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Similarity scores are among the many original sabermetric concepts first introduced by Bill James. James initially created the concept as a way to effectively compare non- Hall of Fame players to players in the Hall, to see who was either on track to make the HOF, or to determine if any eligible players had been snubbed by the selection committee.
The NBA also posts to the statistics section of its Web site a simple composite efficiency statistic, denoted EFF and derived by the formula, ((Points + Rebounds + Assists + Steals + Blocks) − ((Field Goals Attempted − Field Goals Made) + (Free Throws Attempted − Free Throws Made) + Turnovers)). [2]
New basketball positions were classified by Stanford University student Muthu Alagappan, who while working for the data visualization company Ayasdi, mapped the network of one season NBA players linking them by the similarity of their statistics. Then, based on node clusters players were grouped into 13 positions.
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.
For two objects and having descriptors, the similarity is defined as: = = =, where the w i j k {\displaystyle w_{ijk}} are non-negative weights usually set to 1 {\displaystyle 1} [ 2 ] and s i j k {\displaystyle s_{ijk}} is the similarity between the two objects regarding their k {\displaystyle k} -th variable.
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
SimRank is a general similarity measure, based on a simple and intuitive graph-theoretic model.SimRank is applicable in any domain with object-to-object relationships, that measures similarity of the structural context in which objects occur, based on their relationships with other objects.
Some systems assume parity among all members of the league, such as each team being built from an equitable pool of players via a draft or free agency system as is done in many major league sports such as the NFL, MLB, NBA, and NHL. This is certainly not the case in collegiate leagues such as Division I-A football or men's and women's basketball.