A novel numerical model and an efficient algorithm are developed to calculate the powers of signal and noise light waves in multiple wavelengths bidirectionally pumping fiber Raman amplifiers. The relationship between the noises, including the amplified spontaneous emission noise and the double Rayleigh backscattering noise, and the degree of pumping directionality is studied. According to the simulation results there exists an optimal degree of pumping directionality, at which the total noise power drops to its lowest value. Furthermore, an optimization of evaluating factor considering both the optical signal to noise ratio and nonlinear distortion impact is put forward. After optimization, fiber Raman amplifiers can achieve not only flat gain spectrum but also the best balance between optical signal to noise ratio and nonlinear distortion impact.