Effective SNR mapping (ESM) is a powerful technique for optimizing the performance of orthogonal frequency division multiplexing (OFDM) based wireless systems. ESM transforms a vector of subcarrier SNRs into a scalar effective SNR, which represents the SNR that would yield the same error performance in an equivalent system operating over an additive white Gaussian noise (AWGN) channel. This technique significantly simplifies the development of adaptive coding and modulation (ACM) algorithms. As the distribution of the effective SNR, when only imperfect and outdated channel state information (CSI) is available, cannot be expressed in closed form, we develop an approximate statistical model which is based on the beta distribution. Our model is compared in terms of approximation accuracy against models based on the Gaussian distribution, the gamma distribution and the more complex Pearson and generalized extreme value (GEV) distributions.