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In the early 20th century there was a mathematician names Lanchaster, who calculated that in modern times the punch of military units is not proportional to their number, but rises in its square.
For instance, when you have five units, and your opponent has three of equal quality, then the balance of power isn't really 5:3, but it's 5Â² : 3Â², i.e 25:9
This means that the enemy will in average destroy 9 of your 25 units of punch, leaving you with 16 of them. 16 units of punch is the punch of four units.
In other words, when five units fight three enemies of equal quality, then four of the five will survive in average, while wiping out the three enemies.
However, this also has implications on technological advantages. In order to make up for numerical disadvantage of 1:2 you do not only need 2:1 firepower advantage, but 2Â²:1, 4:1. That's because with your own firepower your resilience does not increase, you remain fragile.
If you do the math, then you'll find out that a fight of 10 marines with 4 attacks each versus 20 marines with 1 attack each is an exactly fair fight. it's a bit suprising, but accurate. Both sides will kill exactly as many percent of their enemies as the other does: The 10 marines with 4 attacks each get twice as many attacks as there are enemies, and so do the 20 marines with one attack each. Two attacks for each enemy marine from both sides' point of view.
Now, how does this relate to tyranids?
There are plenty of upgrades that enhance the punch or resilience of tyranids. With the above knowledge we can correctly assess if these are worth it. An upgrade which provides an punch increase of a factor of 1.5 isn't worth increasing the bug's cost by 1.5 times, but only sqrt(1.5) times.
E.g. in case of hormagaunts the toxin sac upgrade provides such a 50% punch increase, yet it's worth only a 22.5% increase in price even if the gaunts get to benefit of it all the time. Since the actual price of the upgrade is 20% in case of otherwise "naked" gaunts, it would be slightly worth it if the gaunts get to benefit of it all the time.
But since they don't get to benefit of it when there is a shootout, the remaining marginal 2% efficiency increase is not worth that cost.
The weapon skill adrenal glands are a different matter. Their 1.333 punch increase against marines is worth an 15.5% increase in price, yet they get it for 10%. That's a relative 5% (1.155/1.1)increase in efficiency, which may be worth the additional vulnerability to ranged weapons. Of course in case of shooty gaunts the vulnerability to ranged weapons is less of an issue in regards to upgrades which also enhance the gaunts' shootiness.
The same logic also applies to resilience. 10 marines with four wounds each vs 20 marines with one wound each is a fair fight too, 0.5 attacks per enemy wounds on both sides.
A VC/strangler/ES carnifex can get +25% resilience with a 9.8% increase in cost. 1.25 times the normal resilience is worth 1.12 times the cost, that's an increase in efficiency by about 2%, which works in both ranged and close combat. Therefore the upgrade is worth it.
Similar logic applies to basically all upgrades...it's an effective tool to evaluate them if the precise increase of performance is known.
Last edited by ArchonAstaroth; August 26th, 2005 at 15:34.
ummmm.... ok..... but you do know that that doesnt apply to 40k right????
the Lanchaster guy prolly calculated this stuff before the atomic bomb for one thing, meaning that the theory is bunk, and it applies to earth level warfare, in fights involving humans, and basic human tech(rifles shotguns, solid slug weaponry) and if you add tanks into the mix that screws up the equation even further, seeing as how tanks at the very beginning of the 20th century had armor that could be shot thru like tissue paper(well sorta...) and was this done before or after the airplane, cuz if it was done before, then the equation gets REALLY screwy, but back to the point, the only army this would really apply to is the IG, cuz tyranids fight in a drastically different way then any human can, etc. etc.
