In the last generation, sabermetrics has exploded into the mainstream, growing from home calculations by Bill James and others into Wins Above Replacement being casually discussed on Baseball Tonight. Sabermetrics is important to baseball; it is an innovative way of evaluating players and teams and provides intellectual tools to better understand the game. That’s the most basic motivation behind sabermetric analysis: to better understand the statistics of baseball in order to become more efficient and successful.
Within the realm of baseball statistics, each team attempts to approach the same mathematical singularity: a perfect winning percentage. Conceptually, singularities are instances when a function output approaches a particular number (also called a limit, which may be infinity). Think of it this way: take the number 1 and divide it by 10. The result is 0.1, divide by 10 again and it becomes 0.01. Repeating the process gives us 0.001, 0.0001, 0.00001… and so on. The outputs are becoming increasingly small but never quite reaching zero. In a graph, this function would eventually result in a near perfect horizontal line indistinguishable from the x-axis, without ever touching it. Similarly, a function that approaches infinite value would appear as a vertical line on a graph. Singularities, or limits, are detectable because while function outputs may never explicitly reach them, the limit can be seen visually within a graph. What’s even more incredible is that these asymptotes actually occur in nature. Black holes, mathematically, are asymptotes within the “graph” of spacetime in which the gravity is so immensely powerful that nothing can escape, not even light (which itself moves at asymptotic speed). The space at the center of a black hole is referred to as a singularity, a point infinitesimally small such that it essentially has zero volume. Even more amazing, modern science has seemingly discovered traces of the origins of our universe through singularity detection. Supporting the Big Bang Theory, these findings strengthen the notion that everything in existence all began from a single point, a singularity, which held all mass and had infinite density while occupying zero physical space. That an object can contain infinite mass within zero space is difficult to conceptualize, let alone visualize; that’s the nature of singularities.
The singular objective of baseball is to win every game. Winning every game mathematically requires one of two scenarios; either a team allows zero runs, or they score an infinite number of runs, both resulting in one team scoring 100% of the runs, assuring 100% of the wins. Because the objective is to win the game, and the only way to assure victory is to score the most runs, then the only two ways players can contribute to winning are by scoring runs or by preventing the opponent from doing so. Under that conclusion, the most accurate metrics for evaluating performance must be explicitly linked to either runs scored or runs allowed and thus linked to wins.