In basketball, as in other team games, there are moments that do not follow the rules.

In that case, when a contestant tries to put the ball into the basket, the rules are violated against him, then at such moments the referee may award a free throw to the basket to the offending team.

Free throw in basketball: what is it, basic rules

The history of this throw begins with the birth of basketball itself. James Naismith while being a teacher physical culture College in Springfield, I thought about how to diversify my lessons, where gymnastic elements were constantly performed.

Photo 1. Inventor of basketball James Naismith. In his hands he holds one of the first basketballs and a basket into which the projectile is thrown.

His idea was to tie fruit baskets to the railing of the balcony in gym and divide the children into two teams. Thereby 1891 considered the birth of basketball and its main rules, which were 13.

At what distance from the shield is

Initially, one point was awarded for a penalty kick. But the free throw line has changed. Initially, it was located at a distance 6 meters, and then later 4 years, the distance is reduced up to 4.6 m from the shield.

Reference. Such a throw is assigned as a result of a personal or technical foul.

How many free kicks can be, in what case they are awarded, how many points they bring

Depending on the violation, a different number of penalties may be set.

So, when a violation of the rules occurs on an athlete who was not going to throw, and the team of the player who violated the rules more than 5 fouls, then two free throws are awarded.

If the participant was going to make a throw, and the rules were violated against him, but the throw-in itself turned out to be accurate, then the throw is counted, and also assigned one penalty.

In the case of an unsuccessful throw, as many penalties are set as the number of points that could be scored with a successful throw. For example, if a basketball player was about to throw a ball from three-point position, then determine three penalties.

Attention! In the case of a personal foul, the penalty imposed for the violation shall be athlete against whom the rules were violated. In the event of a technical foul, the throw-in may take any basketball player on the affected team.

Any number of free throws can be called per game, since it depends on the nature of the game of each basketball player.

If there are few violations for which penalties are awarded, then the number of shots will not be large. When there are many such violations, there are more throws.

A free throw and the consequences arising from it end in the following cases:

• The ball hits the basket from above, gets stuck in it or goes through it.
• The projectile can no longer hit the target after touching the ring.
• The ball touched the floor.
• The projectile for the game became dead.

Rules for the participant taking the throw-in

• The basketball player must stand beyond the line designated for such cases, but inside the semicircle.
• Need to make a throw within 5 seconds.
• The athlete can throw in any way, the main thing is that the ball does not touch the floor.
• Until the face-off is completely completed, a basketball player is not allowed to touch the free throw line.
• The player must not cheat, doing an imitation of casting.

Behavior of other players

• The lane along the free throw area may contain five people, three of them defending and two attacking.
• First position on both sides of the restricted area can be occupied by the players of the team in whose direction the throw is made.
• Athletes need to take only those positions that were assigned to them.

Photo 2. Performing a free throw in basketball. In this case, the players occupy a special position in the penalty area.

• These basketball players cannot enter the restricted and neutral zone, to leave his place until the thrower has released the ball from his hands.
• Participants must not touch the projectile before it hits the target or touch with the ring until it becomes clear that he can no longer do this.
• At the moment the ball touches the ring it is forbidden to touch the shield, ring and basket.
• For players it is not allowed to extend the arms through the bottom of the basket and touch the projectile.
• You can not leave your places until the projectile flies from the athlete making a free kick.

Marking the area in the free throw zone, as the zones are called

The zone for such a throw is called trapezoid play area, where the semicircle is at the top. The front line makes up the base of this trapezoid. Its length is 6 meters. Opposite the front line, a free throw line is drawn, constituting the top of the trapezoid, with a length of - 3.6 meters.

Photo 3. Diagram of a basketball court. The arrows indicate the various lines and zones, including the penalty area.

The distance between the nearest edges of the front and penalty lines is equal to 5.8 m Thus, the free throw zone is limited by the end line, the penalty area and the two lines that connect them. Its color should be the same as the color of the central circle.

The throw area is represented by two semicircles where the face-off line is in the middle. Inside the restricted area, a semicircle must be drawn with a dotted line. All other lines are normal.

What is the technique and execution phases

• Both hands underneath. Is the most in a simple way. When casting, you need to aim at a point located above the front edge of the ring. In order for the ball to fly the desired distance, the throw is regulated by bending the legs and swinging the arms.
• Both hands from the chest.
• One hand off the shoulder. The most common way.

