Simplified Wargaming
via
Dupuy's
Quantified Judgment Model

Bibliography:

Options of Command by Trevor N. Dupuy
Brassey's Encyclopedia of Land Forces and Warfare by Franklin D. Margiotta
War Games by Thomas B. Allen

The Quantified Judgement Model

OutcomeBattle = PowerRed / PowerBlue
PowerRed = NumbersRed * VariablesRed * QualityRed
PowerBlue = NumbersBlue * VariablesBlue * QualityBlue

Where:

NumbersRed/Blue = Number of Troops on each side
VariablesRed/Blue = Variables in favor of each side. Usually fortifications, prepared fighting positions, etc.
QualityRed/Blue = Quality of troops on each side.

EXAMPLE: The French Army (Red) encounters the Prussian Army (Blue) on the battlefield. The French Army consists of 4,000 veterans, while the Prussian Army has 3,000 green troops entrenched behind a stone wall.

We define the stone wall entrenchment as having a variable modifier of 1.5, and the quality rating of green troops as 0.5, while veterans have a rating of 1.5. It results in this set of calculations:

PowerRed = 4,000 * 1 * 1.5 = 6,000
PowerBlue = 3,000 * 1.5 * 0.5 = 2,250
6,000 / 2,250 = 2.66

The Outcome Ratio is 2.66 in favor of the French Army. They sweep the battlefield of the Prussians.

Obviously, this simple formula only works if both sides are essentially evenly matched with the same types of equipment and practice roughly the same types of combat formations.

You can modify the QJM further to take into account even more factors; such as mixed types of troops. You could arbitrarily declare that a tank is worth 25 men, et cetera; or modify the Law further to take into account more variables.

Modified QJM Power Calculation

PowerBlue/Red = Quantity * Quality * TLI * EffectivenessFortification

Suggested Quality Ratings for the Modified QJM:

0.1 = African Militas / Typical Science Fiction Militaries (I'm looking at you, Star Trek)
0.5 = Green Troops
1.0 = Average Troops
1.2 = Crack Troops
1.5 = Elite Troops

Computing TLI (Theoretical Lethality Index) for a semi-mobile weapon system:

TLI = ROF * Targets * Damage * Range * Accuracy * Reliability

Where:

ROF = Rate of Fire Per Minute
Targets = Targets hit with each attack. An anti-tank missile or AP round would have a Target of 1 against armor; while a High Explosive Fragmentation shell would have a Target of 10 against infantry.
Damage: Probability of destroying the target if it is hit.
Range: Effective range of the weapon in meters
Accuracy: Percentage of time the weapon actually hits it's target
Reliability: Percentage of time the weapon actually can fire.

Computing TLI (Theoretical Lethality Index) for a highly-mobile weapon system:

TLI = [ ( ROF * Targets * Damage * Range * Accuracy * Reliability * MOF * ROA) + PF ] * RFE * FCE * ASE * WHT * AME * CL

Where:

ROF = Rate of Fire Per Minute
Targets = Targets hit with each attack. An anti-tank missile or AP round would have a Target of 1 against armor; while a High Explosive Fragmentation shell would have a Target of 10 against infantry.
Damage: Probability of destroying the target if it is hit.
Range: Effective range of the weapon in meters
Accuracy: Percentage of time the weapon actually hits it's target
Reliability: Percentage of time the weapon actually can fire.
MOF: Battlefield Mobility Factor
ROA: Radius of Action Factor
PF: Punishment Factor
RFE: Rapidity of Fire Effect (Armored Vehicles Only)
FCE: Fire Control Effect (Armored Vehicles Only)
ASE: Ammunition Supply Effect (Armored Vehicles Only)
WHT: Wheels/Halftrack Effect (Armored Vehicles Only)
AME: Amphibious Capability Effect (Armored Vehicles Only)
CL: Ceiling Effect (Aircraft Only)

Computing the Battlefield Mobility Factor (MOF)

0.15 * SQRT(Speed)

Speed is measured in km/h.

Computing the Radius of Action Factor (ROA)

0.08 * SQRT(RoadRange)

Road Range is measured in kilometers.

Computing the Punishment Factor (PF)

(Weight / 2)3/2

Weight is measured in metric tons.

“Official” HERO TLIs

(Divide by 5000 to get OLI at present battlefield dispersal levels)

Weapons System

TLI

Weapons System

TLI

T-72 MBT

4,885,000

M1 Abrams MBT

4,920,000

T-80 MBT

6,460,000

M1A1 Abrams MBT

5,245,000

BMP-2 IFV

2,070,000

M2 Bradley IFV

2,670,000

152mm 2S3 SPH

1,080,000

M109A1/2/3 SPH

1115000

BM-21 Grad MRLS

2,020,000

MRLS (227mm)

1555000

AK-47 Rifle

950

M-16 Rifle Family

1,850 (A1)
1,900 (A2)

Suggested Effectiveness Ratings for Fortifications for the Modified QJM:

1.0 = Attacking or Defending in the Open
1.3 = Fighting from a Hasty Position
1.5 = Fighting from a Prepared Position
1.6 = Fighting from a Fortified Position