BACKGROUND: Fastest mean (MV HYPOTHESIS: Goodness-of-fit would be higher for individualized compared with generalized RTF-velocity relationships and comparable for both execution equipment conditions (with or without straps), and the MV STUDY DESIGN: Cross-sectional study. LEVEL OF EVIDENCE: Level 3. METHODS: After determining the PBP 1-repetition maximum (1RM), 20 resistance-trained male athletes performed 2 sessions randomly, with and without lifting straps, consisting of single sets to failure against the same load sequence (60% to 80% to 70% 1RM). Generalized (pooling data from all subjects) and individualized (separately for each subject using multiple-point or 2-point methods) RTF-velocity relationships were constructed. RESULTS: Individualized RTF-velocity relationships were always stronger than generalized RFT-velocity relationships, but comparable with (MV CONCLUSION: The use of lifting straps during the Smith machine PBP exercise does not affect the goodness-of-fit of the RTF-velocity relationships or the velocity values associated with different RTFs. However, caution should be exercised when using different methods. CLINICAL RELEVANCE: The benefits of the RTF-velocity relationships can be extrapolated when using lifting straps, and the 2-point method can also be used as a quick and more fatigue-free procedure. Nevertheless, it is imperative for coaches to ensure that these relationships are reflective of fatigue experienced during training.