In the context of detection of speaker recognition identity impersonation , we observed that the waveform probability mass function (PMF) of genuine speech differs from significantly of of PMF from identity theft extracts. This is true for synthesized or converted speech as well as for replayed speech. In this work, we mainly ask whether this observation has a significant impact on spoofing detection performance. In a second step, we want to reduce the distribution gap of waveforms between authentic speech and spoofing speech. We propose a genuiniza-tion of the spoofing speech (by analogy with Gaussianisation), i.e. to obtain spoofing speech with a PMF close to the PMF of genuine speech. Our genuinization is evaluated on ASVspoof 2019 challenge datasets, using the baseline system provided by the challenge organization. In the case of constant Q cep-stral coefficients (CQCC) features, the genuinization leads to a degradation of the baseline system performance by a factor of 10, which shows a potentially large impact of the distribution os waveforms on spoofing detection performance. However, by ''playing" with all configurations, we also observed different behaviors, including performance improvements in specific cases. This leads us to conclude that waveform distribution plays an important role and must be taken into account by anti-spoofing systems.