from what you expect and may be significantly more effective than your enemy expects (see Grenzer example in main casualty algorithm post)