Short arming the ball in Football is when a player who is throwing the ball, usually the quarterback, does not extend their arm completely and make the complete motion of the throw. Instead, they mostly use their elbow and wrist to complete the throw and the ball is released around the head area rather than at the end of their extended arm.
Short arming is primarily an issue for pitchers in Baseball, but can also affect quarterbacks. New techniques in passing the ball in recent years have alleviated some of the problems surrounding short arming and it has become an accepted way of passing the ball.
The main draw towards short arming the ball is that is normally comes naturally. When learning to pass the ball, usually at a young age, passers don't understand how to use their full arm to complete the throw and they short arm the pass. This can be corrected over time, but short arming can also be taught to be just as useful as 'long arming', or using a full arm to pass the ball.
Another bonus of short arming is that it gets the ball out quicker with the ball being released around the head area. Aaron Rodgers, one of the NFL's premier passers, releases the ball around his head to get the ball out very quickly.
Firstly, short arming can often put a strain on the passers wrist and elbow areas. Too much strain can cause injuries in the future for the passer. Secondly, short arming the ball often leads to the ball 'floating', or hanging in the air for a long time after the pass. This is because there is more of an upward motion than a forward motion when short arming the ball.