Three-point shots in basketball. NBA betting. Throw with one hand from above - “hook”

In basketball, as in other team games, there are moments that go against the rules.

In that case, when a participant tries to throw the ball into the basket, the rules are violated against him, then in such moments the referee can award a free throw into the basket to the offending team.

Free throw in basketball: what is it, basic rules

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

Photo 1. Basketball inventor 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 railings of the balcony in gym and divide the children into two teams. Thereby 1891 considered the birth of basketball and his main rules, of which there were 13.

At what distance from the shield is it performed?

Initially, a penalty was awarded one point. But the free throw line has undergone its changes. At first it was located at a distance 6 meters, and then, later 4 years, the distance has been reduced up to 4.6 m from the shield.

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

How many penalties can there be, in what case are they awarded, how many points are they worth?

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

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

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

In the event of an unsuccessful shot, the number of free throws is set as many points as could have been scored with a successful shot. For example, if a basketball player was about to throw the ball from three-point position, then determine three free throws.

Attention! In the event of a personal foul, the penalty assigned for the violation is carried out by an athlete against whom the rules were violated. In the case of a technical foul, the throw-in may be any basketball player of the affected team.

Any number of free throws may be called during a game, since it depends on the nature of the game of each basketball player.

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

A penalty throw and its consequences end in the following cases:

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

Rules for the competitor taking the throw-in

A basketball player must stand beyond the line designated for such cases, but inside a semicircle.
You need to make a cast within 5 seconds.
The athlete can throw in any way, the main thing is that the ball does not touch the floor.
Until the throw-in is completely completed, A basketball player has no right to touch the free throw line.
The player must not cheat, doing an imitation of casting.

Behavior of other players

The strip along the free throw area may contain five people, three of them defending and two attacking.
The first position on both sides of the restricted area players of the team in whose direction the throw is being made can be occupied.
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 are not allowed to enter the restricted or neutral zone., leave your seat until the athlete making the throw-in releases the ball from his hands.
Participants are not allowed to touch the projectile until it hits the target or touching the ring until it becomes clear that he will no longer be able to do this.
At the moment of contact between the ball and the ring It is prohibited to touch the backboard, ring and basket.
For players It is not allowed to extend your arms through the bottom of the basket and touch the apparatus.
You cannot leave your seats until the projectile leaves the athlete taking a free kick.

Marking the court in the free throw zone, what are the zones called?

The zone for such a throw is called trapezoid-shaped playing area, where there is a semicircle at the top. The facial line forms the base of this trapezoid. Its length is 6 meters. Opposite the baseline, a free throw line is drawn, constituting the top of a trapezoid, length - 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 end line and the penalty line is 5.8 m. Thus, the penalty area is limited to 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 throwing area is represented by two semicircles, where the throw-in line runs in the middle. Inside the limited area, the semicircle should be drawn with a dotted line. And all other lines are normal.

What is the technique and phases of execution

With both hands from below. Is the most in a simple way. When making a cast, you need to aim at a point located above the leading edge of the ring. In order for the ball to fly the required distance, the throw is adjusted by bending the legs and swinging the arms.
With both hands from the chest.
One hand from the shoulder. The most common way.

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

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

The first phase of the throw is just an offering in a circular motion projectile to chest, then the knees are extended and the arms are extended.

Peter

How many dice rolls does it take to defeat a brute force attack?

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

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

David Schwartz

I hope you mean a paper wallet and not a brain wallet. Brain wallets do not use randomness.

Answers

Tim S.

Throwing one stamp gives 6 possible results. The private key is a 256-bit number. But its address includes a 160-bit hash, so that's all you need to use. To know 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 particular 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 sequentially - for example, don't always write the smaller of the two first because you'll remove some entropy) and write down the numbers in order (e.g. "132415614..."), you can use this to populate a cryptographic random number generator, which can provide you with a private key that is as secure as possible.

The Electrum 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 dice rolls.

