 For many goal-directed activities it is important to distinguish between quality and progress. Quality is primarily an activity-oriented concept, concerning the skill and competence in the performance of some task. Progress is a result-oriented concept, concerning the success of a product relative to some goal. All acceptable work in science has to fulfill certain standards of quality. But it seems that there are no necessary connections between quality and progress in science. Sometimes very well-qualified research projects fail to produce important new results, while less competent but more lucky works lead to success. Nevertheless, the skillful use of the methods of science will make progress highly probable. Hence, the best practical strategy in promoting scientific progress is to support high-quality research. 