As computers with tens of thousands of processors successfully deliver high performance power for solving some of the so called “grand challenge” applications, scalability is becoming an important metric in the evaluation of parallel architectures and algorithms. The authors carefully investigate the prediction of scalability and its application. With a simple formula, they show the relation between scalability, single processor computing power, and degradation of parallelism. They conduct a case study on a multi ring KSR-1 shared virtual memory machine. However, the prediction formula and methodology proposed in the study are not bound to any algorithm or architecture. They can be applied to any algorithm-machine combination. Experimental and theoretical results show that the influence of variation of ensemble size is predictable. Therefore, the performance of an algorithm on a sophisticated, hierarchical architecture can be predicted, and the best algorithm-machine combination can be selected for a given application.