Penal battalion. How NBA bosses have gone crazy

Daryl Mowry and Dan Reed's idea to reduce free throws exposed existing divisions within NBA leadership.

When looking for an image for an article about free throws, you may be surprised to find that there actually aren’t that many relevant photos.

A search for the phrase “NBA free throws” in the Getty Images photo bank returns about 25 thousand matches, and most of the photos were taken literally as carbon copies. They depict basketball players, mostly world-famous, with the ball in their hands and their gaze directed at the opponent’s hoop, which they need to hit at all costs. The expression on the players’ faces can hardly be called absent, but it doesn’t even come close to reflecting the tension that we are accustomed to associate with a match in the strongest league on the planet (especially when it comes to playoff matches). The free throw is one of the few moments in any match where the photographer can take his time composing the shot. No acrobatics, twisted ankles, gestures or inimitable facial expressions. If you put the appropriate equipment in the hands of ordinary fans, 10 out of 10 people will be able to achieve, if not the same as the pros, then at least a passable result.

Last season, on average 26 times per game, spectators in the stands and in front of television screens were forced to watch NBA players make free throws. An ordinary match of the regular season could boast about 47 attempts from the line performed by basketball players from both teams. It's kind of small world inside a big one, in which the excitement caused by the dynamics of the game episode instantly leads to disappointment, as soon as the referee’s whistle sounds.

Mowry: “The NBA is an entertainment product, and the more direct basketball there is in a given match, the better.”

Far-sighted people (often experts and journalists, sometimes coaches and functionaries) can discuss the specifics of free throws as much as they want, calling them an appropriate punishment for breaking the rules or a necessary evil that basketball has to put up with one way or another. But at the same time, it is difficult to deny that performing almost fifty attempts for two teams takes about 15-20 minutes of pure time from ordinary fans and, above all, television companies. And this despite the fact that the free kicks themselves rarely remain in the memory or become the most memorable episodes of the fights. If we draw parallels with the work of the editor of a sports publication, then penalties are that “water”, the less of which there is in the text, the better. It is for this reason that many foreign companies that buy the rights to show NBA matches cut out the relevant moments, and the spectators in the stands, as soon as the whistle blows, instantly lose interest in what is happening on the court, preferring to bury their noses in the screens of their smartphones.

Several months ago, during the NBA regular season break for the All-Star Game, club presidents of basketball operations and association representatives, regardless of the situation in which it was recorded. The president of the Development League and the general manager of Houston were among the most influential supporters of progressive innovations. There was no talk of changing the rules in the foreseeable future, but the NBA leadership was definitely interested in shortening the duration of a basketball game, and the idea, which seemed crazy at first glance, gained the right to life. Of course, it was not the association itself that had to test it, but the Development League.

The essence of Reed and Mowry's proposal was as follows: if a player was fouled while shooting or a foul was called after the team whose player committed the offense had already exhausted the team penalty limit, the injured basketball player must shoot one free throw. At the same time, its “cost” should vary from one point, if we are talking about an end-van, to three, if a violation of the rules occurred during a throw from behind the arc.

If such innovations are adopted, then instead of 47 attempts per game for two teams, we will get an average of only 26. The average time it takes to shoot free throws simply does not exist, but no one forbids anyone from counting, as they say, by eye. Having undertaken it, we can come to the conclusion that about 45 seconds pass between the whistle, which records a violation of the rules, and the moment when the ball reaches the ring after the execution of the second free throw, and in the case of one attempt (after an “end-and-one” or technical note) – 30. But these numbers vary greatly from case to case: for example, if the center violated the rules in the fight for a rebound on someone else’s backboard, then the process of both teams and the referees crossing the entire court takes almost an eternity. But we can safely take as an axiom the fact that the second and third throws take approximately 15 seconds each, and as a result we will get more than five minutes of saved dirty time.

