Math in Basketball – How Math Is Used in Sports – Cool Math
At first glance, basketball and math seemingly have little in common. While basketball is hugely popular in American schools, math has a considerably smaller fan following. However, a closer look at the sport reveals that there is a considerable amount of math in basketball. Pointing out how math is used in basketball is a great way to get your kids more excited about angles and percentages, while helping them realize how important math is in everyday life.
The angle at which the ball is thrown is determined as the angle made by the extension of the player's arms and a perpendicular line starting from the player's hips.
The math in basketball involves a wide range of math topics. Kids can practice geometry, percentages and even basic mathematical operations while playing or watching a game of basketball.
Geometry in basketball
Whether they realize it or not, basketball players make use of many geometric concepts while playing a game. The most basic of these ideas is in the dimensions of the basketball court. The diameter of the hoop (18 in), the diameter of the ball (9.4 in), the width of the court (50 ft) and the length from the three point line to the hoop (19 ft) are all standard measures that must be adhered to in any basketball court. Knowing these measurements is useful for kids who would like to practice basketball at home without access to a full-fledged basketball court.
The path the basketball will take once it’s shot comes down to the angle at which it is shot, the force applied and the height of the player’s arms. When shooting from behind the free throw line, a smaller angle is necessary to get the ball through the hoop. However, when making a field throw, a larger angle is called for. When a defender is trying to block the shot, a higher shot is necessary. In this case, the elbows should be as close to the face as possible.
Understanding arcs will help determine how best to shoot the ball. Basketball players understand that throwing the ball right at the basket will not help it go into the hoop. On the other hand, shooting the ball in an arc will increase its chances of falling through the hoop. Getting the arc right is important to ensure that the ball does not fall in the wrong place.
The best height to dribble can also be determined mathematically. When standing in one place, dribble from a lower height to maintain better control of the ball. When running, dribbling from the height of your hips will allow you to move faster. To pass the ball while dribbling, use straighter angles to pass the ball along a greater distance.
Understanding geometry is also important for good defense. This will help predict the player’s moves, and also determine how to face the player. Facing the player directly will give the player greater space to move on either side. However, facing the player at an angle will curb his freedom. Mathematics can also be used to decide how to stand while going on defense. The more you bend your knees, the quicker you can move. Utilizing geometry, math in basketball plays a crucial role in the actual playing of the sport.
Statistics in basketball
Statistics is essential for analyzing a game of basketball. For players, statistics can be used to determine individual strengths and weaknesses. For spectators, statistics is used to determine the value of players and analyze the performance of an individual or the entire team. Percentages are a common way of comparing players’ performances. It is used to get values like the rebound rate, which is the percentage of missed shots a player rebounds while on the court. Statistics is also used to rank a player based on the number of shots, steals and assists made during a game. Averages are used to get values like the points per game average, and ratios are used to get values like the turnover to assist ratio.
Addition and Subtraction in Basketball
For young basketball fans, math in basketball is a great opportunity to practice simple skills like counting, addition and subtraction. Young kids can add up the points made in every shot to get the team’s total score. Kids can also be asked to use subtraction to determine how many points a team will need to catch up with the leading team, or to win the game.
More than 94' - Rusty LaRue
5/17/2014
The newest trend in basketball is the use of advanced statistics not only to evaluate teams but individual players as well. Player Efficiency Ratings strive to drill all the stats a player accumulates down to one number that represents their effect on the game and individual productivity. The amount of statistical information and ratings available on the NBA is mind boggling. If you visit the NBA Stats Glossary you can see all the available stats and ratings. As a coach, I have often utilized player efficiency ratings as a way to motivate and track a player's progress.
Back when I played in the NBA the EFF rating was used the most and often included on the box score. The NBA's Efficiency Rating is a single number measure of a player's overall contribution (both positive and negative) to a game he plays in. It is calculated as follows: (Points + Rebounds + Assists + Steals + Blocks) - ((Field Goals Att. - Field Goals Made) + (Free Throws Att. -Free Throws Made) + Turnovers). The biggest problem with the EFF rating is it does not factor in minutes played so therefore measures productivity but not really efficiency. Players who play more minutes are more than likely going to have a higher number. The positive to the EFF is that it is very easy to calculate.
