Amanda Knapp
Plus-minus, a mathematical symbol that can be written as ±, +/−, or ±, has multiple meanings and applications. In mathematics, it can represent both positive and negative solutions for a given value, indicating the uncertainty of a measurement or statistic. Plus-minus is also used in sports as a statistic to evaluate a player's impact on the game. This metric was first used in ice hockey in the 1950s and has since been adopted by other sports, such as basketball. In sports, plus-minus measures the difference between a team's total scoring and their opponent's when a particular player is in the game. While this statistic provides valuable insights, it also has limitations, such as being influenced by the performance of teammates and the quality of opposing teams.
| Characteristics | Values |
|---|---|
| Plus-minus symbol | ±, +/-, +/- |
| What it indicates | Positive and negative solutions, range of error or uncertainty |
| Use in sports | A statistic used to measure a player's impact on the game |
| Use in mathematics | Indicates a quantity whose algebraically positive and negative values serve to bracket a range of values |
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What You'll Learn
Plus-minus in sports
The plus-minus statistic is calculated by looking at the difference in the team's total score versus the opponent's when a particular player is in the game. In ice hockey, for example, when a team at even strength or shorthanded scores a goal, all players on the ice for that team will register a plus, while the opposing players on the ice will register a minus. There are some drawbacks to this traditional calculation, as it does not include all types of goals and does not apply to goaltenders. Situational plus-minus (Sit +/-) is an alternative calculation that includes all types of "team-based" goals, excluding only penalty shots and shootout goals.
Each goal is weighted based on the number of skaters (not goaltenders) on the ice. The plus-minus rating is then calculated by dividing the number of skaters on the ice for the team that conceded a goal by the number of skaters on the ice for the scoring team. This results in a positive value for the scoring team and a negative value for the conceding team.
The effectiveness of the plus-minus statistic in accurately conveying a player's individual performance has been questioned. While it provides a quantitative measure of a player's impact, it is directly influenced by overall team performance and does not account for the situational context of goals.
In sports betting, plus and minus signs are also used to indicate favourites and underdogs. Minus numbers generally represent favourites and indicate a rate of return less than 1-to-1. Plus numbers typically represent underdogs and higher rates of return. For example, a baseball team with odds of -145 is a favourite with a 59.2% implied chance of winning, whereas a +180 underdog in basketball would return $180 in profit for every $100 wagered.
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Plus-minus sign in mathematics
The plus-minus sign in mathematics, represented as ±, is a versatile symbol with several important uses. Firstly, it serves as a concise representation of both the addition and subtraction operations. In this context, it indicates that a value can be either positive or negative. For example, ±5 denotes the set of numbers {-5, +5}. This notation is particularly useful when expressing equations or expressions with multiple solutions, encompassing both positive and negative outcomes.
Another critical application of the plus-minus sign is in indicating the uncertainty or margin of error in measurements, scientific notation, or statistical data. When used in this context, the plus-minus symbol communicates the range of values within which the true value is expected to lie. For instance, a measurement of 10 ± 0.5 signifies that the actual value falls within the interval [9.5, 10.5]. This notation is invaluable in conveying the precision and reliability of a given measurement or statistical estimate.
Furthermore, the plus-minus sign can be employed to represent the range of values that a quantity can take. In this usage, the symbol captures the variability or spread of values associated with a particular measurement or calculation. For example, if a data set exhibits values ranging from 5 to 10, it can be expressed as [5 ± 5]. This notation succinctly conveys the scope of values encompassed by the data.
The plus-minus sign is a powerful tool in mathematics, offering a concise and versatile means of expressing multiple concepts. Its ability to convey both positive and negative values, indicate uncertainty, and represent ranges of values makes it a fundamental symbol in mathematical notation and communication.
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Plus-Minus, a 1963 composition by Karlheinz Stockhausen
Plus-Minus is a musical composition by Karlheinz Stockhausen, first written in 1963 and redrafted in 1974. It is a "polyvalent process composition", designed as a project for composition students attending the first Cologne Courses for New Music, held at the Rheinische Musikhochschule in October to December 1963.
The piece is an extreme instance of the new, open type of composition Stockhausen was developing at the time. It evolved from a number of conversations with his lover, Mary Bauermeister, in Siculiana and Palermo. Together, they sketched the beginnings of Plus-Minus in the sand on the seashore, creating graphic symbols for seven different types of sound material, ranging from precisely pitched sounds to noise-rich and timbrally indeterminate sounds. Each of the seven pages of the score has 53 of these symbols arranged in a grid, with more pages of text explaining how to interpret them.
