Okay kiddo, let's imagine that you have a toy car race track in your bedroom. You have two toy cars and you want to see how well they race against each other.
Now, you want to measure how good your toy cars are at racing against each other. This is where the Nash-Sutcliffe model efficiency coefficient comes in.
This model is used by scientists and engineers to compare how well a real-world system behaves compared to a predicted model. In our case, the real-world system is the toy cars racing and the predicted model is how we think they will race.
Imagine you have a ruler and you measure the distance the toy car travels in one minute. You can do this for both cars and then compare them.
Now, you create a model where you predict how fast the toy cars will travel. To do this, you use things like the weight of the toy cars, the size of the wheels, and how much energy the cars have when you wind them up.
You compare the real-world measurements to the predicted model and this will tell you how good your model is at predicting how the cars will race against each other.
If the real-world measurements match perfectly with the predicted model, then the Nash-Sutcliffe model efficiency coefficient will be 1. This means that your model is really good at predicting how the toy cars will race.
If the real-world measurements are way off from the predicted model, then the Nash-Sutcliffe model efficiency coefficient will be low, meaning that your model is not very accurate at predicting how the toy cars will race.
Like this, engineers and scientists use the Nash-Sutcliffe model efficiency coefficient to figure out how well a model is predicting behavior for real-world systems.