Softballs are rated based on two metrics - Coefficient Of Restitution (COR - pronounced like core) and compression. COR represents how "bouncy" the ball is. The higher the COR, the more bouncy the ball is and, generally, the farther it will fly. COR is the percentage of reduction in speed for a ball bouncing off a wall. If a ball is thrown at a wall at 80 miles per hour and bounces off at 40 miles per hour, the speed has been reduced by 50%. The ball would be rated with a COR of .50 (referred to as a fifty COR ball). If your league plays with a .44 COR ball, the speed bouncing off the wall would be 35 miles per hour.
Softball compression is a measure of how hard a softball is. The higher the compression, the harder the ball, and generally, the farther it will fly. Compression is measured by how many pounds of force are needed to squeeze two sides of the ball in by a total of one-quarter of an inch. If a test shows that it takes 375 pounds of force to squeeze the ball by one-quarter inch, the ball is certified as a 375 pound compression ball. The ASA has only approved two levels of compression - 375 pounds and 525 pounds. 375 pound balls are softer than 525's. The ASA "rounds up" to assign the compression rating. For example, if the test shows it only takes 325 pounds of force to achieve the one-quarter inch squeeze, the ball will be rated as a 375 compression ball. This means your league may be playing with a ball rated as 375 compression, but it is really softer than a true 375 compression ball because of the "rounding up."