Adjusted Plus Minus
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Adjusted Plus Minus
Adjusted Plus-Minus (often abbreviated APM) is a basketball analytic that attempts to predict the impact of an individual player on the scoring margin of a game by controlling for the rest of the players on the court at any given time. The metric is derived using play-by-play data to keep track of all substitution and possession ending actions. It was first implemented by the Dallas Mavericks in the early 2000s after owner Mark Cuban commissioned data scientists Jeff Sagarin, Wayne Winston, and Dan Rosenbaum, who developed the metric alongside their WINVAL conversion to aid in player salary determination. In combination with other innovations, this gave the Mavericks one of the most progressive front offices in the league at the time. Since APM's creation several derivative metrics attempting to improve on the skeleton have been created. Advantages The APM skeleton has been utilized so heavily since the metric's conception because, assuming a large enough sample size, it offers ...
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Advanced Statistics In Basketball
Advanced statistics, also known as analytics or APBRmetrics, in basketball refers to the analysis of basketball statistics using objective evidence. APBRmetrics takes its name from the acronym APBR, which stands for the Association for Professional Basketball Research. According to ''The Sporting News'', the APBRmetrics message board was "the birthplace of basketball analytics". Advanced basketball statistics include effective field goal percentage (eFG%), true shooting percentage (TS%), on-court/off-court plus–minus, adjusted plus-minus (APM), real plus/minus (RPM), player efficiency rating (PER), offense efficiency rating, offensive rating, defensive rating, similarity score, tendex, and player tracking. A more complete explanation of basketball analytics is available in "A Starting Point for Analyzing Basketball Statistics" in the ''Journal of Quantitative Analysis in Sports''. Notable basketball analytics practitioners The field of basketball analytics practitioners i ...
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Dallas Mavericks
The Dallas Mavericks (often referred to as the Mavs) are an American professional basketball team based in Dallas. The Mavericks compete in the National Basketball Association (NBA) as a member of the Southwest Division (NBA), Southwest Division of the Western Conference (NBA), Western Conference. The team plays its home games at American Airlines Center, which it shares with the National Hockey League's Dallas Stars. Throughout the 1980s, the Mavericks were a perennial playoff team, led by List of NBA All-Stars, All-Stars Rolando Blackman and Mark Aguirre. The team struggled during the 1990s, entering into a period of rebuilding. In 1998, the franchise's fortunes would change drastically with the acquisition of Dirk Nowitzki, who would become the cornerstone of the most successful period in franchise history, leading the team to its first NBA Finals appearance in 2006 NBA Finals, 2006 and its only NBA championship in 2011 NBA Finals, 2011. The Mavericks later entered a rebuil ...
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Mark Cuban
Mark Cuban (born July 31, 1958) is an American businessman and television personality. He is the former principal owner and current minority owner of the Dallas Mavericks of the National Basketball Association (NBA) and co-owner of 2929 Entertainment. He is also one of the main "sharks" on the American Broadcasting Company, ABC reality television series ''Shark Tank''. As of May 2025, ''Forbes'' has estimated his net worth to be $5.7 billion. Born in Pittsburgh, Pittsburgh, Pennsylvania, Cuban was involved in ventures from a young age, from selling garbage bags to running newspapers during a strike. He graduated from the Kelley School of Business at Indiana University and embarked on a diverse business career that included founding MicroSolutions and Broadcast.com, both of which he sold at substantial profits. Cuban's investments span various industries, from technology and media to sports and entertainment. He has been a prominent figure in the NBA, known for his active involveme ...
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Jeff Sagarin
Jeff Sagarin (born 1948) is an American sports statistician known for his development of a method for ranking and rating sports teams in a variety of sports. His Sagarin Ratings have been a regular feature in the ''USA Today'' sports section from 1985 to 2023, have been used by the NCAA Tournament Selection Committee to help determine the participants in the NCAA Men's Division I Basketball Championship tournament since 1984, and were part of the college football Bowl Championship Series throughout its history from 1998 to 2014. Background Sagarin attended New Rochelle High School, earned a Bachelor of Science in mathematics from the Massachusetts Institute of Technology in 1970 and an M.B.A. from Indiana University School of Business in 1983. He grew up outside New York City in Westchester County in New Rochelle, New York. In 1977 he moved to Bloomington, Indiana. In 1986 he created the computer game '' Hoops'' with Wayne L. Winston. Method Sagarin, like the developers of many ...