The newest efficiency rating in the NBA is the Player Impact Estimate (PIE). PIE measures a player's overall statistical contribution against the total statistics in games they play in. PIE yields results which are comparable to other advanced statistics (e.g. PER which I discuss below) using the following formula: (PTS + FGM + FTM - FGA - FTA + DREB + (.5 * OREB) + AST + STL + (. 5 * BLK) - PF - TO) / (GmPTS + GmFGM + GmFTM - GmFGA - GmFTA + GmDREB + (.5 * GmOREB) + GmAST + GmSTL + (.5 * GmBLK) - GmPF - GmTO). While I have never used PIE with any of my teams I do like that it creates a statistic relative to the game. Basically it is giving you a percentage showing how much of a positive or negative impact a player had on a game.
One of the simplest efficiency stats which is now shown on all NBA box scores is the +/-. The +/- stat looks at point differential when players are in and out of a game, demonstrating how teams perform with various combinations. While I like and use this statistic, I don't feel it truly represents a single player's impact on the game.
If you want to take player efficiency stats to an even more detailed analysis you can take a look at John Hollinger's PER on ESPN. The PER is an extremely complicated formula based on minutes played, pace and other factors. Due to how complicated it is, PER is not a stat coaches outside of the NBA and NCAA can use with their players because it's nearly impossible to calculate.
Because of this, I created a much simpler PER which I oddly enough named "Simple PER". Simple PER is calculated as follows: (2FG Made*2) - (2FG Attempted*.75) + (3FG Made*3) – (3FG Attempted*.84) + (FT Made) - (FT Attempted*-.65) + Rebounds + Assists + Blocks + Steals - Turnovers. Similar to PER, the Simple PER only gives positives for scoring if you shoot a decent percentage (see picture for breakeven shooting percentages). If a player scores a ton of points but shoots a very low percentage then they would not have a positive Simple PER. I chose a relatively low breakeven shooting percentage but that can be adjusted as needed. I like this formula because it is simple to calculate but factors in shooting percentages.
No player efficiency rating is perfect because it is practically impossible to drill down a player's impact into one number. However, these formulas and numbers if used consistently can be a great way to evaluate, motivate and educate players on the game and their impact on helping the team win.
Rusty LaRue
Semi-random thoughts on life, leadership, and the game I love.
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The language of basketball. Pick-and-roll, Pick-and-pop, Isolation
28 August
Our site presents the fifth issue of the rubric Language of Basketball . In it, we talk about basketball terms - borrowed words, specific expressions and jargon - the language that all participants and fans of the game speak. Each word is accompanied by a video tutorial with illustrative examples.
We bring to your attention the fifth series of the project The language of basketball , in which we will analyze three terms in detail: pick-and-roll, pick-and-pop, and isolation.
Pick & roll and, after both of their defenders move towards the latter, begins to move towards the ring (roll) and receives a pass to an open throw. In the classic version, this combination should end with a pass from the defender to the post, after which he scores a simple two points from under the ring. However, now there are many variations of the drawing of the so-called "two". For example, a defender after leaving the screen can throw from a distance or go into the pass. Also, pick-and-rolls are often used to create unequal exchanges, which are then successfully used by attacking players to aggravate the situation. Pick and roll is one of the easiest ways for the attacking team to gain an advantage over the opponent. Currently, there is no uniquely effective defense system that can cope with this combination. There are many different options for building a pick-and-roll defense, but none of them guarantee success. That is why this combination is the most popular in modern basketball and is present in the arsenal of every team.
Pick and pop (eng. Pick and Pop ) Pick and pop is a variation of pick and roll. Unlike the basic combination, the “big” one here does not fall under the ring, but rather rolls back to the arc. Having received the ball from the point guard, he attacks from a distance. This interaction is not as effective and popular as pick-and-roll, but more and more teams are introducing it into their arsenal. The advent of pick-and-pop had its impact on the game. If earlier the fourth-fifth “numbers” spent most of the time near the three-second zone, now they are increasingly entering the arc, from where they attack with a fairly high percentage. Almost any VTB United League team has such snipers among the "big" ones. Moreover, CSKA forward Andrey Vorontsevich became the most effective long-range driver of the past season, outperforming a whole group of recognized snipers-defenders in this race. Other “big” ones also successfully use pick-and-pops and attack from a distance. Among them are Sergey Monya, Konstantinos Kaimakoglu, Kaspars Berzins, Travis Peterson and Rolands Freimanis.