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There are no atomic bombs in 40k games.the Lanchaster guy prolly calculated this stuff before the atomic bomb for one thing,Actually it fully applies as i demonstrated above with the marine example.meaning that the theory is bunk,So what?in fights involving humans, and basic human tech(rifles shotguns, solid slug weaponry) and if you add tanks into the mix that screws up the equation even further, seeing as how tanks at the very beginning of the 20th century had armor that could be shot thru like tissue paper(well sorta...)It fully applies to aerial combat. And there aren't really airplanes in 40K anyway either...flyers aren't really comparable.and was this done before or after the airplane, cuz if it was done before, then the equation gets REALLY screwy,It has nothing to do with humans. It applies whereever force can be concentrated against an opponent. Be it in ranged or in close combat, be it on the ground or in the air.but back to the point, the only army this would really apply to is the IG, cuz tyranids fight in a drastically different way then any human can, etc. etc.
Nice find and a great post. I like looking at armies and their wargear from different standpoints and this standpoint has a lot of credibility in many, but not all instances.
Some pieces of wargear involve too many factors to accurately equate their usefulness in terms of a percentage increase.
However, I think it is still a useful tool if applied correctly.
Nice. I read it and it sounds about right to me based on my experience. Are you like studying the history of ware fare or something?Any way could you maybe do like a quick reference post or sheet for it showing the equations?
Originally Posted by The Paint Monkey
I didnt know some one came up with an actual written mathematical formula, but its an old concept, and one I had also noticed (mainly in WarCraft 2, when going in battleship-battleship fights)
I always viewed the relative strength of my unit versus my opposition (when Initiative is not a factor), as a comparison of the collective damage and collective HP/Wounds my opponant and I have:
......damage you do . . . . . Your Hitpoints/wounds
------------------------.. X ..--------------------------
their Hitpoints/wounds..........damage they do.
Taking Initiaitve into account isnt much harder.
Last edited by Zarathustra; August 26th, 2005 at 09:22.
As of Tyranid 5th Ed. codex I have the Gaunts I wanted. I did, however, loose the sniperfexs I relied upon and they were more important then the gaunts.
so if the marines have0.5 attacks per wound, and say two wounds were caused. The 20 marines would lose two attacks, while the 10 marines would lose 0.
the ten marines would have 38 wounds, the 18 attacks doubled (to see if it is 0.5 still) would get 36, meaning that it becomes worse than 0.5 attacks per wound.
The twenty marines would have 18 wounds, the ten attacks doubled make 20. Meaning that the number of attcks per wound would be betetr than 0.5.
So it only works in the first turn of combat. After that the ten marines steadily kill off the 20
please correct me if im wrong
The ten marines would lose 0.5 attack, as "half a marine" is dead. Of course, in the game no half marines can die, but it still has to be taken into account - it's the average of all possible numbers of losses. The ten marines also may lose four models if the 20 ones are extremely lucky with their attacks, or none at all if the opposite is true. Therefore accurate averages have to be used, else you constantly round down the casualties in favour of the ten marines.so if the marines have0.5 attacks per wound, and say two wounds were caused. The 20 marines would lose two attacks, while the 10 marines would lose 0.
Of course, the price of things like initiative, or a better chance to harm AV10 and so on cannot be calculated this way - but things which enhance punch against the primary opponent or enhance toughness can be evaluated.
I'm not very good at numbers, (to be honest, I had trouble finnishing the thread starter, Sorry Archon, my fault, not yours). But, from what I gleaned, this Lanchaster dude studied Sun Tzu. He, Sun Tzu, had a rule that I believe was the rule of thirds. He took almost every situation a soldier could be in and showed the casualty rates as related in thirds, (ie. an attacking force will lose one third more casualties than a defending force, etc), and his numbers have proven, statistically, accurate. It's kinda funny, these guys wrote these treatises long before many of the modern weapons were designed, or even conceived of, and yet they are still studied.
FYI - cute historical point, Sun Tzu's treatise named The Art of War was actually a resume to the Chinese emperor, (can't remember which one), for the job of General. Man my resume is only a page long.
Last edited by THE Hersh; August 26th, 2005 at 14:07. Reason: spelling, go figer, and clarify
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How do I increase the combat ability for each upgrade? In what way do I calculate it? And how does this particular theory or whatever work, how did this guy work it out ?
Sorry for those questions, but as you can see, I'm even worse than the hersh, and I want to know what this guy did to reach this conclusion.