1. Lanchester’s Laws in Space

2. Overview Introduce Lanchester’s Laws Show a game demo Go through the math How to apply to game design

3. 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?

4. “…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.”

5. See Also The Designer's Notebook: Kicking Butt by the Numbers: Lanchester's Laws – Ernest Adams

6. Game Demo

7. 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.

8. Lanchester’s Laws Model relationship between numerical advantage (N) and firepower advantage (F)

9. 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?

10. Case 1: Thunderdome

11. Case 2: Gun Fight

12. Case 1: Thunderdome Ninja HP 12345678910Fighter HP Start10 Round 110 9 Round 210 8 Round 310 7 Round 410 6 Round 510 5 Round 610 4 Round 710 3 Round 810 2 Round 9101 Round 1000

13. Case 1: Thunderdome Equilibrium: (Lanchester’s Linear Law)

14. The Math: NinjasFighters Damage (kills/round)

15. The Math: NinjasFighters Damage (kills/round)

16. The Math: NinjasFighters Damage (kills/round)

17. The Math: NinjasFighters Damage (kills/round) Army Size

18. The Math: NinjasFighters Damage (kills/round) Army Size

19. The Math: NinjasFighters Damage (kills/round) Army Size

20. The Math: NinjasFighters Damage (kills/round) Army Size Casualties Per Round

21. The Math: NinjasFighters Damage (kills/round) Army Size Casualties Per Round

22. The Math: NinjasFighters Damage (kills/round) Army Size Casualties Per Round % Army Lost per Round

23. The Math: NinjasFighters Damage (kills/round) Army Size Casualties Per Round % Army Lost per Round

24. The Math: =

28. It could be multiple Thunderdomes 1-on-1 fighting is the important property

29. Case 2: Gun Fight Combatants gang up for maximum attrition. No Overkill No “Underkill”

30. 4 Ninjas vs. 1 Fighter Ninja HP 1234Fighter HP Start10 Round 110 6 Round 210 3 Round 3101 Round 400

31. 32 Ninjas vs. 10 Fighter NinjasFighters Start3210 Round 1226.8 Round 2154.6 Round 3103.1 Round 462.1 Round 531.5 Round 611.2 Round 701.1

32. One More Ninja NinjasFighters Start3210 Round 1226.8 Round 2154.6 Round 3103.1 Round 462.1 Round 531.5 Round 611.2 Round 701.1 NinjasFighters Start3310 Round 1236.7 Round 2164.4 Round 3112.8 Round 481.7 Round 560.9 Round 650.3 Round 740

33. Case 2: Gun Fight Equilibrium: (Lanchester’s Square Law)

34. The Math: NinjasFighters Weapon Damage (kills/sec) Army Size

35. The Math: NinjasFighters Weapon Damage (kills/sec) Army Size Total Kills Per Second

36. The Math: NinjasFighters Weapon Damage (kills/sec) Army Size Total Kills Per Second % Army Lost per Second

37. The Math: % Army Lost per Second =

38. The Math:

42. Lanchester’s Laws Thunderdome Gun Fight

43. Point Value of a Unit How many Ninjas is a unit worth? Solve for N.

44. Point Value of a Unit Thunderdome Gun Fight

45. Variable Hitpoints

46. Thunderdome Gun Fight – 2 guys can beat 2x firepower OR 2x health – But not both. Works for heterogeneous armies.

47. Two extremes Thunderdome Gun Fight In General

48. k represents inefficiency Sources of inefficiency: Limited range and/or movement Limited space Overkill Underkill Wikipedia: Modern calculations use k =⅔

49. Possibly two different k values Point Value

50. Factors that Don’t Affect Efficiency Multipliers on F – fire rate – to-hit chance Multipliers on H – dodge chance – damage reduction

51. Factors that Don’t Fit the Model Healing/Regeneration Per-hit damage thresholds Etc.

52. Back to Lightspeed Brigade Different ship sizes and ship costs Rock/Paper/Scissors relationship

53. Ship Values ShipCostFire RateDamage Hit Points Fighter0.2115 Cruiser23535 Dreadnought30.453575

54. Point Values (k =.5) ShipCostFire RateDamage Hit Points Point ValuePV/Cost Fighter0.21152.211.2 Cruiser2353522.911.5 Dreadnought30.45357534.411.5

55. Point Values (k = 2/3) ShipCostFire RateDamage Hit Points Point ValuePV/Cost Fighter0.21152.914.6 Cruiser2353565.132.5 Dreadnought30.453575111.737.2

56. Creating Rock/Paper/Scissors Create match-ups that are inefficient for each side.

57. Overkill ShipCostFire RateDamage Hit Points Fighter0.2115 Cruiser23535 Dreadnought30.453575

58. Range ShipCostFire RateDamage Hit PointsRange Fighter0.211550 Cruiser2353565 Dreadnought30.453575100

59. AI changes were needed Dreadnoughts: Don’t bother shooting at fighters. Cruisers: Change targets quickly. Only steer at one target.

60. Explicit R/P/S Mechanics Avoided One less rule to learn Leave room for future expansion

61. 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.

62. 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.

63. Questions?