Isolation Isolation or "aizo" is a basketball term for a combination in which an attacking player tries to beat his guardian one on one and hit someone else's basket. At the same time, his teammates try to stretch the opponent's defense with their movements and give the attacker space to beat. Isolations are often used by teams that have individually strong players. Their success comes from a combination of athleticism, speed and good dribbling. At the same time, Keith Langford or Sonny Weems, for example, are characterized by power passes in which they literally push through their opponents. But Tyreke Rice and Aaron Jackson rely more on their own speed. "Aizo" usually come to the fore at the end of tense matches, when the leaders are ready to take responsibility and the fate of the fight is decided by one throw. At the same time, isolations are very effective during the match, when the attacking player has a clear advantage in class over the defender.
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Rules of Basketball
How the rules have changed in your favorite game
How the rules have changed in your favorite game
WE ALL LOVE TO PLAY BASKETBALL, BUT DO YOU KNOW THE RULES FOR EXACT?
Basketball was invented by James Naismith in 1891. Then everything was different: playgrounds, baskets, balls…
!!! Read about the evolution of balls in the article:
Basketball was invented by James Naismith in 1891. Then everything was different: playgrounds, baskets, balls…
!!! Read about the evolution of balls in the article:
The history of basketballs
The history of basketballs
What balls are played now and how it happened
Beginning
The rules have also changed a lot during this time. Initially, there were only 13 of them in basketball:
The ball can be thrown in any direction with one or two hands.
The ball may be hit with one or both hands in any direction, but never with the fist.
The player cannot run with the ball. The player must throw the ball from the point at which he caught it, except for a player running at high speed.
The ball must be held with the hands. You can not use the forearms and body to hold the ball.
In any case, hitting, grabbing, holding and pushing the opponent is not allowed. The first violation of this rule by any player shall be called a foul; the second foul disqualifies him until the next ball is scored, and if there was an obvious intention to injure the player, then a disqualification for the entire game. It is not allowed to replace a disqualified player.
Punching the ball is a violation of points 2 and 4, the penalty is described in point 5. commit no foul).
A point is scored if a ball thrown or bouncing off the floor hits the basket and stays there. Defending players are not allowed to touch the ball or basket while shooting. If the ball touches the edge and the opponents move the basket, then a point is scored.
If the ball goes out of bounds, it must be dropped into the field by the first player to touch it. In the event of a dispute, the referee must throw the ball into the field. The thrower is allowed to hold the ball for five seconds. If he holds it longer, then the ball is given to the opponent. If either side tries to play for time, the referee must give them a foul.
The referee must monitor the actions of the players and fouls, and notify the referee of three consecutive fouls. He shall have the power to disqualify players under rule 5.
The referee must watch the ball and determine when the ball is in play (inbounds) and when it is out of bounds (out of bounds), which side should be in possession of the ball, and any other actions that the referee would normally take .
The game consists of two halves of 15 minutes each with a break of 5 minutes between them.
The side with the most goals during this time period is the winner.
The most important rule change in the history of basketball was the introduction of dribbling. In the original version of the game, this was prohibited by paragraph 3 of the rules.
One of the first changes in the game and the rules was the replacement of the basket with a ring with a net. It seemed to be very inconvenient to climb after the ball every time after a hit. Around the same time, free throws, dribbling appeared, and the composition of the teams was fixed for 5 players on the court at the same time. Before that, in some matches, up to 50 people could be on the court at the same time. All this happened back in 1896-1897.
The emergence of FIBA (International Basketball Federation)
Basketball in the early 20th century became more popular and the rules in each country could be different. This was one of the reasons why FIBA appeared in 1932 year. At the first FIBA Congress, the teams were approved (5 people and 2 substitutes), and it was decided that after each goal there would be a throw-in in the center. This rule was removed after 4 years to reduce the advantage of tall players.
