Fantasy sports leagues and mathematics
Fantasy sports leagues are a popular form of online entertainment where participants act as managers of virtual teams composed of real athletes from various sports, such as baseball, football, basketball, and more. These leagues primarily revolve around scoring based on the real-world performance statistics of the athletes, which are mathematically compiled to generate "fantasy points." The emergence of the Internet has significantly transformed the fantasy sports landscape, making participation more accessible and allowing real-time data tracking and automated point calculations.
The origins of fantasy sports can be traced back to games like Strat-O-Matic, which used player statistics and random number generation. Over time, the fantasy sports model evolved, particularly with the introduction of formats like Rotisserie League Baseball, which emphasized real-time performance data. Mathematicians and statisticians have increasingly engaged with fantasy sports, applying various mathematical methods to optimize player drafting strategies and analyze game outcomes.
In addition to being a recreational activity, fantasy sports have been utilized in educational settings to enhance mathematical understanding and engagement among students, helping to bridge gender gaps in mathematics achievement. Despite its growth, the fantasy sports industry has faced scrutiny regarding its classification as gambling, raising legal and ethical questions that continue to evolve.
Fantasy sports leagues and mathematics
Summary: Fantasy sports leagues employ a variety of algorithms to predict player performance and to rank players and teams within each league.
In fantasy sports leagues, players act as the owners and managers of virtual sports teams that are typically composed of real players who are active in a given sport during a competitive season. Performance statistics for individual athletes on a fantasy owner’s roster, who usually belong to many different teams in the sport in real life, are mathematically combined to produce “fantasy points” for the owner. Often, owners may trade athletes or must make other types of decisions about who on their roster will be counted as “active” for a given period of competition, just like real managers. Fantasy baseball and fantasy football have historically been the most popular but fantasy leagues have evolved for many other sports, including basketball, golf, hockey, soccer, auto racing, and even cricket. Different leagues, even within the same sport, use a variety of formats, statistics, and weighting schemes to compute fantasy points. Season winners are usually the owners who have accrued the most fantasy points. While such games have existed in one form or another since at least the end of World War II, the development of the Internet drastically changed the nature and popularity of fantasy sports leagues by providing real-time access to data and tools for automated computation, making the activity more accessible for a broader range of participants. There are estimated to be millions of fantasy sports players in the United States alone. In the twenty-first century, mathematicians and others study fantasy sports leagues, and they have become a tool in mathematics classrooms as well.
History
Fantasy sports leagues grew from other types of sports simulator games that used data from past seasons and random number generation to determine the outcomes of simulated games. One of these was Strat-O-Matic, a board game using player statistics cards and dice that was developed by Hal Richman. It premiered in 1961 and still exists in both card and computerized forms. Richman began developing the game as a child because he “loved baseball and numbers” and disliked what he saw as unrealistic randomness in other baseball board games. He released the game while earning his undergraduate mathematics degree. John Burgeson, an IBM computer programmer, created a computer fantasy baseball simulator in 1960 that used random numbers and player statistics to generate a play-by-play description of a game between two teams. Many real baseball managers reportedly played fantasy-style games when they were young. According to writer Alan Schwartz, “That’s how they learned how to apply the mathematics of risk-taking.”
In the 1970s and 1980s, early fantasy leagues began to emerge for baseball and football. Writer Daniel Okrent developed Rotisserie League Baseball, which was named after the restaurant where players conducted the first draft. “Rotisserie baseball” is now a standard term for this widely-used format. It differed from most older games by using current-season statistics and data as they occurred rather than past seasons’ statistics. This style of play became popular after an Inside Sports magazine article described the rules of the game and discussed the league’s first season. Statistician George William “Bill” James also developed the analytical methodology of sabremetrics around this time and his Bill James Baseball Abstract was widely used by fantasy players. Similar mathematical analyses were produced for fantasy football by Fantasy Football magazine, which evolved into the print and online Fantasy Football Index (and also Fantasy Baseball Index). These publications and many others provided mathematically modeled variables, such as dollar values, statistical projections, and optimization strategies, for fantasy players. Sometimes the modeling proved useful enough that the writers went on to advise real teams.
