Growth compounds. If you improve 1% at a skill everyday, by the end of a year, you are 38 times better at it (1.01^365).
However, this doesn’t strike us as being realisitic. I improve a little everyday at computer programming, but I certainly haven’t seen a 38x annual boost in productivity. My own experience corresponds to an increase of about 0.05% a day, leading to being about 6 times better at the end of a year (1.005^365).
But decay compounds as well. If you fail to practice, your skill decays at a steady rate. If a skill that decays at 1% per day, only 3% of this skill is retained after a year (0.99^365). Thankfully, growth and decay are asymmetric. Assuming that decay happens at a rate of 0.01% a day, a skill that isn’t practiced for a year decays to 70% of its original value. This value feels more realistic.
Further, it is much easier to revive a decayed skill than to learn a new skill. Assuming that this revivial happens at the rate of 1% a day, a skill that has been neglected for a year can be revived with just 36 days of practice.
Of course, this math is simplistic. Yet, it reflects the key to building and retaining skills – a routine of daily practice for new skills, with regular refreshes to keep the old ones alive.
Observations 