Over the next few years, the main changes were related to the number of personal fouls, the number of players on the bench and the introduction of a time limit for getting the ball into the opponent's half of the court.
More changes came in 1952 after the Olympic Games. The game became very boring, because the teams held the ball, having received a minimal lead in the score. Everyone understood this and searched for solutions for several years in order to save the life of basketball. At 1954 Danny Biason proposed to the NBA to limit the time for the shot to 24 seconds. At the 1956 Olympics, there was a similar rule: it was necessary to make a throw in 30 seconds. At the same time, to add equality between defense and attack, another rule familiar to us appeared: you need to start dribbling the ball before the supporting leg comes off.
Then the game became similar to the modern one from a technical point of view: dribbling, shots, a three-second zone appeared. In 1979, the NBA added a three-point line, and in 19In 1984, FIBA also added an arc.
!!! An article about the evolution of the three-point shot and interesting facts:
10 interesting facts about the three-point shot.
10 interesting facts about the three-point shot.
Three-pointer evolution and insane records.
Changes in the rules and basketball since 1956 have included the number of free throws, the situations when these free throws are given, as well as individual and team remarks. Some rules were introduced, and a few years later they were canceled. For example, the "3 for 2" rule: if a player was fouled in the shooting phase, then if one of the first two shots was missed, he could make another free throw. This rule was later removed.
Since the 1990s there have been constant changes: the emergence of alley-oops, changes in the timing and rewriting of the rules of running, which continue to this day.
From the most interesting: if the team has 0.3 seconds or less to throw the ball from behind, then it must be a one-touch throw. It takes at least 0.4 seconds to perform a full throw.
Derrick Fisher made similar throws:
And here is a small selection of videos of how they throw in 0.
Basketball players understand that throwing the ball right at the basket will not help it go into the hoop. On the other hand, shooting the ball in an arc will increase its chances of falling through the hoop. Getting the arc right is important to ensure that the ball does not fall in the wrong place.
The more you bend your knees, the quicker you can move. Utilizing geometry, math in basketball plays a crucial role in the actual playing of the sport.
Young kids can add up the points made in every shot to get the team’s total score. Kids can also be asked to use subtraction to determine how many points a team will need to catch up with the leading team, or to win the game.
The NBA's Efficiency Rating is a single number measure of a player's overall contribution (both positive and negative) to a game he plays in. It is calculated as follows: (Points + Rebounds + Assists + Steals + Blocks) - ((Field Goals Att. - Field Goals Made) + (Free Throws Att. -Free Throws Made) + Turnovers). The biggest problem with the EFF rating is it does not factor in minutes played so therefore measures productivity but not really efficiency. Players who play more minutes are more than likely going to have a higher number. The positive to the EFF is that it is very easy to calculate. 
5 * BLK) - PF - TO) / (GmPTS + GmFGM + GmFTM - GmFGA - GmFTA + GmDREB + (.5 * GmOREB) + GmAST + GmSTL + (.5 * GmBLK) - GmPF - GmTO). While I have never used PIE with any of my teams I do like that it creates a statistic relative to the game. Basically it is giving you a percentage showing how much of a positive or negative impact a player had on a game.
Each word is accompanied by a video tutorial with illustrative examples. 
Currently, there is no uniquely effective defense system that can cope with this combination. There are many different options for building a pick-and-roll defense, but none of them guarantee success. That is why this combination is the most popular in modern basketball and is present in the arsenal of every team. 
Almost any VTB United League team has such snipers among the "big" ones. 
At the same time, Keith Langford or Sonny Weems, for example, are characterized by power passes in which they literally push through their opponents. But Tyreke Rice and Aaron Jackson rely more on their own speed. 
Then everything was different: playgrounds, baskets, balls… 
If he holds it longer, then the ball is given to the opponent. If either side tries to play for time, the referee must give them a foul. 
It seemed to be very inconvenient to climb after the ball every time after a hit. Around the same time, free throws, dribbling appeared, and the composition of the teams was fixed for 5 players on the court at the same time. Before that, in some matches, up to 50 people could be on the court at the same time. All this happened back in 1896-1897. 