The basic idea of Plus-Minus is that seven musical motifs, or "Characters", appear over and over again in different sequences. The result is usually a wide variety of short melodic motifs that, as the parts multiply in repetitions, form a periodic structure. Theoretically, it could be possible to get a maximum of 13 repeating Body chords and 39 Limb notes from just a single 3-Limbed Body (13 + (3 x 13)), creating a "groovy" sound.
Plus-Minus is a composition for one or several performers, with a variable performing length depending on the version worked out from the given materials. Twenty-five different versions were made by the students in 1963, for a wide variety of forces, including one for four harps, one for three harps and two pianos, and one for choir and chamber orchestra. The first public performance was given in Rome in June 1964 by Cornelius Cardew and Frederic Rzewski, each of whom realised one page of the score.
Stockhausen never completed or recorded an "official" version of Plus-Minus, but it represents a significant moment in the composer's career, showcasing his extraordinary musical innovation and attention to detail.
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+/- an American indietronic band
+/- (pronounced as Plus/Minus or Plus Minus) is an American indietronic band formed in New York in 2001. The band name is inspired by the plus–minus sign used in mathematics, which can mean either plus or minus or indicate the uncertainty of a measurement or statistic.
The band's music can be described as a fusion of independent rock and electronic elements, including synthesizers, samplers, drum machines, and computer programs. This blend of genres, known as "indietronica" or "indie electronic," emerged in the early 1990s in the United Kingdom. +/- draws influences from early electronic composition pioneers such as Silver Apples, Beaver and Krause, White Noise, the United States of America, Fifty Foot Hose, and Gong. These pioneers are known for their experimental work in combining psychedelic rock with oscillators and synthesizers.
The American duo Suicide, who emerged from the New York punk scene in the 1970s, is also a notable influence on +/-. Suicide's hybrid of electronics and punk, featuring drum machines and synthesizers, bridges the gap between these seemingly disparate genres. +/- builds on these influences, creating their unique sound within the indietronic genre.
While +/- has been active since 2001, the specific details of their albums, tours, and other milestones are beyond the scope of this search. However, it is clear that +/- occupies a space within the indietronic genre, drawing on a rich history of electronic music experimentation and innovation.
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Plus-minus method, a geophysical method to interpret seismic refraction profiles
The Plus-Minus method, also known as CRM (Conventional Reciprocal Method), is a geophysical approach for interpreting seismic refraction profiles and analysing seismic refraction data. It was developed by J. G. Hagedoorn and presented at the fifteenth meeting of the European Association of Exploration Geophysicists in London in 1958.
This method is based on the analysis of the so-called 'plus time' and 'minus time', which are computed from the travel times of waves from two symmetrical shot points to each geophone. By adding the travel times, relative depths can be determined, while subtracting them gives the velocities of the refractor. The Plus-Minus method involves drawing linear segments for direct and refracted waves, with the direct wave arrival having a slope equal to 1/vw (weathering velocity) and the refracted wave arrival having a slope equal to 1/vb (bedrock velocity).
The Plus-Minus method offers a simple and comprehensible way to visualise and interpret seismic processes by focusing on wavefronts rather than rays or trajectories, which are less sharply defined and challenging to observe due to long wavelengths in seismic processes. It is particularly useful for shallow refraction investigations and determining weathering corrections for refraction and reflection work.
While the Plus-Minus method provides valuable insights, it is important to note that it introduces errors during the extrapolation process. However, these errors can be corrected to a certain extent. The method is well-suited for analysing undulating layer boundaries with slope angles less than approximately 10 degrees. It is widely used in geophysical exploration to detect subsurface structures, delineate lithologic layers, and identify distinct materials, especially at contaminated sites.
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Frequently asked questions
The plus-minus symbol (±) is used to indicate both positive and negative solutions for a given value. It can also represent the range of error or uncertainty in a measurement or statistic.
Plus-minus in sports is a statistic used to measure a player's impact on the game. It calculates the change in the score when a given player is on or off the court/ice. In basketball, it is calculated as the difference between team points scored and allowed while a specific player is on the court.
Plus-minus provides instant insight into a player's impact on the game. It can help identify undervalued players who consistently contribute to winning but may not have impressive traditional statistics. Plus-minus can also be used to identify optimal lineup combinations.
Yes, plus-minus has some drawbacks. It is heavily influenced by the performance of teammates, and a great player on a poor team may have negative values. Plus-minus is also sensitive to sample size, and single-game data can be misleading. It does not account for the quality of opponents or specific game contexts.
Plus-minus can refer to a geophysical method to interpret seismic refraction profiles. In mathematics, the plus-minus symbol can indicate the uncertainty of a measurement. Plus-minus is also the name of an American indietronic band formed in 2001.
