Baseball statistics

Summary: Baseball is a mathematically rich sport, especially with regard to its array of statistics.

Though America’s favorite sport for more than a century, the game of baseball has undergone many changes, many in response to statistics gathered regarding all parts of the game. At first, the statistics were limited to scorecard data but have expanded to include every action and detail of the game. More so, this gathering and analysis of data has expanded beyond the realm of statistical analysis, as mathematics is now used to examine all aspects of baseball—the physical characteristics and performance of its players, the analysis and modeling of each element (hitting, fielding, pitching, strategies), and the combined geometry and physics surrounding the game.

Although some fans object to this intrusion of mathematics into a competitive sport, most accept or even depend on the mathematical aspects as enriching their enjoyment of the game itself. That is, mathematics has become the arbiter in arguments, the stimulus for “hot stove league” discussions, a tool to help identify either patterns of team strengths and weaknesses or optimal strategies, and a decision-making tool for gamblers and fantasy league participants.

Sabermetrics

Bill James, a baseball writer, historian, and statistician, gave authenticity to the use of statistics in analyzing all aspects of baseball through his pioneering mathematics and statistics work. Multiple editions of his Baseball Abstract in the 1980s changed not only the play of the game itself but also how it is viewed by fans, and are the predecessor to many modern Web sites dedicated to analysis of the sport. James revolutionized the way mathematics is used to analyze sports to determine why some teams win and others lose. He coined the term “sabermetrics,” which is derived from the Society for American Baseball Research acronym SABR, for his analytical and modeling methods. In 2006, Time magazine named him one of the most influential people in the world.

Mathematical statistics provide perspectives that explain game occurrences, provide comparative rankings of teams and players, and assist in managerial decision making. The primary example is the simple use of ratios, means, and medians as both descriptive and inferential statistics for a player, position, game, season, or career. Some examples include the following:

• Batting average, slugging percentage, on-base percentage, and batter’s run average
• Effect of artificial turf on numbers of ground ball hits or base stealers’ performances
• Performance of hitters and pitchers in different environments (outdoor versus dome stadiums; night games versus day games)
• Expected strike zones for umpires, given a pitcher or batter is right- or left-handed

Going beyond these descriptive statistics, the game of baseball can be analyzed using very sophisticated techniques. Some examples include the following:

• Connections between a player’s characteristics and training regimens relative to game performance, or even to document the effects of steroid use
• Trend analysis, based on either a player’s or team’s performance (hitting, pitching, fielding) over the past five, 10, and 15 games
• Importance of pitcher throwing a “first strike”
• Effects of bringing in the infield when the bases are loaded with less than two outs
• Team winning tendencies based on run differential in innings seven, eight, and nine
• Impact of rule changes on pitching and hitting, such as the effects of elevating the pitching mound or changing foul-line distances to outfield fences
• Determination of coaching strategies such as sacrifice bunts, pitch-outs, stealing home, intentional walks, shifts of fielders for certain hitters, or use of pinch hitters and relief pitchers
• Determining the “best” all-time player in a particular position (for example, centerfielder, hitter, relief pitcher, base-stealer)
• Selection of players by professional teams during annual drafts, using both historical data for each player’s performance and physical data
• Use of statistical data during contract negotiations between a player and management, or even the release or trading of players based on team needs

Mathematical probabilities, odds, and expected values can help examine the chances of particular events happening within a game or across games:

• Probability that the World Series will go four, five, six, or seven games
• Use of odds to determine personal or professional betting strategies
• Use of conditional probabilities to determine lineups or use of pinch hitters, reflecting the probability of a batter getting a hit given that the pitcher is right- or left-handed
• Correlations between a team’s wins per season and player payrolls, or pitcher salaries and their ERAs
• Probability of a record being broken, either by a team or player, such as Joe DiMaggio’s 56-game hitting streak

Though difficult to implement practically, geometry, trigonometry, and calculus can shed light on other important ideas:

• Length of a home run
• Actions of different pitches such as a curve ball, slider, fastball with movement, or forkball
• Determination or alteration of a hitter’s batting stance or position in the batter’s box
• Use of angles in fielding balls off outfield walls

Game theory also is used as part of the decision-making process within a baseball environment, leading to choices of optimal tactics. Some specific decisions are as follows:

• A manager’s choice of batting lineups and pitching moves, relative to the opposing manager’s choices
• A manager’s calling for shifts of fielders, pitch-outs, or steals at times within a game
• A manager trying to argue, influence, or reverse decisions by umpires
• A manager’s use of techniques to motivate specific players
• A team’s selection of players during a draft, dependent on the player’s apparent abilities, the inferred needs of other teams, and the specific draft round
• Contract negotiations involving players, agents, and team management

Finally, using all of these statistical data and mathematical modeling techniques, one can create realistic simulations of baseball games or end-of-year series, possibly using computer animations.

At the collegiate and professional levels, managers are increasingly using mathematics to remain competitive, even hiring mathematical statisticians as important parts of their staff. However, some authors and fans suggest that the team with the best players and managers will usually win, despite any use of sophisticated mathematics.

Bibliography

Albert, Jim, and Jay Bennett. Curve Ball: Baseball, Statistics, and the Role of Chance in the Game. New York: Springer-Verlag, 2001.

Cook, Earnshaw. Percentage Baseball. Cambridge, MA: MIT Press, 1966.

Eastway, Rob, and John Haigh. Beating the Odds: The Hidden Mathematics of Sport. London: Robson Books, 2007.

Ross, Ken. Mathematician at the Ballpark: Odds and Probabilities for Baseball Fans. New York: Pi Press, 2004.

Schell, Michael. Baseball’s All-Time Best Hitters: How Statistics Can Level the Playing Field. Princeton, NJ: Princeton University Press, 1999.

Schwarz, Alan. The Numbers Game: Baseball’s Lifelong Fascination with Statistics. New York: St. Martin’s Press, 2004.