According to the heavy arrow proponants, resistance to penetration is a formula that increases by the square of the velocity of the projectile, not the mass of the projectile. The faster the velocity, the more the resistance to penetration. Therefore an arrow that derives it's energy largely from speed rather than mass will slow down quicker than an arrow than an arrow that that derives its energy largely from mass.
Shoot a fast carbon arrow into water and see how fast it slowsdown, shoot a slow heavy fiberglass fish arrow into water, and you get lethal penetrationquite deep.