The signal-to-noise ratio (SNR) of Brillouin optical time-domain analyzers (BOTDA) is modelled and experimentally validated, using direct detection with and without the use of optical pre-amplification. The behavior of SNR as a function of the Brillouin gain and the probe power reaching the photo detection is analyzed in depth using this developed model and checked using two photodetectors with different specifications. It proves that a pre-amplification associated to a good-quality photodetector and a well-matched post-processing filtering can secure the highest SNR for direct-detection BOTDA. Such an optimal SNR presents only a 2.3 dB penalty compared to the ideal shot-noise-limited case that can only be reached using rather sophisticated configurations. In addition, the model here established predicts the SNR at any fiber position in any given experimental condition.