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A basketball team fields 6 players, they score four points before the violation is noticed. What is the correct decision by the officials?

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Which league is that?

In FIBA, the points are valid, a technical foul is given to the coach, registered as "B1", and 1 of the players must leave the court

Source: FIBA Interpretations 36-7 and 36-8

36-7 Statement.

After it is discovered that a team is participating with more than 5 players, it is also discovered that points have been scored or a foul has been committed by a player of this team while participating illegally. All such points shall remain valid and any foul(s) committed by (or against) that player shall be considered as player fouls.

36-8 Example:

With the game clock running, team A has 6 players on the playing court. This is discovered and the game is interrupted after: (a) A1 commits an offensive foul. (b) A1 scores a field goal. (c) B1 fouls A1 during his unsuccessful shot for a field goal. (d) The sixth player has left the playing court. Interpretation: (a) A1’s foul is a player foul. (b) A1’s field goal shall count. (c) A1 shall attempt 2 or 3 free throws. (a), (b) and (c) The sixth team A player must leave the playing court. In all cases, in addition a technical foul shall be charged against coach A, recorded as 'B1'. (d) A technical foul shall be charged against coach A, recorded as 'B1'.

In the NBA instead, after the free-throw for the technical foul, the coach of the other team (the one who had the correct number of players) is given the option to nullify the points or to resume the game as it was

Source: Rule no. 12 (A) Section III

Section III—Number of Players

a. If the ball is put into play and remains in play with one team having six or more players on the court, a non-unsportsmanlike technical foul will be assessed on the team with too many players and such team would lose possession if it had possession at the time the violation was discovered. Immediately following the free throw awarded for the technical foul, the team with the correct number of players will instruct the Crew Chief to: (1)resume play from the point in time when the technical foul was assessed, under the same conditions as would have prevailed had there been no error with a throw-in, jump ball or foul shot, as appropriate. If the ball is to be put into play with a throw-in, the team who shot the free throw will be awarded possession unless that team just scored and the error was discovered prior to the throw-in being released by the team with six or more players. (2) nullify all play that occurred from the point in time when the ball was put into play with one team having six or more players on the court and ending when the technical foul was assessed, reset the game and shot clock to the point in time when the ball was put into play, and if the ball was put into play by: (a) a throw-in, the ball shall be returned to the original throw-in spot with the ball awarded to the team with the correct number of players, or (b) a missed free throw that remained in play, a jump ball shall be held at center court between any two players in the game, or (c) a jump ball, the ball shall be returned to the original jump ball spot and a jump ball held with the same two players. EXCEPTION: Acts of unsportsmanlike conduct and all flagrant fouls, and points scored from any resulting free throws, shall not be nullified. b. Other errors involving the wrong number of players at the start of play, four or less, will be penalized with a non-unsportsmanlike technical foul and play shall resume from the point-of-interruption. EXCEPTION to a and b: If the violation occurs on (1) a free throw attempt which is to be followed by another free throw attempt, or (2) a free throw attempt that is not going to remain in play, (3) throw-in before the ball is released, (4) prior to a personal foul being assessed, or (5) jump ball before the ball is released.

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