Reference. Before 1950 throwing with one hand from the shoulder was performed extremely rarely, most often at that time they used a throw with two hands.

When taking a throw-in, it is very important to be in a relaxed state, calmly look at the target, take the most comfortable posture : Spread your legs shoulder-width apart and slightly bend at the knees.

The first phase of the throw just is the offering roundabout projectile to chest, then the knees are extended and the arms extended.

This article provides detailed information about the effectiveness of scoring, the use of the three-point line in modern league NBA (since 2010), reasons for the increase in three-point shots, including how Stephen Curry and the Golden State Warriors (GSW) were able to win the team's tough 2014-2015 season championship. thanks to an effective set of points.

It has been more than three decades since the introduction of the three-point line in basketball. Although she was not mentioned in the original 13 rules, she is important element playing basketball and for the past 5 years has been in the spotlight in the NBA.

To begin, let's go back in time to the start of the 2013-2014 NBA season. LeBron James and the Heat, which already had some of the most famous and iconic players on its roster, played out the NBA Championship season by beating the San Antonio Spurs 4-3 in the NBA Finals.

However, when the season began, something changed. As most people know, by that time LeBron James and the other four players starting lineup already played as a team, but one player suddenly began to stand out more and more. That player was Shane Battier.

Battier cannot be attributed to typical players. Day after day, he's been looking at game footage since 2009, when the NBA began using video analytics ubiquitously. He studied the playing inclinations of basketball players with such thoroughness that it interested the coaching staff of the league and raised the question “What if ..?”.

This story can be treated as another funny case, but it was then that the situation began to change.

Insure rates

Clearly, other factors also played a role. Executives who included Sam Hinkie (former head of PHI headquarters), Daryl Morey (currently general manager of HOU), and Bob Myers (at this moment serves as general manager of GSW), began to pay attention to the importance of numbers and statistical analysis at the end of the season of league games.

Increasing the number of three-point shots

In truth, the introduction of the three-point line, which took place before the 1979-1980 NBA season, was deliberate and changed the game by expanding on the original 13 rules of modern basketball.

Above is a graph that clearly shows that since the introduction of the three-point line, scoring trends have changed dramatically throughout the NBA. But how does this prove the point that shooting from the three-point line contributes to a significant increase in performance?

The obvious answer is that the value of the shot made has now increased for the outside observer. However, in order to better understand the essence of this phenomenon, let's study the graph below.

Over the past 8 NBA seasons (from 2010 to 2018), the number of 3-point hit attempts has skyrocketed as teams realize that it takes a lot more effort to get a point, and therefore the scoring of those attempts has also increased.

Naturally, if the frequency of one type of throw increases, then the number of throws of another type decreases. According to basketball-reference.com, where all the data for this article is taken from, the most popular type of shot in NBA games since the mid-80s. and until the early 2000s. There was a shot from an average distance.

All teams agreed that attempts to make three-point shots, especially from the corner, are statistically 20-35% more likely to win the game, as indicated by the results of calculating the contribution of players to the overall victory. These calculations are widely used by team analysts and data scientists throughout the league.

Bob Myers, GM of GSW, is one of the most established senior managers who has come to prioritize playing with the numbers as a key to winning.

So far, the Golden State have managed to remain a successful team thanks to Stephen Curry's scoring shots with ease from behind the arc (close to the middle of the court). Clay Thompson effectively assists Curry in making those 3-point shots. They were even collectively nicknamed the Splash Brothers as the league leaders in scoring three-point shots.

3-Point Shots and NBA Betting

It's safe to say that in today's NBA, the phenomenon of efficient scoring has become a trend that influences the betting process. Players can bet more efficiently with enhanced statistics now available to the general public.

In my final comment, I would say that the effectiveness of high-scoring three-point shots is clear. Making shots of this type resulted in higher scoring, raising the NBA league average to 100–101, which is the same as when the 3-point line was first introduced.

However, there is one interesting pattern that is becoming more and more obvious. The upward trend in three-point shots is due to players who, unlike traditional defenders, forwards and centers, can play in most positions on the court.

As the number of players capable of playing most positions increases in the league, there may be an increase in mid-range shots or two-point shots from long range, as well as a gradual increase in the popularity of hitting fouls.

Bettors should keep track of information on the stats.nba.com website. This resource contains the most accurate statistics available to the general public. This data can help you understand how teams play basketball players.

