Sabermetrics is the empirical analysis of baseball, especially baseball statistics that measure in-game activity. Sabermetricians collect and summarize the relevant data from this in-game activity to answer specific questions. The term is derived from the acronym SABR, which stands for the Society for American Baseball Research, founded in 1971. The term sabermetrics was coined by Bill James, who is one of its pioneers and is often considered its most prominent advocate and public face.
Henry Chadwick, a sportswriter in New York, developed the boxscore in 1858. This was the first way statisticians were able to describe the sport of baseball. The creation of the boxscore has given baseball statisticians a summary of the individual and team performances for a given game. David Smith founded Retrosheet in 1989, with the objective of computerizing the box score of every major league baseball game ever played, in order to more accurately collect and compare the statistics of the game.
Sabermetrics research began in the middle of the 20th century. Earnshaw Cook was one of the earliest researchers that contributed to this idea. Cook gathered the majority of his research into his 1964 book, Percentage Baseball. The book was the first of its kind to gain national media attention, although it was widely criticized and not accepted by most baseball organizations. The idea of advanced baseball statistics did not become prominent in the baseball community until Bill James began writing his annual Baseball Abstracts in 1977.
Bill James believed that people misunderstood how the game of baseball was played, claiming that it is actually defined by the conditions under which the sport is played. Sabermetricians, sometimes considered baseball statisticians, began trying to replace the longtime favorite statistic known as the batting average. It has been claimed that team batting average provides a relatively poor fit for team runs scored. Sabermetric reasoning would say that runs win ballgames, and that a good measure of a player's worth is his ability to help his team score more runs than the opposing team.
Before Bill James was able to bring the concept of sabermetrics to known topic, Davey Johnson used an IBM System/360 at team owner Jerold Hoffberger's brewery to write a FORTRAN baseball computer simulation while playing for the Baltimore Orioles in the early 1970s. He unsuccessfully used his results in an attempt to propose the idea that he should bat second in the lineup to his manager Earl Weaver. He wrote IBM BASIC programs to help him manage the Tidewater Tides, and after becoming manager of the New York Mets in 1984, he arranged for a team employee to write a dBASE II application to compile and store advanced metrics on team statistics. Craig R. Wright was another employee in Major League Baseball, working with the Texas Rangers in the early 1980s. During his time with the Rangers, he became known as the first front office employee in MLB history to work under the title Sabermetrician.
The Oakland Athletics began to use a more quantitative approach to baseball by focusing on sabermetric principles in the 1990s. This initially began with Sandy Alderson as the former general manager of the team when he used the principles toward obtaining relatively undervalued players. His ideas were continued when Billy Beane took over as general manager in 1997, a job he held until 2015, and hired his assistant Paul DePodesta. His approaches to baseball soon gained national recognition when Michael Lewis published Moneyball: The Art of Winning an Unfair Game in 2003 to detail Beane's use of Sabermetrics. In 2011, a film based on Lewis' book also called Moneyball was released to further provide insight into the techniques use in the Oakland Athletics' front office.
Sabermetrics was created in an attempt for baseball fans to learn about the sport through objective evidence. This is performed by evaluating players in every aspect of the game, specifically batting, pitching, and fielding. These evaluation measures are usually phrased in terms of either runs or team wins as older statistics were deemed ineffective.
The traditional measure of batting performance is considered to be the batting average. To calculate the batting average, the number of base hits was divided by the total number of at-bats. Bill James, along with other fathers of sabermetrics, proved this measure to be flawed as it ignores any other way a batter can reach base besides a hit. This led to the creation of the On-base percentage, which takes walks and hit-by-pitches into consideration. To calculate the On-Base percentage, the total number of hits + bases on balls + hit by pitch are divided by plate appearances.
Another flaw with the traditional measure of the batting average is that it will not take doubles, triples, and home runs into consideration and will give each hit the same value. Thus, a measure that will distinguish between these different hit outcomes, the slugging percentage, was created. To calculate the slugging percentage, the total number of bases of all hits is divided by the total numbers of time at bat. Stephen Jay Gould proposed that the disappearance of .400 batting average is actually a sign of general improvement in batting. This is because, in the modern era, players are becoming more focused on hitting for power than for average. Therefore, it has become more valuable to compare players using the slugging percentage and on-base percentage over the batting average.
These two improved sabermetric measures are important skills to measure in a batter and have been combined to create the modern statistic OPS. On-base plus slugging is the sum of the on-base percentage and the slugging percentage. This modern statistic has become useful in comparing players and is a powerful method of predicting runs scored from a certain player.
