In a recent work, we presented a discriminative backend for speaker verification that achieved good out-of-the-box calibration performance on most tested conditions containing varying levels of mismatch to the training conditions. This backend mimics the standard PLDA-based backend process used in most current speaker verification systems, including the calibration stage. All parameters of the backend are jointly trained to optimize the binary cross-entropy for the speaker verification task. Calibration robustness is achieved by making the parameters of the calibration stage a function of vectors representing the conditions of the signal, which are extracted using a model trained to predict condition labels. In this work, we propose a simplified version of this backend where the vectors used to compute the calibration parameters are estimated within the backend, without the need for a condition prediction model. We show that this simplified method provides similar performance to the previously proposed method while being simpler to implement, and having less requirements on the training data. Further, we provide an analysis of different aspects of the method including the effect of initialization, the nature of the vectors used to compute the calibration parameters, and the effect that the random seed and the number of training epochs has on performance. We also compare the proposed method with the trial-based calibration (TBC) method that, to our knowledge, was the state-of-the-art for achieving good calibration across varying conditions. We show that the proposed method outperforms TBC while also being several orders of magnitude faster to run, comparable to the standard PLDA baseline.