“The NBA is an entertainment product, and the more direct basketball there is in a given match, the better,” says Mowry. – Numerous surveys conducted at different times only confirm this. The game gets better when there are fewer stops. The pauses, some of which are lengthy, make the audience feel melancholy. Basketball is the most beautiful game in the world, and the closer we can get to having two well-prepared teams play each other without unnecessary and unnecessary interruptions, the better.”

Last season, the Development League tried other innovations to reduce dirty time in basketball games - from reducing the number of timeouts to requiring teams to make substitutions faster - reducing the average time of a match by two minutes. This is not as little as it might seem at first glance, but not even half of those five, which will allow you to save by reducing the number of penalties by more than half. And, more importantly, this time will be erased solely from pauses and stoppages in the game, which in no way compares to the proposal to reduce the length of the quarter from 12 minutes to 10, robbing the fans of a total of 8 minutes of exciting spectacle.

According to various sources, Reed actively promoted the idea of reducing the number of penalties last spring, after a meeting of general managers of association clubs, and often raised the sensitive issue during telephone conversations and informal meetings with representatives of Development League clubs. As a result, the innovation became one of the items on the program of the clubs’ founding meeting in August, but by that time the head of the second most important basketball league in North America had left his post, taking the position of head of the department for partnerships with sports organizations on Facebook. Having lost the support of an influential functionary, the concept, naturally, was not accepted.

“The very idea of reducing the number of free throws to one is of some interest,” commented the Vice President of the Development League for Basketball Operations on the situation surrounding the innovations. Chris Alpert. “But, after consulting with experts, we came to the conclusion that it will significantly affect the integrity of the game and the statistics of basketball players. And we are not eager to artificially create contradictions either in the first case or in the second.”

“The extra 15-20 minutes of “dirty” time resulting from numerous pauses and stops helps basketball players maintain and restore strength during intense matches.”

In support of Alpert's statement, the Development League published interesting statistical calculations confirming that basketball players take the second free throw better than the first (76.3% of shots versus 71.1% in Development League matches, and 77.7% versus 73.2% - in NBA matches). The trend continues in the case of three free throws - the percentage of completions increases from the first attempt to the last. If we are talking about a single throw after an end-to-end, then in the Development League their accuracy is 71.8%, and in association matches – 72.8%. The organization obviously operated with the last two figures, arguing that the players’ statistics would certainly suffer from the innovations.

But how much will giving up two or three free throws for the sake of just one affect the total percentage of shots taken for the season? If we take into account the dry statistics, then indeed, it will become somewhat worse than now. But in general, the innovations will have absolutely no effect on the dynamics of the game. After all, firstly, and secondly, all teams will be on equal terms. The value and importance of free throws has varied since their introduction to the game, and over the past 50 years, free throw percentages have risen substantially to reach a high of over 70 percent. At the same time, the international rules for blocking shots, the implementation of which the Development League initiated in 2010, influenced the final statistics of players much more significantly than Morey and Reed could imagine. In particular, this concerns the number of blocked shots among the bigs, the number of which has rapidly increased from season to season.

You should also take into account the fact that existing statistics will not fully reflect the percentage of free throws made by a basketball player. For example, 75 percent accuracy from the line will not mean that a particular player scored exactly three-quarters of the points after being fouled that he could have. Roughly speaking, if a conditional player goes to the line four times during a match, three of which were due to fouls on shots with middle distance, and another one after the “end-and-one”, then, having sent 3 out of 4 attempts to the target, the Miami defender can bring to the team’s treasury 71% of the points that he should have (in the event that the miss falls on one of shots worth 2 points) and 86% (if the shot after the ball scored with a foul turns out to be missed). All this is true, but in general, a season consisting of 82 matches will reduce the mathematical effect of innovations to almost absolute zero.

