Last post, I began talking about what the purposes and limitations of scientific analysis are. Essentially, the purpose of science is to develop models of the real world from the basis of empirical observations. We want to apply this idea to baseball players so that we can both analyze past performance to determine what is and has been valuable and to help predict future performance.
Of these two, the latter is probably more important in that it is useful for decision making. However, it's not too useful to make a good tool for predicting performance if one does not first know what performance is valuable.
So what do we want from a model of a baseball player? Essentially, we want a way of describing a player so that we can draw conclusions easily about how valuable that player is in many situations. Now, it's virtually impossible to create a model of a person. People are complex. We can't possible model Manny Ramirez's mind and all of its quirks. Its impossible.
Fortunately, it's also not that useful. We don't care how Manny thinks. We care about how he performs. We only care about his mindset inasmuch as it translates to on-field performance.
The best place to start, therefore, is to try and quantify tangible baseball skills. For any given skill, we will call this quantification of that skill a player's "true talent level." This true talent level is the player's actual ability for a certain skill. For example, if we say that Alex Rodriquez's true talent level for hitting home runs is that he will hit one home run for every twelve plate appearances he receives, then we are saying that this is exactly how Alex will perform if we give him an infinite number of plate appearances. Of course, this is impossible, which is one of the reasons why a player doesn't have the exact same statistics every year.
The other reason is that a player's true talent level is always changing. Players play injured, age, and sometimes sleep funny. Furthermore, many things complicate our measurement of true talent level, not the least of which are the facts that players play in differing stadiums and face different pitchers. Therefore, when we talk about a player's true talent level, we are really talking about our best estimate of their true talent level, given various assumptions and data.
Often when talking about an abstract baseball point, I'll begin with assuming that we know exactly the true talent level of a player for a particular skill. We can do this because even if we can't exactly measure a player's true talent level, he still has one (as far as out model is concerned).
So our first task when analyzing players is to try and quantify their true talent level for various baseball skills. We'll look at the best way to do this later.