For any given input size, different inputs typically require different amounts of space and time. Hence we can discuss for either the average case or for the worst case. It is usually much easier to compute worst-case complexity. In complexity theory we generally subject our equations to some extreme simplifications. This is called an order statistic.
Small problems are almost always feasible to compute.
Tweaking the code can improve the coefficients, but the order statistic is a function of the algorithm itself.