data visualizationterminology
Say one has two variables that change with time in a cyclical manner but instead of plotting time on the x-axis, one plots them directly —without applying a transform or any kind of manipulation. I know it is absolutely not brain surgery, but I once encountered a name for this and I cannot recall what it is. What is it called?
Matlab had an animated plot called a comet plot, but it wasn't that. It wasn't an arrow plot either (also that would be a quiver plot in my mind).
There are two sides to this question: the mathematical aspect, and the causal (inferential) aspect.
In the mathematical sense, a dependent variable y is a function f of an independent variable x: $y = f(x), f \subset X \times Y$. In this sense, the set X is the set of all players, and the set Y is the set of home run rates. The function f connects the chosen player and his (or her) home run rate. However, this relation can be inversed by use of the inverse function $f^{-1}$, in the sense of $y=f(x) \Leftrightarrow x = f^{-1}(y)$
However, I understand your question as pertaining to the inferential structure. In terms of your question, what depends on what? Clearly, the home run rate depends on the player, because it is a function of some characteristics of the player - his speed, striking prowess, etc. In that sense, the data itself is imbued by a causal structure: if the player changed - say, went into heavy training or used enhancing drugs - he or she could improve performance.
I hope this goes somewhere in answering your question.
You should be able to do exactly this by downloading the free Gapminder software, or even by using it in the cloud. Here's an example using data not from 3 points in time but from up to 35:
Alternatively, you will have greater control, and will be able to use whatever data you like, if you learn how to use Google Charts in conjunction with R. Both are free as well, but R at least is not a simple matter to learn. See the demo under "Examples."
Best Answer
A phase space is a space where all possible states of a time-varying system are represented. This matches your plot because all possible configurations of those 2 variables are represented on the plane of the graph.
The concept of "time" is only represented implicitly as the path between the observed data. This is clearer if we animate the plot so that the earliest data are plotted first, and then we add data sequentially during the animation.