All of those sports require quickness, strength, some endurance, explosiveness and thousands of hours of training. Surely, improved recovery would benefit dopers as well. There you have it...
It won't be the only factor, but all skills being equal 9or at comparable level), the doper prevails by a large margin. And if you are exhausted after many rounds, your skills deteriorate in that crucial third round, last few minutes, or in the play off rounds.
If there is money in the sport, or at least a glory (as in any Olympic sport), there is doping. You can bet your life on it.