Peter

How many rolls of the die are needed to defeat an attack with brute force?

At bitaddress.org, I decided to use Brain Wallet and create my own physical randomness using bones. (I understand that playing dice is more efficient than typing dozens of random keys on a keyboard.)

How many rolls are needed to create a passphrase that would defeat a brute force attack on my keys?

David Schwartz

I hope you mean paper wallet and not brain wallet. Brain wallets don't use randomness.

Answers

Tim S.

Throwing one die gives 6 possible outcomes. The private key is a 256 bit number. But its address includes a 160-bit hash, so that's the one you should use. To find out how many dice rolls you need to get that much entropy, you need to know when 6^n > 2^160 (because the probability of a certain sequence of n dice rolls is 1/6^n). This is equal to ceil(log(2) * 160 / log(6)) or 62.

So if you roll a die 62 times (or a pair of dice 31 times, etc.) but be sure to count the die separately and in a consistent manner - e.g. don't always write the lower of two first because you'd remove some entropy) and write down the numbers in order (e.g. "132415614..."), you can use this to populate a cryptographic random number generator that can provide you with a private key as secure as possible.

Electrum's seed is 128 bits, and is believed (at least by those who created and use it) to be secure enough that not only one private key, but also All your private keys. To match this entropy, you need 50 die rolls.

A well-known American basketball analyst who worked in the NBA teams Denver Nuggets and Seattle Supersonics, the author of the book on basketball statistics Basketball on paper, Dean Oliver identified four key factors in the game that most affect the final result.

These four factors refer to four different basketball skills and they are fairly independent of each other.

The first and most important factor in the game is getting the ball into the basket. From the very first days, as soon as basketball was invented by James Naismith, his main task was to get the ball into the basket and not let the other team score. In this regard, nothing has changed since the invention of the game. However, simply counting the percentage of hits from the game is not entirely correct. For example, if a player made 6 field goals and all 2-pointers and scored 3 times, then he scored 6 points with a field goal percentage of 50. If a basketball player made 6 field goals, all three-pointers and hit 2 times, he scored those 6 points for 6 attacks, but his field goal percentage is only 33. Therefore, the effective field goal percentage indicator was taken as an estimate of the field goal hitting factor, which is calculated by the following formula:

Eph. PP% \u003d (P + 0.5 * ZB 3 points) / SI, where

P - the total number of hits from the game

ZB 3 points - three-point goals scored

SI - the total number of shots from the game.

The second factor that affects the game is the careful attitude to the ball and minimizing the number of ball losses in the game. This factor can be very important, especially in children's and youth matches, where dribbling and passing are not yet fully learned elements of the game in the arsenal of young basketball players. It is possible that some very young players are not able to get the ball across the half court, which means there is no way to even shoot in attack. In professional basketball, this problem is not so pronounced due to the fact that each team has several players who are able to pass the ball to the opponents' half, so pressing all over the court at the highest level is far less often successful than in children's or youth competitions. . However, in fact high level the number of ball losses can play a decisive role in the success or failure of the team. Since losses deprive the attacking team of even the opportunity to make a throw in the attack.

This factor is best expressed as the ratio of total turnovers to total possessions in the match.

% PT = PT/Vl, where

PT - the total number of losses in the match,

Vl - The total number of possessions of the team in the match.

Vl \u003d SI - PdN + PT + 0.4 * ShTv, where

SI - the total number of shots from the game;

PT - the total number of losses in the match;

ШТв - the number of free throws taken.

The third factor that affects the result of the match is offensive rebounds. If a team is able to recover the ball after misses, then by and large it is able to solve the problem of the first factor - the effective percentage of hitting. It is clear that with offensive rebounds, the goal remains to score the ball into the basket, but the possibility of re-attacking the ring can serve well in matches when the shot simply simply “does not work”.

Dean Oliver looks at a team's offensive rebounding ability by calculating the ratio of offensive rebounding to total offensive rebounding.

PdN % = PdN / (PdN + PdZ prot), where

PdN - the number of rebounds in the attack;

PdZ prot - the number of rebounds of the opposing team on their shield.

The fourth factor is the ability to get on the free throw line as often as possible. It is the ability to shoot free throws, and not “score free throws” or show a high percentage of hits from free throws. Teams that line up on the free throw line are more likely to be more effective than teams that score higher free throw percentages. There can be exceptions to the rules in any match, and teams can lose matches without hitting free throws, but in the long run, the ability to get on the free throw line often allows teams to win more matches than a few misses from the penalty line lose.

