Two very pithy and powerful analytical expressions for saturated signal gain and signal output power of fiber optical parametric amplifiers are educed with numerical analysis. Those are realized in three steps, first, a series of numerical values are worked out by numerically solving the couple NLS equations that governed the fiber parameter process. Then the function form for saturated signal gain is figured out by control variates method. At last, adopting least square method, three coefficients are finely obtained with the maximum relative error (in terms of calculated saturated signal gain with numerical integration) no more than 0.46‰. At the same time, the analytical expression for saturated signal output power is worked out as well. Results of this work agree well with existing experiment results.