For a beam propagating through turbulence, the statistics of the Strehl ratio are determined by recognizing that the real and imaginary parts of the on-axis far-field pattern can be represented as the sum of many contributions from the aperture. With this in mind, the central limit theorem (CLT) can be used to develop the statistics of the real and imaginary parts of the optical field, which through the appropriate mathematical manipulations as described here can then be used to develop the probability distribution of the far-field irradiance. The results obtained in this way (which we call the CLT theory or analysis) provide an analytic expression that agrees with the results of detailed wave-optics simulations. This provides an approach by which the statistics of the Strehl ratio can be rapidly determined. A key feature of this work is that the analytic results depend on the values of a few relevant turbulence parameters that include $r_0,f_{\mathrm{G}}$ , and ${\sigma }_l^2$ . Therefore, a measurement of these parameters at various sites of interest allows us to rapidly assess the detailed nature of the statistical fluctuations of the far-field irradiance that will be experienced at these locations.