**Blatantly Stolen from SomethingAwful**The Law of Diminishing Marginal Returns is an economics theorem that states that as you consume more of a single product, the value of that product to you goes down. That is, the marginal return decreases. This is an intuitive concept that an economics teacher described with Big Macs: The first Big Mac you eat is delicious, but the third is disgusting and greasy.

We can apply this concept to the idea of a ninja battle rather simply. Let us define a Law of Diminishing Marginal Ninja Power: "As the number of ninjas on a side increases (past one), the power of that force decreases." By this law, the most powerful ninja force would be a single ninja. An curve can be set up for this law of the form:

N(x) = ne^-x

The constant n is the yet unknown ?ninja? coefficient that actually specifies the curve, and N(x) is the power of a force of a certain number of ninja.

We can find proof of this statement in nearly every ninja film, but a powerful example is the recent film Kill Bill Vol. 1. For those that have not seen the film yet, please skip the remainder of this paragraph and go to the next.

In the battle between The Bride and the Crazy 88s, we have an excellent experiment in ninja battles. We have a controlled environment where there is a single ninja facing down 88(?) ninjas on the opposing force. The battle progress quickly and bloodily, with The Bride wiping out scores of ninjas in just a few minutes. As the number of ninjas on the Crazy 88s decreases, the force seems to actually become better, with The Bride forced to spend more time on the killing of each ninja. When the Crazy 88s are finally depleted to the optimum number of ninjas, 1, The Bride lets him go rather than waste a lot of time finishing him off.

The Law of Diminishing Marginal Returns has an opposite, of course, with the Law of Increasing Marginal Returns, which I believe is much rarer in economics, if it exists at all in that field. It has the same effect, except that with each additional unit, the marginal return actually becomes greater. This law we can apply to the number of zombies in a horror film. As the number of zombies increases, the power of the zombie force increases by a greater and greater amount. This is another graphable curve, of the form

Z(x) = ze^x

The constant z is in this case the ?zombie? coefficient, and Z(x) is the power of a force of a certain number of zombies.

This law is another intuitive concept ? a single zombie poses no threat to even a weakling. Even a second is no great threat. The fifth, however, makes a dangerous group; a tenth makes a deadly brigade; a fiftieth creates an undead horde; and once you get a hundred zombies together, you?re just sporked.

Now that we have our definitions down, we can consider how these two laws interact. There are some questions we can ask and explore simply through discussion, but others may require actual experimentation. For example, at what point do the two curves intersect? That is, how many zombies, X, would it take to over power a certain number of ninjas, Y? How do these curves change when you use ?fast type? zombies? In what way can we even measure N(x) and Z(x)? I guess we could use a comparable number of Delta Force Strike Operatives, but even this force faces a curve of its own. Additionally, how do the implications of these curves affect other battles of attrition, such as the one between the peaceful Dinosaurs and monstrous Bunnies?

In conclusion, the mathematics of battle forces opens up a completely new field of study for Something Awful. I am sure that with time and effort we can answer these questions, and pave the way to the ultimate simulator of great battles: the ?GBS Zombie/Robot/Pirate/Ninja/Barbarian Simulator 9000!?