In fact, the reasons for Reed's refusal to support the innovations he initiated should be sought not in empirical indicators, but in cultural values. Leaving aside the financial component of the functioning of the Development League, which brings a small profit to those who invest in the organization’s clubs, it exists in order, firstly, to provide players with the opportunity to adapt to the specifics of overseas basketball and progress in order to eventually get the opportunity to play in NBA, and secondly, to serve as a platform for experiments initiated by the association itself. These two goals do not contradict each other, but they also do not coexist in peace and harmony, as it might seem to an outsider. More than once or twice I have heard and read radically opposite statements on this matter. Basketball players who have seen a lot along the way mediocre, who have already completed their playing careers, talk about the importance of the existence of the Development League precisely as a platform for basketball players who did not gain a foothold in the NBA at the first attempt, providing them with the opportunity to resuscitate their own career without extreme measures such as moving to Europe or China. The functionaries of the “new wave”, each of whom wants to bring something of their own to the game, on the contrary, are confident that the organization in which farm clubs perform is a kind of time machine that allows, when changing certain basic settings, to see how basketball might look like a decade or two later.

Throughout his 10 years of work in the NBA, Reed was in the second camp, and his resignation was greeted with regret by people who supported radical and not so radical changes in modern basketball. Mowry and his colleagues at various times described Deng as a man who appreciated the ideas of others, knew how to implement them, and had enough influence to informally convince his own opponents of the feasibility of a particular innovation, avoiding public disagreements and conflicts.

Largely due to the lack of an accepted classification of the above-mentioned purposes of the existence of the Development League into primary and secondary, the NBA still cannot decide on a candidate for Reed’s successor, and hopes to fill the vacant position, at best, by mid-November, when the organization’s regular season starts. Apparently, the choice will be made in favor of innovation, since among NBA general managers the opinion that something needs to be changed in the existing system prevails over the desire of representatives of the older generation of specialists to keep everything in place. Personal opinion Adam Silver it is unlikely that anything will change even if he decides to go against the grain.

For this reason, the discussion about changes in the rules of free throws can be presented as the next stage of a natural conflict between two generations, pitting tradition against research, development and experimentation. It is much easier, of course, to think that the idea failed due to the reluctance of the functionaries to cut to the quick and change the existing idea of basketball, which had developed over years and decades. But in fact, every initiative, no matter how utopian and alien it may seem at first glance, requires detailed discussion and elaboration in order to obtain a digestible form over time. Surely general managers of NBA clubs and the leadership of the association will return to the conversation about reducing the number of free throws more than once or twice more in order to come to a killer argument for or against, and subsequently build on it.

For example, it would not be paradoxical to say that the extra 15-20 minutes of “dirty” time resulting from numerous pauses and stops help basketball players maintain and restore strength during intense matches. We do not undertake to say with certainty whether this is actually the case or not, but this argument is much more objective than the conditional impact of innovations on player statistics. Moreover, in the era information technologies, When

By and large, the NBA can choose the most convenient development of events for itself, and appoint a nameless executive to the post of President of the Development League, who would submit to the collective opinion and voice only the ideas of the majority. Such an outcome is also likely for the simple reason that North America There are enough mediocre specialists who believe that they are quite capable of leading an organization that almost everywhere copies its “big brother” in its activities. In a word, even if any kind of misunderstanding or problematic situation suddenly arises in the process of activity, they can be eliminated or resolved “in the same way” even without having sufficient authority, flexibility of mind or the ability to find a common language with all parties to the conflict.

But at the current stage of their existence, the NBA and the Development League have come to the conclusion that they must improve their own commercial and financial performance at any cost. Therefore, an influential person must be found to fill the position left vacant by Reed, who could correctly set priorities and, over time, turn the organization into a testing ground for various ideas. And not at all because innovation in the existing system is more important than the progress of the basketball players themselves. The fact is that the association and its farm league have raised a sufficient number of really cool specialists who know how to work directly with players. A functionary with remarkable strategic thinking is much more difficult to find.

After the publication of an article about the importance of tempo in basketball, many began to actively use this tool in their analyzes. More and more letters began to arrive in the mail asking for an explanation of how to correctly count possessions and attacks in a basketball match.

