Numbers, Predictions and WarThe choice of what method to use to resolve combat is – in my opinion – the most important decision a wargames designer can make. Get this wrong, and however good the rest of the rules mechanisms used may be, the design will fail.
The problem is that combat is not an easily quantifiable event because it ultimately depends upon human interaction, a notoriously difficult thing to model. There are people who have spent a considerable amount of time and effort trying to achieve this seemingly impossible goal, and the writings of one of these – Colonel Trevor Dupuy – occupy a place on the top shelf of my bookcase of wargaming books.
The three main books he wrote about combat are:
- NUMBERS, PREDICTIONS AND WAR: USING HISTORY TO EVALUATE COMBAT FACTORS AND PREDICT THE OUTCOME OF BATTLES (1979)
- UNDERSTANDING WAR – HISTORY AND THEORY OF COMBAT (1987 & 1992)
- ATTRITION: FORECASTING BATTLE CASULATIES AND EQUIPMENT LOSSES IN MODERN WAR (1990)
In the first of these books Colonel Dupuy explains how he and his colleagues at HERO (the Historical Evaluation and Research Organisation) developed the concept of QJMA – the Quantified Judgement Method of Analysis of Historical Combat data. They analysed the data relating to over one hundred battles and developed a very long and complicated formula that produced results that, when the specific data was added, accorded with the actual results of the battles they had studied. They appeared to have identified a mathematical model that could be used to predict the outcomes of battles.
The second book takes the theory forward, and compares the methodology – now referred to as QJM (the Quantified Judgement Method) – with other theories of combat.
The book begins with what Dupuy termed ‘The Timeless Verities of Combat’. These are:
- Offensive action is essential to positive combat results.
- Defensive strength is greater than offensive strength.
- Defensive posture is necessary when successful offense is impossible.
- Flank or rear attack is more likely to succeed than frontal attack.
- Initiative permits application of preponderant combat power.
- Defenders’ chances of success are directly proportional to fortification strength.
- An attacker willing to pay the price can always penetrate the strongest defences.
- Successful defence requires depth and reserves.
- Superior combat power always wins.
- Surprise substantially enhances combat power.
- Firepower kills, disrupts, suppresses, and causes dispersion.
- Combat activities are always slower, less productive, and less efficient than anticipated.
- Combat is too complex to be described in a single, simple aphorism.
The book also describes the QJM Combat Power Formula in considerable detail, although the description begins with Clausewitz’s Law of Numbers and shows how QJM relates to it. Put simply they both boil down to:
P = N x V x Qwhere:
P = Power (In QJM this is termed Combat Power)
N = Numbers (In QJM this is termed Force Strength)
V = Variables (In QJM this is termed Environmental and Operational Factors)
Q = Quality (In QJM this is termed Combat Effectiveness Value)
By comparing the Combat Power of both sides in a combat, the results of that combat should be predictable. It is thinking behind this basic formula that I will be using to develop my own combat resolution system.
It is worth noting that the Combat Effectiveness Value used in Colonel Dupuy’s work seems to show that certain nations produce more effective soldiers than others. For example, in his third book the use of QJM demonstrates that during World Wars I and II German soldiers were 1.2 times more effective that British, French, and American soldiers, and up to 3.0 times more effective than Russians. It also shows that during the Arab-Israeli Wars Israeli soldiers were at least 2.0 times more effective than their Arab opponents. Some commentators have cited this as showing that Colonel Dupuy can only get his formulae to work by ‘fudging’ the data; others have sought to examine how and why this apparent ‘national superiority’ has come about.
Applying the concepts behind QJMTaking concepts behind the QJM Combat Power Formula as a starting point I have chosen a very simple method of combat resolution that combines the following factors:
- A numerical value for each type of unit based upon its training, equipment, and experience.
- Numerical values that represent transient effects on combat (e.g. terrain, surprise).
- An element of chance (i.e. the use of a dice).
When the Combat Power of both sides are compared, a result is generated using a system that is not very dissimilar for that used in Phil Barker’s DBA and TABLE TOP BATTLES by Mike and Joyce Smith.
The numerical values I have chosen for each type of unit are:
1: Basic combat value for all units
+0: Poor quality General*
+0: Poor quality infantry and cavalry
+1: Average quality General*
+1: Conscript infantry and cavalry
+1: Transport
+2: Good quality General*
+2: Equipped with light AFVs
+2: Regular infantry and cavalry
+2: Artillery
+3: Exceptional quality General*
+3: Equipped with medium AFVs
+3: Elite infantry
+4: Equipped with heavy AFVs
+5: Equipped with very heavy AFVs
Note: The starred (*) additons to the basic combat value only apply to command units.
Therefore an inexperienced (conscript) Russian Rifle Regiment will have a combat value of 2 (basic combat value plus 1 for being conscript infantry) whereas an elite German
Panzer Grenadier unit will have a combat value of 4 (basic combat value plus 4 for being elite infantry).
The numerical values I have chosen for each transient effect on combat are:
- Add the command stand’s combat value: If a unit’s division, corps, and/or army command stand is in an adjacent hex, add the command stand’s combat value.
- +1: If the firing stand is artillery firing at a target that is in an adjacent square.
- -2: If the target stand is in defence works, inside a wood, or inside a built-up area.
The element of chance is represent by the use of:
- A D12 (for the Germans).
- A D10 (for the Russians and Axis allies).
The choice of different dice has been made in light of the work done by Colonel Dupuy to show that the soldiers of different nations have different Combat Effectiveness Values.
Resolving CombatWhen combat occurs, both sides take the combat value of the unit that is involved in the combat, add the numerical values of any relevant transient effects and the dice score that they throw, and this give that unit’s Combat Power. These are then compared, and a result is generated.
The combat results are:
- If the attacking unit’s Combat Power is lower than the defending unit’s Combat Power, the combat has been ineffective.
- If the attacking unit’s and defending unit’s Combat Powers are equal, each unit throws a D12 or D10 (as appropriate) and the unit with the lowest score stays in its current position and reduces its combat value by one.
- If the defending unit’s Combat Power is less than the attacking unit’s Combat Power but more than half of the attacking unit’s Combat Power, the defending unit stays in its current position and reduces its combat value by one.
- If the defending unit’s Combat Power is less than half of the attacking unit’s Combat Power, but more than a quarter of the attacking unit's Combat Power, the defending unit reduces its combat value by two.
- If the defending unit’s Combat Power is less than a quarter of the attacking unit’s Combat Power, the defending unit reduces its combat value by two and withdraws until it is at least one hex away from an enemy unit.
Note: If a unit has to withdraw more than four hexes to comply with a combat result
or it is prevented from doing so because of an obstacle or enemy unit, the withdrawing unit is deemed to have been destroyed.
The combat resolution system will need vigorous play-testing, but as it is built upon a reasonably sound body of theory and previous experience I hope that any modifications will be minimal.
