Left half in hockey is the left midfield. Their job depends on the strenghts of the rest of the team. If the team is strong, the left half's job is to stop the ball from passing the 25m line and hit it back into the D for their forwards to score. If their team is weak then the left half will be more a defender and should stay back to be another defender. The position of left half, is difficult to play because it is on the left hand side so requires a lot of reverse stick work, a strong hit (to play the ball up to the forwards) and the player has to be extrememly fit (to run back and forth to defend and attack.)
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It is a kind of right midfield position. The right half is responsible for most sideline and free hits on that side of the field, tackling or marking the opposing left wing, "switching" (passing the ball back, across, then forward to gain an open area in the forward area), linking passes between the fullbacks to the wing or inside forward/inner, and supporting them and the centrehalf or centreforward in offense or the fullbacks in defense, as well as involvement in many setpieces. As they are heavily involved in all aspects of play, the halves must be fit, skilled in both attacking and defending, and possess a wide variety of skills.
Technically, any player apart from the goalie can go anywhere on the field. But a right half would be expected to do both defense and offense, so anywhere along the length of the field, and on the right side of the field, are the areas of operation for that position.
Halves are a combination role, involved in both attack and defense, and link each together. The left half covers the left side of the field, generally from the defensive baseline to the offensive 23-metre line.