How many warmup pitches are allowed?

How many warmup pitches are allowed by a pitcher between innings?

    Eight warmup pitches are allowed, in one minute 

A league may limit the number of preparatory pitches to less than eight. Some leagues allow only four or five preparatory pitches between innings, to move the game along.


From the MLB Official Rules


8.03
When a pitcher takes his position at the beginning of each inning, or when he relieves another pitcher, he shall be permitted to pitch not to exceed eight preparatory pitches to his catcher during which play shall be suspended. A league by its own action may limit the number of preparatory pitches to less than eight preparatory pitches. Such preparatory pitches shall not consume more than one minute of time. If a sudden emergency causes a pitcher to be summoned into the game without any opportunity to warm up, the umpire-in-chief shall allow him as many pitches as the umpire deems necessary.

8.04
When the bases are unoccupied, the pitcher shall deliver the ball to the batter within 12 seconds after he receives the ball. Each time the pitcher delays the game by violating this rule, the umpire shall call “Ball.” The 12-second timing starts when the pitcher is in possession of the ball and the batter is in the box, alert to the pitcher. The timing stops when the pitcher releases the ball.

The intent of this rule is to avoid unnecessary delays. The umpire shall insist that the catcher return the ball promptly to the pitcher, and that the pitcher take his position on the rubber promptly. Obvious delay by the pitcher should instantly be penalized by the umpire.