Phase measurement is widely used in all areas, and all phase FFT(apFFT) has outstanding accuracy in phase measuring among existing methods. To disclose the underlying reasons of the superiority of apFFT in measuring phases compared to other existing methods, based on [1], this paper combines the distribution characteristics of spectral leakages and theory of parameter estimation ,thus successfully leading to one Cramer-Rao lower bound (CRLB) involving 2 unknown parameters estimation suitable to apFFT measuring phases. Based on this, the relationship of apFFT phase error and the frequency offset distribution is also deduced. Moreover, it is also pointed that the novel CRLB is 12dB lower than the traditional CRLB involving three parameters. Consequently, this paper draws several conclusions of apFFT measuring phases under different signal to noise ratios and different frequency offsets. Simulation indicates that the phase measuring variance of apFFT can be defined by CRLB2 with different SNRs and different frequency offsets, verifying these conclusions and correctness of the novel CRLB.