Androgens are responsible for the growth spurt of adolescence and for the eventual termination of linear growth which is brought about by the fusion of the epiphyseal growth centers. In children, exogenous androgens accelerate linear growth rates, but may cause a disproportionate advancement in bone maturation. Use over long periods may result in fusion of the epiphyseal growth centers and termination of growth process. Androgens have been reported to stimulate the production of red blood cells by enhancing the production of erythropoietic stimulating factor.
The second theory is similar and is known as "evolutionary neuroandrogenic (ENA) theory of male aggression".   Testosterone and other androgens have evolved to masculinize a brain in order to be competitive even to the point of risking harm to the person and others. By doing so, individuals with masculinized brains as a result of pre-natal and adult life testosterone and androgens enhance their resource acquiring abilities in order to survive, attract and copulate with mates as much as possible.  The masculinization of the brain is not just mediated by testosterone levels at the adult stage, but also testosterone exposure in the womb as a fetus. Higher pre-natal testosterone indicated by a low digit ratio as well as adult testosterone levels increased risk of fouls or aggression among male players in a soccer game.  Studies have also found higher pre-natal testosterone or lower digit ratio to be correlated with higher aggression in males.     
For the off-season athlete there is no anabolic steroid more important or beneficial than testosterone. High levels of testosterone will promote significant increases in lean muscle mass and strength. This is assuming that the individual is consuming adequate calories. Compounds like Testosterone Propionate are not magical, you will still need to feed your body enough calories. During an off-season period of growth, this means total caloric intake will need to be slightly above maintenance. This will, unfortunately, promote body fat gain. However, the key to a successful off-season is gaining lean tissue while minimizing body fat gain to the fullest extent possible. By supplementing with Testosterone Propionate you will be able to achieve this more efficiently. High testosterone levels will promote a stronger metabolic rate. This is not a license to eat like there’s no end in sight, but you should be able to make better use of your calories.