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Player Efficiency Rating
The player efficiency rating (PER) is John Hollinger's all-in-one basketball rating, which attempts to collect or boil down all of a player's contributions into one number. Using a detailed formula, Hollinger developed a system that rates every player's statistical performance. Overview PER strives to measure a player's per-minute performance, while adjusting for pace. A league-average PER is always 15.00, which permits comparisons of player performance across seasons. PER takes into account positive results, including field goals, free throws, 3-pointers, assists, rebounds, blocks and steals and negative results, including missed shots, turnovers and personal fouls. The formula adds positive stats and subtracts negative ones through a statistical point value system. The rating for each player is then adjusted to a per-minute basis so that, for example, substitutes can be compared with starters in playing time debates. It is also adjusted for the team's pace. In the end, one ...
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Pace Of Play
In baseball, pace of play refers to the length of time between in-game action, specifically the length of time a pitcher takes between their pitches. A slow pace of play can extend the length of games, which is regarded as an issue in college baseball and professional baseball. To accelerate the pace of play, leagues have instituted rule changes, such as the implementation of a pitch clock in Major League Baseball. Background Game length in Major League Baseball (MLB) has increased over time, with the 1988 New York Yankees being the first team to average over three hours per game. From 2004 through 2014, MLB games increased from an average of 2.85 hours to 3.13 hours. This was in spite of decreases in scoring, with MLB teams scoring 4.1 runs per game in 2014, down from 5.14 in 2000. The amount of time a pitcher takes between pitches directly affects pace of play, and varies widely. In the 2022 MLB season, the last season before the league implemented a pitch clock, the slowest w ...
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NBA Most Valuable Player Award
The NBA Most Valuable Player (MVP) is an annual National Basketball Association (NBA) award given since the 1955–56 season to the best performing player of the regular season. Since the 2022–23 season, winners receive the Michael Jordan Trophy, named after the five-time MVP. Prior to 2021, the winner received the Maurice Podoloff Trophy, which was named in honor of the first commissioner (then president) of the NBA, who served from 1946 until 1963. With the switch to the Michael Jordan Trophy, his name was moved to a new Maurice Podoloff Trophy given to the team with the best regular season record. Until the , the MVP was selected by a vote of NBA players. Since the , the award is decided by a panel of sportswriters and broadcasters throughout the United States and Canada. Each member of the voting panel casts a vote for first to fifth place selections. Each first-place vote is worth 10 points; each second-place vote is worth seven; each third-place vote is worth f ...
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Ridge Regression
Ridge regression (also known as Tikhonov regularization, named for Andrey Tikhonov) is a method of estimating the coefficients of multiple- regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. It is a method of regularization of ill-posed problems. It is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters. In general, the method provides improved efficiency in parameter estimation problems in exchange for a tolerable amount of bias (see bias–variance tradeoff). The theory was first introduced by Hoerl and Kennard in 1970 in their ''Technometrics'' papers "Ridge regressions: biased estimation of nonorthogonal problems" and "Ridge regressions: applications in nonorthogonal problems". Ridge regression was developed as a possible solution to the imprecision of least ...
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Prior Probability
A prior probability distribution of an uncertain quantity, simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable. In Bayesian statistics, Bayes' rule prescribes how to update the prior with new information to obtain the posterior probability distribution, which is the conditional distribution of the uncertain quantity given new data. Historically, the choice of priors was often constrained to a conjugate family of a given likelihood function, so that it would result in a tractable posterior of the same family. The widespread availability of Markov chain Monte Carlo methods, however, has made this less of a concern. There are many ways to const ...
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