I can't speak to cycling but I can speak about golf (no snickers please
). I can only imagine that the benefits of a highly aerobic sport would see huge benefits in the long run from sobriety. Golf was my passion from the time I was 11 years old and I had reached the collegiate level when my alcoholism really kicked in. It ultimately derailed a possible professional career in the sport.
I first got sober at the age of 29. Golf is tricky because it's one of those sports where you can actually drink while playing. The first couple of months after getting sober I couldn't even play due to how strongly I related golf with alcohol. My first year sober I played almost no golf at all. The following spring I started playing again and the results were amazing. My focus, hand eye coordination, and every other facet of the game had improved immensely.
One year later (in the spring) I was playing at the highest level of my life and took a part-time job at an exclusive 54 hole private club because the job included playing privileges as a benefit. Within 3 months I had enrolled in the PGA of America program, passed their playing aptitude test and was promoted to assistant golf professional at this club. The following year I played in several local and regional professional tours as well as 2 Web.com Tour events and 1 PGA Tour event (through local qualifying).
Unfortunately that's as far as I made it, but I would have never made it that far if I hadn't gotten sober. Long story short, I eventually started drinking again and my golf career was over within a year.