The number of sets and reps depends on your goal: strength ranges from 1 to 5 reps, muscle size 6 to 12 reps, and endurance 15 to 25 reps.
If only if it was this simple. Powerlifters train in the rep range of 1 to 5, bodybuilders 6 to 12, and all other endurance athletes train in the high reps range of 15 reps and beyond.
Based on the principle of specificity this is true, but only to a certain degree. As an advanced athlete you begin to reach a level where gaining anything is hard to do and seldom occurs. Elite athletes often need to train outside of normal boundaries to reach new levels.
For example, an elite powerlifter might have to deadlift in the 20 rep range for awhile in order to further increase their strength boundaries. Likewise, a bodybuilder that typically trains their back with high rep lat pull-downs and seated cable rows can greatly benefit from heavy low rep deadlifts.
Regardless of the rep ranges you choose, having a quantified number of sets and reps provides an invaluable way to measure training volume.
High volume programs based on sets and reps provide an easy way to manipulate training volume. German volume 10 x 10 and Vince Gironda’s 8 x 8 are extreme examples of high volume routines. Nevertheless, these volume programs yield a quantified amount of work completed. The result is a training variable that can be manipulated.
For example, if you are accustomed to bench pressing 150 lbs for 5 sets x 10 reps, the total pounds bench pressed in a workout would be 7,500 lbs . The total work done or workout volume is measured in total pounds lifted.
If the number of sets is reduced to 4 sets the total pounds lifted or work done is halved to 6,000 lbs. The total work has been reduced, creating a the need to increase other training variables such as intensity. To balance this deficit, intensity can be increased by adding 5 or 10 lbs to the lift.
The reduction in volume can be offset with an increase in intensity – lifting a heavier weight. This juggling act between volume and intensity can be repeated over time – the end result is a training cycle.