Assume that you own a farm huge enough to employ every individual residing in the town nearby. And you know that each worker you employ can gather 3 units per hour. Also, assuming that you are not a greedy bastard, the cost of a worker is 1 unit per hour for you. So the math is simple, your profit for every single hour can be defined as: P = 2W, where P means “profit” and W means “workers.”

Our equation P = 2W is called a linear model. It is called linear, because there is a direct relation with the number of workers and the profit. It is simple. If you have 1 worker, your profit is 2 units. If you have 2 workers, it is 4 units, if you have 3 workers your profit is 6 units. Wow, you are rich already.

“There is a saturation point of productivity and when you cross that limit, the productivity you get for each extra worker will start decreasing.”

Unfortunately though, things don’t work like that in real life. To start with, I think it is almost like a fairy tale to believe that we can find a boss who agrees to pay 1/3 of the gatherings to his workers. But then comes the efficiency problem.  If a worker keeps working for consecutive hours, it is very obvious that he will get tired and will start working slower. And besides, not two people are the same, so you can’t expect two different individuals to perform identical. This is the nature of things.

And besides, even if each of the workers are totally identical, you can’t really expect to see your profits rising with each of the additional workers. They teach in Economics 101 that there is a saturation point of productivity and when you cross that limit, the productivity you get for each extra worker will start decreasing.

Think about it. In real life, you can’t find a farm big enough to employ everybody. So it means there is a space limit. How big is your farm? Perhaps it is big enough for 100 workers to work at the same time. Or maybe 200 workers, or even maybe 1000 workers. So what happens when you exceed the space limit? It means every additional worker will start occupying sharing  the space of another worker, so the overall productivity will start declining.

“We are old enough to know this is not the case in real life. But also, we are young enough to play games and that’s all matters.”

So you see, this linear model doesn’t actually fit with real life. In fact, the entire economical model system depends on some assumptions. You assume that each worker works the same, you assume they don’t get tired, you assume you are the best boss ever etc…  We are old enough to know this is not the case, right?

But also, we are young enough to play games and that’s all matters. We don’t have to deal with some real world problems. We have got our own online problems. And amazingly enough, most of these problems can be defined as a linear model.

In an online strategy game, if the game tells you that the average productivity of a worker is 4 units, you know that it is exactly 4 units and it doesn’t change. If the game tells you that a particular tank has 1000 hit points in a war, you know that it will always be 1000 independent from all the variables such as the weather, the morale of the pilot, the ground etc, which you would see in real life.

So, consider this as a long introduction of my series where I will try to tell you about the basics of linear models and how you can benefit it in a strategy game, far easier than you would ever imagine. You will not need anything more than you already have: a web browser, and you will learn how you can use a mathematical tool to make the best of your resources in your favorite online game.