Lanchester’s Power [Linear and Square] Laws mean that combat in science fiction RPGs will usually be fundamentally different than combat in fantasy RPGs. Or the designer will have to somehow compensate, as in Star Wars.
F. W. Lanchester, a polymath, inventor, and co-founder of operations research (a subfield of applied mathematics), examined before and during World War I the effects of melee and firepower in attritional combat. This examination was part of Lanchester’s Power Laws. Here we’re discussing how these differences mean that combat in fantasy RPGs, as compared with science fiction RPGs, will usually be fundamentally different unless the designer somehow compensates, as in Star Wars.
Lanchester calculated that in attritional melee the strength of a force is proportional to its number, because there is no action at a distance (“Lanchester’s Linear Law”). It amounts to a 1 vs. 1 environment. In an era of firepower, where military units can act at a distance, the strength of a force in attritional combat is proportional to the square of its numbers. (Hence, “Lanchester’s Square Law.”)
For example, in a melee of 5 vs 10 (or 5,000 vs 10,000), in the time it takes the 5 to inflict one damage, the 10 will inflict two damage (or 1,000 and 2,000 damage). In a firepower situation, the 5 have a relative strength of 25, while the 10 have a relative strength of 100, or 1 to 4. So in the time it takes the 5 to inflict one damage, the 10 will inflict four.
Thinking in immediately practical terms, imagine a typical sword/axe/club melee in an RPG versus a typical pistol and rifle and grenade fight today, and more in a future of blasters. (Keep in mind, the monsters we often fight are also melee weapons, in effect.) Without the effects of fantasy superheroes, the melee is man-against-man, and even a great swordsman cannot dominate a big melee. In the fight of today or the future, a man with a ranged weapon, especially an automatic weapon or an explosive-projecting weapon, can kill dozens in a short time.
A designer of a science fiction RPG faces a problem; firepower-based combat must be very different from melee combat, and probably less satisfying for the players. What can the author/designer do to solve this problem plausibly?
Star Wars compensates for this with the Jedi and light sabers. An adequately trained Jedi with a light saber can block huge numbers of blaster bolts without fail (even though it’s physically impossible if three shots are on target at the same time). He/she can use their light saber to overcome opposing armor and other factors associated with advanced weapons technology, right down to cutting through steel bulkheads. The more or less artificial scarcity of light sabers assures that few soldiers have these advantages, quite apart from the Jedi’s Force powers. Of course, Star Wars Stormtroopers can’t hit the broad side of a barn, either, nor do they use automatic weapons and explosives much.
In many ways, you can think of melee vs firepower as the difference between knife fights and automatic/semi-automatic gunfights. The movie Starship Troopers just ignores tanks and aircraft in order to provide a more visceral melee-like experience as troops fight monsters at short range and hand-to-hand. “Let’s ignore our invulnerable stuff and only bring a knife to the knife fight.” Duh. I think of E. R. Burroughs’ Barsoom stories, where many melees took place in a land with very long-range rifles and explosive bullets, because of “honor” - it was dishonorable to escalate a swordfight to a gunfight. This is one way that an author or designer can compensate for firepower: just don’t use it (except for ship-to-ship combat).
Back to fantasy. What about archery? Standard archery is much closer to melee than firepower, owing to short range, slow action (crossbows), and ammunition limitations. When English longbowmen dominated battles in the Hundred Years War*, they used a weapon that could be fired rapidly by skilled archers, yet use a large supply of ammunition because England was mobilized to mass produce (and transport) arrows. After the development of muskets, longbows would still have been a better weapon given skilled archers and a massive supply of arrows; but musket ammunition was far more compact and easily produced, and it was far easier to train a man to fire a musket adequately, than to fire a longbow rapidly.
Where fantasy moves into the realms of firepower is magic-users using fireballs, lightning bolts, and similar area effect damage spells. Which may help us understand why spellcasters can be the “ace in the hole” and can dominate a battle. Dragon fire may have similar effects.
In other words, there’s rarely a pure melee or pure firepower skirmish situation in games. Yet the higher you move on the spectrum from tactical to strategic, the more Lanchester’s Linear and Square Laws take effect, even though his mathematics only applied to a specific kind of battle. I have simplified the specific circumstances of the Laws for this short piece. You can get more detail from the Wikipedia article cited above.
I’m sure readers can provide many other examples of ways authors and designers have returned science fiction skirmishes to melee parameters.
