The coffee brewing process has two parameters which can be practically measured, and a few more which cannot. The first measurable parameter is the concentration of coffee solids in the final product, as a fraction of its mass. The most accurate way of measuring this is to evaporate all the water and measure the mass of the solids left behind; this is rather impractical to do often, however, so other instruments have been developed. Tastes vary, but the consensus seems to be that the desired concentration of solids in coffee other than espresso is 1.3% to 1.5%.
The second measurable parameter is the amount of coffee extracted from the beans, measured as a decrease in the mass of the beans. Measuring this requires drying the beans after brewing, which is also tedious and time-consuming; for this reason, this parameter is usually inferred instead of measured directly. The desired amount of extraction is usually given as 20% of the bean mass for ideal flavor. Some people may prefer less, but almost nobody prefers more; the motivation for going higher is economy, not flavor. This brewing chart is a good summary, although they like their coffee somewhat more dilute.
The amount of coffee extracted depends on three factors - the temperature of the water, the surface area to volume ratio of the coffee (determined by the fineness of the grind), and the amount of time the coffee is left in the water. If one of these parameters is increased, the total amount of coffee extracted into the water will also increase, unless one of the other parameters is decreased. For example, if the coffee is ground finer, but then the amount of time it is in contact with the water is shortened by a corresponding amount, the total amount of coffee extracted into the water will remain constant.
Although fineness of grind and time can be perfectly substituted for each other, the same is not true of temperature. As the temperature changes, it affects not only the extraction rate, but also which components of the coffee are extracted. It is possible to extract coffee with room temperature water - by waiting six to twelve hours - and in fact, this is done, called “cold brewing”. However, the flavor profile of this coffee differs somewhat from coffee extracted with near-boiling water. Most people prefer one over the other, although they are divided as to which they prefer. Pressure has a similar effect - espresso, brewed at around 9 atmospheres, also extracts differently. While it might be possible to measure these effects with a mass spectrometer, they are, in practice, judged subjectively.