Before the Internet, coordinating fantasy sports and calculating points could be time consuming. Data came largely from print sources, which were time delayed. A standard 162-game baseball schedule required near-daily computations for each owner in the league. Fantasy football was somewhat less challenging because of the smaller number of games in a season, but most fantasy methods had to restrict the number of variables used. Some commercial statistical services started to fill this need by compiling databases of sports statistics and providing services to calculate points—for a fee. Results were mailed or faxed; later, they could be sent electronically. The development of the World Wide Web in the mid-1990s facilitated and often automated the process of tracking player statistics and calculating points and league standings. Fantasy players could also quickly communicate with each other using e-mail, message boards, and chat rooms, resulting in online communities and worldwide leagues. Researchers have modeled this growth using sociologist Everett Rogers’s diffusion of innovation theory. The curve of fantasy players over time exhibits the classic S-shape of slow initial growth among early innovators and adopters, a middle period of accelerated growth, and a saturation of the market leading to a leveling off or slower growth period. The rapid growth of fantasy sports in the late twentieth century led to issues related to its potential classification as gambling, fairness in prizes, and the legal rights of players or teams to control the dissemination and use of statistical information about professional athletes, especially when outside companies were making a profit from such use.
After an employee of the popular online daily fantasy sports site DraftKings won thousands of dollars betting on another fantasy sports site, FanDuel, in 2015, questions were raised about the questionable legality and practices of such sites. While fantasy sports is federally deemed a legal form of gambling, inquiries were launched by the Federal Bureau of Investigations as well as several states to review whether participating in this activity involved enough elements of chance to constitute it as an illegal form of gambling. Although it was recognized that a great amount of skill is required, the states of Nevada, New York, Illinois, and Texas ultimately decided to ban the games as illegal gambling that also involved too much chance; unlike traditional fantasy sports, they argued, these sites control the betting and directly profit from wagers.
Mathematical and Social Connections
The line between fantasy sports and real sports is often blurred and mathematical methods used in one are often applied to the other. For example, mathematicians have explored a concept often called the “magic number” or elimination number, which quantifies the number of games a team must win to avoid being eliminated from the championship. The problem is popular in computer science classes. A common solution is to compare the number of games a team has left to play to the win-loss difference of the nearest rival. Researchers found that the numbers for all teams may be found simultaneously as they are a function of the number of games won plus the number of games left to play. Other mathematicians investigate optimal strategies for drafting players to teams using methods such as stochastic dynamic programming and deterministic dynamic programming coupled with various types of mathematical modeling and decision making. Some have researched the extent to which players rely on mathematical modeling and statistical methods instead of on heuristics and personal preferences. Mathematics teachers have found some success in using fantasy sports to motivate students and to help them succeed. Additional evidence suggests that fantasy sports may help reduce gender gaps in mathematics achievement. Some girls have stated that fantasy sports are “cool” and help them relate to boys as equals, and women are involved in the creation and management of fantasy leagues. For example, Jordan Zucker, who has an undergraduate degree in mathematics, created the Girls’ Guide to Fantasy Football Web site and manages an all-female fantasy football league.
Bibliography
Alba, Davey. "DraftKings and FanDuel Scandal Is a Cautionary Startup Tale." Wired. Condé Nast, 9 Oct. 2015. Web. 4 Feb. 2016.
Duara, Nigel. "States Crack Down on Fantasy Sports, Calling Them Games of Chance, Not Skill." Los Angeles Times. Tribune, 2 Jan. 2016. Web. 4 Feb. 2016.
Fantasy Sports and Mathematics. http://www.fantasysportsmath.com.
Fry, Michael, Andrew Lundberg, and Jeffrey Ohlmann. “A Player Selection Heuristic for a Sports League Draft.” Journal of Quantitative Analysis in Sports 3.2 (2007). Print.
James, Bill. The Bill James Handbook 2011. Chicago: ACTA, 2010. Print.
Schwarz, Alan. The Numbers Game: Baseball’s Lifelong Fascination with Statistics. New York: St. Martin’s, 2004. Print.