1) Calculate the ratio of STv / SI, where

ШТв - the total number of free throws made;

2) the ability to hit free throws SHZ/SI is calculated, where

ШТз - the number of free throws scored;

SI is the total number of field goals made.

In the book, an analysis of statistical indicators was carried out, where Dean Oliver determined that not all factors are equally equivalent. A team can outperform rivals in three of the four factors and still lose. A team can stand out in three categories, but be weak in the fourth and achieve an average result. Determining the value of each of these factors is very important and helps determine the strategy for building a successful team.

If we evaluate the importance and value of factors on a 10-point scale, then:

1. Effective percentage of hit - 10 points.

2. The ratio of losses to the total number of possessions - 5-6 points.

3. The percentage of rebounds in the attack - 4-5 points.

4. The ability to often shoot free throws - 2-3 points.

As a percentage of importance, these factors will be arranged in the following form:

1. Effective hit percentage (40%).

2. The ratio of losses to the total number of possessions - (25%).

3. Percentage of offensive rebounds - (20%).

4. The ability to often shoot free throws - (15%).

Doing your statistical research for NBA matches, you can see that the team that showed the highest field goal percentage won 79% of the games.

The importance of hitting in basketball is undeniable, but if a team loses the ball, then they also lose the opportunity to not only hit, but even attempt a shot. In the NBA, the teams with the fewest turnovers win 58% of their matches. And if the percentage of hitting the two opponents at the end of the game was approximately the same, then the teams that lost the ball less often won 69% of the matches.

With the two teams roughly equal in hitting percentages, offensive rebounding is another important factor – the team that collected the most offensive rebounds won 63% of their matches.

Teams that get fewer personal comments win 67% of the time.

On average, a basketball team makes 65-70 basket shots and up to 20-25 free throws per game. At the same time, the preparation for the throw itself is the main content of the entire game. But getting into the basket is the main goal in basketball. There are several types of throws for different positions and situations. During the game you can observe their diversity. At the same time, each player has his own technique, both dribbling and throwing the ball. All of this combined with a healthy competitive feel makes for a spectacular show.

Types of ball throws in the basket in basketball

1. Throw with two hands from the chest

This type of throw is actively used to throw the ball into the basket, mainly from long distances. Also, such throws take place in the absence of active opposition from the defender of the other team. In preparation for such a throw, the ball is clasped with the fingers of both hands, after which it is carried to the level of the face, when the arms are straightened, the ball is sent to the basket along a given arc. If all the calculations of the player are correct, and the throw is accurate, then the ball will fly straight into the opponents' basket.

2. Throw with two hands from above

This type of basketball throw is used from medium distances. Also, this throw is relevant when the opponent is closely guarded. To perform a throw of this kind, the ball is carried overhead, while the arms are slightly bent at the elbows, when the arms are straightened, the ball is sent to the basket. During the straightening of the arms, the ball is given the necessary acceleration and trajectory, allowing it to hit the target exactly - into the "enemy" basket.

3. Throw with two hands from below

A throw of this type in the game is actively used during a quick pass to the shield, as well as during basket attacks in a long jump. To shoot, the player takes the ball in motion under the foot, after which he takes a wide step and makes a jump. With straight arms, the basketball player throws the ball into the basket, while fully extending his body. When straightening the arms, acceleration is given, due to which the ball flies into the basket. It is also extremely important to land correctly after performing this maneuver.

4. Throw with one hand from the shoulder

This is one of the most common types of ball throws in basketball. Applicable at medium and long distances. In this case, the player holds the ball in his right hand at head level, while straightening his arm, the ball goes into the basket.

5. Throw with one hand from above

This type of basketball shot is used quite often to attack on the move from close range, as well as from under the shield. In preparation for the throw, the ball is placed under the right foot. At the highest point of the jump, the player's arm is extended and the ball is pushed into the basket by the fingers.

6. Throw with one hand from above - "hook"

This kind of throw is used by the central players to attack from close and medium distances. To throw, the player turns his left side to the shield, pushes off with his left foot, makes a jump, while right hand with the ball in an arcuate motion rises up and throws it into the basket.

7. Finishing the ball

When the ball is pushed off the backboard, in case of an unsuccessful attack of the basket, the player can catch the ball and throw it into the basket again.