Optimization

Sports are about mathematics whether talking about time, distance, speed, mass, or derivatives thereof like acceleration, momentum, and force. Beyond math, there’s a science to sports that involves the typical phases of scientific testing such as observation, prediction, measurement, and reporting. Even beyond that, a more subatomic level exists based on theory, strategy, and the synaptic responses of players and coaches.

An entire field of study in math, loosely called optimization, is devoted to answering one question: Is there an optimal approach to solving a problem based on a mathematical construct? The answer depends on whether a problem can be defined by its objective(s), boundaries, and availability of reliable data. If all of these elements are present, as in FSO’s approach to fantasy sports, then an optimal solution does exist.

Harry M. Markowitz is often cited as the genius behind the theory. More specifically, as stated in his “Theory of Choice,” Markowitz asserted that an optimal combination of assets could be determined by taking into account two dimensions: performance and risk. Markowitz further defined risk to be a function of 1) individual variances of asset performance, and 2) covariance among assets. In 1990, he received the Nobel Prize in Economics for his efforts. Since Markowitz first published his theory, a plethora of optimization techniques have come into existence to solve complex problems, including: linear, non-linear, mixed integer, quadratic, simplex, global, and stochastic, among others. There categories are not necessarily mutually exclusive. To build you an optimal fantasy football team, FSO structures its practices based on non-linear quadratic optimization. So, what does this mean?
		Harry Markowitz. Source: Meetings of Nobel Laureates

For those familiar with optimization, please note that FSO does not conform to conventional mean-variance practices as frequently seen with optimization engines utilized in other industries. For example, FSO does not seek the highest marginal trade-off between risk and performance, which would represent the combination of players that maximizes expected performance per unit of additional risk. To do so, our customers would likely end up with a low-to-moderate risk profile team, and favorable results per unit of risk, but most likely would not achieve the objective of winning their league. FSO utility functions differ based on league type and are proprietary.