*Reference: Bernard Cornwell’s excellent historical novels about the battles of Crecy and Agincourt. The protagonist is an English longbowman.
F. W. Lanchester, a polymath, inventor, and co-founder of operations research (a subfield of applied mathematics), examined before and during World War I the effects of melee and firepower in attritional combat. This examination was part of Lanchester’s Power Laws. Here we’re discussing how these differences mean that combat in fantasy RPGs, as compared with science fiction RPGs, will usually be fundamentally different unless the designer somehow compensates, as in Star Wars.
Lanchester calculated that in attritional melee the strength of a force is proportional to its number, because there is no action at a distance (“Lanchester’s Linear Law”). It amounts to a 1 vs. 1 environment. In an era of firepower, where military units can act at a distance, the strength of a force in attritional combat is proportional to the square of its numbers. (Hence, “Lanchester’s Square Law.”)
For example, in a melee of 5 vs 10 (or 5,000 vs 10,000), in the time it takes the 5 to inflict one damage, the 10 will inflict two damage (or 1,000 and 2,000 damage). In a firepower situation, the 5 have a relative strength of 25, while the 10 have a relative strength of 100, or 1 to 4. So in the time it takes the 5 to inflict one damage, the 10 will inflict four.
Thinking in immediately practical terms, imagine a typical sword/axe/club melee in an RPG versus a typical pistol and rifle and grenade fight today, and more in a future of blasters. (Keep in mind, the monsters we often fight are also melee weapons, in effect.) Without the effects of fantasy superheroes, the melee is man-against-man, and even a great swordsman cannot dominate a big melee. In the fight of today or the future, a man with a ranged weapon, especially an automatic weapon or an explosive-projecting weapon, can kill dozens in a short time.
A designer of a science fiction RPG faces a problem; firepower-based combat must be very different from melee combat, and probably less satisfying for the players. What can the author/designer do to solve this problem plausibly?
Star Wars compensates for this with the Jedi and light sabers. An adequately trained Jedi with a light saber can block huge numbers of blaster bolts without fail (even though it’s physically impossible if three shots are on target at the same time). He/she can use their light saber to overcome opposing armor and other factors associated with advanced weapons technology, right down to cutting through steel bulkheads. The more or less artificial scarcity of light sabers assures that few soldiers have these advantages, quite apart from the Jedi’s Force powers. Of course, Star Wars Stormtroopers can’t hit the broad side of a barn, either, nor do they use automatic weapons and explosives much.
In many ways, you can think of melee vs firepower as the difference between knife fights and automatic/semi-automatic gunfights. The movie Starship Troopers just ignores tanks and aircraft in order to provide a more visceral melee-like experience as troops fight monsters at short range and hand-to-hand. “Let’s ignore our invulnerable stuff and only bring a knife to the knife fight.” Duh. I think of E. R. Burroughs’ Barsoom stories, where many melees took place in a land with very long-range rifles and explosive bullets, because of “honor” - it was dishonorable to escalate a swordfight to a gunfight. This is one way that an author or designer can compensate for firepower: just don’t use it (except for ship-to-ship combat).
Back to fantasy. What about archery? Standard archery is much closer to melee than firepower, owing to short range, slow action (crossbows), and ammunition limitations. When English longbowmen dominated battles in the Hundred Years War*, they used a weapon that could be fired rapidly by skilled archers, yet use a large supply of ammunition because England was mobilized to mass produce (and transport) arrows. After the development of muskets, longbows would still have been a better weapon given skilled archers and a massive supply of arrows; but musket ammunition was far more compact and easily produced, and it was far easier to train a man to fire a musket adequately, than to fire a longbow rapidly.
Where fantasy moves into the realms of firepower is magic-users using fireballs, lightning bolts, and similar area effect damage spells. Which may help us understand why spellcasters can be the “ace in the hole” and can dominate a battle. Dragon fire may have similar effects.
In other words, there’s rarely a pure melee or pure firepower skirmish situation in games. Yet the higher you move on the spectrum from tactical to strategic, the more Lanchester’s Linear and Square Laws take effect, even though his mathematics only applied to a specific kind of battle. I have simplified the specific circumstances of the Laws for this short piece. You can get more detail from the Wikipedia article cited above.
I’m sure readers can provide many other examples of ways authors and designers have returned science fiction skirmishes to melee parameters.
*Reference: Bernard Cornwell’s excellent historical novels about the battles of Crecy and Agincourt. The protagonist is an English longbowman.
