We introduce a new parameter to discuss the behavior of a genetic algorithm. This parameter is the mean number of exact copies of the best-fit chromosomes from one generation to the next. We believe that the genetic algorithm operates best when this parameter is slightly larger than 1 and we prove two results supporting this belief. We consider the case of the simple genetic algorithm with the roulette wheel selection mechanism. We denote by ℓ the length of the chromosomes, m the population size, p C the crossover probability, and p M the mutation probability. Our results suggest that the mutation and crossover probabilities should be tuned so that, at each generation, the maximal fitness multiplied by (1 - p C)(1 - p M)ℓ is greater than the mean fitness.