There are several scoring formulas that can be used. It all depends on your goals. If you are writing a thesis, then you need to use an exact mathematical formula.

In betting, it is not the accuracy of the calculation that is important, but the consistency of your work. It is important to see the overall picture of the team and the championship, and not rely on those 3-5 matches for which you had time.

The exact formula for counting possessions

Using this formula, you can count the exact number of times your opponent crosses the middle of the field, since it does not take into account possessions that are created after offensive rebounds and compensates for situations where a player commits a foul after a scored shot.

Number of possessions = 0.96 * (FGA – Orb + TO + (0.44*FTA))

Legend:

F.G.A.– number of shots (two-point and three-point)
ORb– offensive rebounds
TO– losses
FTA- number of free throws
The coefficient of 0.44 is applied in order to not take into account situations where a player scores with a foul and takes an additional free kick.
The 0.96 coefficient is used to cover the margin of error that occurs due to team offensive rebounds. For example, in situations where, in the fight for a rebound, the ball goes out of bounds from the defending team, the attacking team gets an opportunity to attack, but it will not be included in the offensive rebounds column.

To count possessions, a simplified formula is most often used that does not include compensation for team offensive rebounds.

Number of possessions = (FGA + TO + (0.44*FTA))

Free throws can also increase the mathematical tempo of the game. For example, in the 2007 Euroleague finals, teams shot 71 free throws. Although there were only 158 opportunities for attack and close to the championship average (162).

Simplified formula

I prefer to consider not only the number of offensive rebounds, but also how well the team competes on offense for the defense. Therefore, in my formula, I take into account the possessions that a team gains through actively fighting on someone else’s backboard:

Number of possessions = 2FG + 3FG + TO + FT/2

Instead of multiplying by 0.44, I always divide the number of penalties by two to make it easier to count in my head, and I always round the value down.

But to objectively calculate your total value, it is important to take into account the speed of the game. Because quite often there are matches in which teams make 15 offensive rebounds, and this gives an extra 30 possessions.

To count the number of attacks in a match, I use the following formula:

Number of attacks = 2FG + 3FG + TO + FT/2 - oRb

Where oRb- offensive rebounds

On average, a basketball team makes 65-70 shots into the basket 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 objective in basketball. There are several types of throws for different positions and situations. During the game you can observe their diversity. Moreover, each player has his own technique, both dribbling and throwing the ball. All this combined with a healthy sense of competition makes for a spectacular show.

Types of throwing the ball into 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 brought to face level; when the arms are straightened, the ball is sent into the basket along a given arc. If all the player’s calculations are correct and the throw is accurate, the ball will fly straight into the opponents’ basket.

2.Throw with two hands from above

This type of basketball shot is used from medium distances. This throw is also relevant when the enemy is closely guarded. To perform a throw of this kind, the ball is carried over the head, with the arms slightly bent at the elbows; when the arms are straightened, the ball is sent into the basket. While straightening the arms, the ball is given the necessary acceleration and trajectory, allowing it to hit the target precisely - the “enemy” basket.

3. Throw with two hands from below

A throw of this type is actively used in the game during a quick pass to the backboard, as well as during attacks on the basket in a long jump. To perform a throw, the player takes the ball in motion under his foot, after which he takes a wide step and jumps. With straight arms, a basketball player throws the ball into the basket, while fully extending his body. When straightening your arms, acceleration is imparted, 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 shots in basketball. Suitable for medium and long distances. In this case, the player holds the ball in his right hand at head level, and when the arm is straightened, the ball is sent into the basket.

5. One-handed overhand throw

This type of basketball shot is used quite often to attack on the move from close distances, as well as from under the backboard. When preparing to throw, the ball is placed under the right foot. At the highest point of the jump, the player's arm straightens and the ball is pushed into the basket with his fingers.

6. Throw with one hand from above - “hook”

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

7. Finishing the ball

When the ball bounces off the backboard, if the basket attack fails, the player can catch the ball and throw it back into the basket.