Lanchester s laws in space
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Lanchester’s Laws in Space. Overview. Introduce Lanchester’s Laws Show a game demo Go through the math How to apply to game design. Lanchester’s Laws. Devised by Frederick Lanchester in WW I Describe the relative strengths of two fighting armies in a war of attrition.

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  • Introduce Lanchester’s Laws

  • Show a game demo

  • Go through the math

  • How to apply to game design

Lanchester s laws
Lanchester’s Laws

  • Devised by Frederick Lanchester in WW I

  • Describe the relative strengths of two fighting armies in a war of attrition.

    What’s better: more troops or bigger guns?

Lanchester s laws in space

“…a man with a firepower of 2X is not worth twice the value of a man with firepower X, but rather as much, after taking into account one hit on either kills just as dead.”

See also
See Also

The Designer's Notebook: Kicking Butt by the Numbers: Lanchester's Laws

  • Ernest Adams

Lightspeed brigade
Lightspeed Brigade

  • Lots of different tradeoffs between firepower, hitpoints and # of units.

  • Need to balance units, but also create R/P/S relationship.

  • Leave room for future content expansion.

Lanchester s laws1
Lanchester’s Laws

Model relationship between numerical advantage (N) and firepower advantage (F)

Example fighters vs ninjas
Example: Fighters vs. Ninjas


  • Everyone has 10 hitpoints

  • Ninjas do 1 hitpoint per round.

  • Fighters do 10 hitpoints per round.

    How many Ninjas can a Fighter defeat?

Case 1 thunderdome
Case 1: Thunderdome

Case 1 thunderdome1
Case 1: Thunderdome

Case 1 thunderdome2
Case 1: Thunderdome


(Lanchester’s Linear Law)

Lanchester s laws in space

  • It could be multiple Thunderdomes

  • 1-on-1 fighting is the important property

Case 2 gun fight1
Case 2: Gun Fight

  • Combatants gang up for maximum attrition.

  • No Overkill

  • No “Underkill”

Case 2 gun fight2
Case 2: Gun Fight


(Lanchester’s Square Law)

Lanchester s laws2
Lanchester’s Laws

  • Thunderdome

  • Gun Fight

Point value of a unit
Point Value of a Unit

  • How many Ninjas is a unit worth?

  • Solve for N.

Point value of a unit1
Point Value of a Unit

  • Thunderdome

  • Gun Fight

Variable hitpoints
Variable Hitpoints

Variable hitpoints1
Variable Hitpoints

  • Thunderdome

  • Gun Fight

    • 2 guys can beat 2x firepower OR 2x health

    • But not both.

  • Works for heterogeneous armies.

Two extremes
Two extremes

  • Thunderdome

  • Gun Fight

  • In General

K represents inefficiency
k represents inefficiency

Sources of inefficiency:

  • Limited range and/or movement

  • Limited space

  • Overkill

  • Underkill

    Wikipedia: Modern calculations use k =⅔

Possibly two different k values
Possibly two different kvalues

  • Point Value

Factors that don t affect efficiency
Factors that Don’t Affect Efficiency

  • Multipliers on F

    • fire rate

    • to-hit chance

  • Multipliers on H

    • dodge chance

    • damage reduction

Factors that don t f it the model
Factors that Don’t Fit the Model

  • Healing/Regeneration

  • Per-hit damage thresholds

  • Etc.

Back to lightspeed brigade
Back to Lightspeed Brigade

  • Different ship sizes and ship costs

  • Rock/Paper/Scissors relationship

Point values k 5
Point Values (k = .5)

Point values k 2 3
Point Values (k = 2/3)

Creating rock paper scissors
Creating Rock/Paper/Scissors

  • Create match-ups that are inefficient for each side.

Ai changes were needed
AI changes were needed

  • Dreadnoughts: Don’t bother shooting at fighters.

  • Cruisers: Change targets quickly. Only steer at one target.

Explicit r p s mechanics avoided
Explicit R/P/S Mechanics Avoided

  • One less rule to learn

  • Leave room for future expansion

If it s r p s why do point values matter
If it’s R/P/S, why do Point Values matter?

  • You could end up with a “lopsided” R/P/S:

    • Rock beats Scissors handily

    • But Paper beats Rock just barely.

To sum up
To Sum Up

  • “Thunderdome” and “Gun Fight” have perfect solutions.

  • Your game lies between them.

  • Lanchester’s laws can give you a head start on point values.

  • Still no substitute for playtest.

  • Spreadsheets are awesome.