Yes, a freshman is exposed to more and, hopefully, better training, but what ultimately leads to the improved speed?
I would argue the speed of practice and play are the likely determinates. As an athlete, you won't make the cut if you don't shift gears and practice and play at a faster pace. This is done everyday, as better athletes and more demanding coaches and practices don't have time for turtles. This daily demand ultimately forces an adaptation. The neural correlates are the obvious upgrades. Improved motor unit recruitment, and likely increased myelination of the specific patterns of movement.
From my perspective, this demand must be the basis of training. The demand for speed must be high year round, as neural development is not an easy or quick process.
The athletes I work with sprint "all-out" on a weekly basis. We often make this into competitive situations with races, chase, and mirror drills. Basically anything that increases the level of motivation. Which leads to some points regarding motivation.
Research has shown that decreased levels of motivation decrease the level of neural output, as electrical stimulation can increase contraction strength after maximal voluntary contraction has been attempted, but upon verbal encouragement the MVC can be increased. Call it what you will, CNS fatigue or other, motivation needs to high to maximize neural development, as the nervous system is the driver of muscle adaptation. Which is also why fatigue needs to be managed to maintain high output with attempts to move fast. Move fast to be fast (specificity).
Plus, the racing, chasing, and mirroring in movement skills leads, not only to increased motivation, but to a greater external focus, which has been scientifically shown to outperform an internal focus almost all the time. Greater external focus improves performance and efficiency. Studies on attentional focus using EMG have shown an external focus leads to decreased muscle activity (efficiency), while improving accuracy, balance, and speed.
Obviously there are times of need which an internal focus may be a necessity, possibly with technique work, but often this can be accomplished with an external focus. "Push the ground away from you" (external) vs. "extend your hips".
Get athletes out of their heads and bodies and free up the higher levels of conciousness to play the game. Let the primitive centers of the brain take care of coordination, intensification and attenuation of movements.
Train fast and motivate through external focus. Neurologically time is limited.