The traditional measure of pitching performance is considered to be the earned run average. It is calculated by dividing the number of earned runs allowed by the number of innings pitched and multiplying by nine because of the nine innings. This statistic provides the number of runs that a pitcher allows per game. It has proven to be flawed as it does not separate the ability of the pitcher from the abilities of the fielders that he plays with. Another classic measure for pitching is a pitcher's winning percentage. Winning percentage is calculated by dividing wins by the number of decisions (wins plus losses). This statistic can also be flawed as it is dependent on the pitcher's teammates' performances at the plate and in the field.
Sabermetricians have attempted to find different measures of pitching performance that does not include the performances of the fielders involved. This led to the creation of defense independent pitching statistics (DIPS) system. Voros McCracken has been credited with the development of this system in 1999. Through his research, McCracken was able to show that there is little to no difference between pitchers in the amount of hits they allow, regardless of their skill level. Some examples of these statistics are defense-independent ERA, fielding independent pitching, and defense-independent component ERA. Other sabermetricians have furthered the work in DIPS, such as Tom Tango who runs the Tango on Baseball sabermetrics website.
Baseball Prospectus created another statistics called the peripheral ERA. This measure of a pitcher's performance takes hits, walks, home runs allowed, and strikeouts while adjusting for ballpark factors. Each ballpark has different dimensions when it comes to the outfield wall so a pitcher should not be measured the same for each of these parks.
Batting average on balls in play (BABIP) is another useful measurement for determining pitcher's performance. When a pitcher has a high BABIP, they will often show improvements in the following season, while a pitcher with low BABIP will often show a decline in the following season. This is based on the statistical concept of regression to the mean. 
Value over replacement player (VORP) is considered a popular sabermetric statistic. This statistic demonstrates how much a player contributes to his team in comparison to a fake replacement player that performs below average. This measurement was founded by Keith Woolner, a former writer for the sabermetric group/website Baseball Prospectus.
Wins above replacement (WAR) is another popular sabermetric statistic that will evaluate a player's contributions to his team. Similar to VORP, WAR compares a certain player to a replacement-level player in order to determine the number of additional wins the player has provided to his team. WAR values vary with hitting positions and are largely determined by a player's successful performance and their amount of playing time.
Calculus in baseball
Many traditional and modern statistics, such as ERA and Wins Shared, don't give a full understanding of what is taking place on the field. To truly understand the physics of baseball, algebraic equations won't do. Calculus is capable of explaining all kinds of aspects of the game, from tracking home run balls over the fence to how often a team should attempt to steal.
Related rates in baseball
Related rates can be used in baseball to give exact calculations of different plays in a game. For example, if a runner is being sent home from third, related rates can be used to show if a throw from the outfield would have been on time or if it was correctly cut off before the plate. Related rates also can aid in determining how fast a player can get around the bases after a batted ball, information that helps in the development of scouting reports and individual player development.
Momentum and force
Momentum and force is a similar application of calculus in baseball. Particularly, the average force on a bat while hitting a ball can be calculated by combining different concepts within applied calculus. First, the change in the ball's Momentum by the external force F(t) must be calculated. The momentum can be found by multiplying the mass and velocity. The external force F(t) is a continuous function of time
Sabermetrics can be used for multiple purposes, but the most common are evaluating past performance and predicting future performance to determine a player's contributions to his team. These may be useful when determining who should win end-of-the-season awards such as MVP and when determining the value of making a certain trade.
Most baseball players tend to play a few years in the minor leagues before they are called up to the major league. The competitive differences coupled with ballpark effects make the exact comparison of a player's statistics a problem. Sabermetricians have been able to clear this problem by adjusting the player's minor league statistics, also known as the Minor-League Equivalency (MLE). Through these adjustments, teams are able to look at a player's performance in both AA and AAA to determine if he is fit to be called up to the majors.
Many sabermetricians are still working hard to contribute to the field through creating new measures and asking new questions. Bill James' two Historical Baseball Abstract editions and Win Shares book have continued to advance the field of sabermetrics, 25 years after he helped start the movement. His former assistant Rob Neyer, who is now a senior writer at ESPN.com and national baseball editor of SBNation, also worked on popularizing sabermetrics since the mid-1980s.
Nate Silver, a former writer and managing partner of Baseball Prospectus, invented PECOTA. This acronym stands for Player Empirical Comparison and Optimization Test Algorithm, and is a sabermetric system for forecasting Major League Baseball player performance. This system has been owned by Baseball Prospectus since 2003 and helps the website's authors invent or improve widely relied upon sabermetric measures and techniques.
Beginning in the 2007 baseball season, the MLB started looking at technology to record detailed information regarding each pitch that is thrown in a game. This became known as the PITCHf/x system which is able to record the speed of the pitch, at its release point and as it crossed the plate, as well as the location and angle of the break of certain pitches through video cameras. FanGraphs is a website that favors this system as well as the analysis of play-by-play data. The website also specializes in publishing advanced baseball statistics as well as graphics that evaluate and track the performance of players and teams.
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