In sport, why are there weight classes? Why is there gender segregation? Anyone who has boxed or grappled with someone 100lb heavier than them understands why. It's because a heavier opponent is generally a stronger opponent, and all other things being equal, the stronger athlete wins. This is true in football, MMA, soccer, dance, and golf. It is intuitively understandable that strength will matter more in some of these sports (a strong dancer is not as crucial as a strong MMA fighter), but strength pervades all aspects of life to some degree. When force production is a requirement of a task, higher strength will make the task easier.
The question then becomes 'how best does one acquire strength for these sports?' The answer by many is 'do exercises that mimic the movements done in the sport.' While this thinking superficially makes sense, it is wrong. Practice and strength acquisition necessarily must have different movements (unless the sport is competitive lifting). If a quarterback wants to be able to throw a football farther, and he trains for this by using a 10lb football, his technique in throwing will fundamentally change. His body will move differently in response to the greater resistance. When the time comes to throw a normal football, he will likely be slightly stronger, but because his technique is now different, his accuracy and precision in throwing the ball will be worse.
Conversely, if strength is acquired generally and then incorporated into the technique of throwing the football, the muscles will be able to exert a greater force on the ball. This will make the ball have a higher initial speed when it leaves the quarterback's hand which will make the football to travel farther. The prescription for this process of strength acquisition is actually quite simple.
The quarterback needs to do exercises that incorporate the most muscle mass and move a great amount of weight. This will stress the muscles without affecting the motor learning associated with these sport movements. These exercises will include the full-depth back squat, the overhead press, the deadlift, and the bench press. The quarterback will schedule his strength training around his practices to ensure he does not lose technical proficiency. As he becomes stronger incrementally, he will also be practicing his sports movements: throwing, strafing, catching the snap and back peddling, and others. This practice will ensure his techniques are solid and maintain that way as he is able to generate more force: on the ground, against other players, against the ball.
All aspects of life are enhanced by increasing the ability to exert a force over an external resistance. The more force oriented the activity, the more crucial the requirement for strength. Attempting to mimic sport based techniques for strength movements is an ineffective way to become stronger for sport. A better way is to acquire strength generally using heavy barbell movements that involve a lot of muscle mass and concurrently practicing the sport movements. The squat, overhead press, deadlift, and bench press are such heavy barbell movements that facilitate this general increase in strength.