This study presented a mathematical model based on the characteristics of the index method and the screening method to examine the effect of selection systems on employee performance. In general, performance gains increase as the selection ratio decreases or as the multiple correlation coefficient between tests and criteria increases. Furthermore, when the selection ratio and the multiple correlation coefficient are identical, the index method resulted in greater performance gains than the screening method. Finally, considerations that must be taken into account when applying such mathematical models to selection practice were discussed.