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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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Presentation Transcript

Overview
Overview

  • 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?


“…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

Suppose:

  • 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

Equilibrium:

(Lanchester’s Linear Law)
















  • 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

Equilibrium:

(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.



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