Abstract: The crossed undulator is an effective method for polarization control in soft X-ray free electron lasers(FELs). Influencing factors were statistically analyzed for polarization control with a crossed undulator in self amplified spontaneous (SASE) FELs. The effects of the coherence length of radiation, and the relative slippage length and power difference of the two field components were analyzed, and the principles for optimizing an polarization control scheme with a crossed undulator were proposed. These principles are that: the radiation should have good longtitudinal coherence, the relative slippage length of the field components should be short, and the power difference of the two field components should be small. This work provides a theoretical basis for optimization of polarization