Velocity offsets of Lyα as a function of the absolute UV magnitude for the MUSE LAEs with C III detections studied here shown by the large symbols and a collection of measurements at redshifts from z ≈ 2 to z = 7.73 collected from Kulas et al. (2012), Schenker et al. (2013), Erb et al. (2014), Stark et al. (2015a, 2017), Henry et al. (2015), Willott et al. (2015), Pentericci et al. (2016), Inoue et al. (2016), Bradač et al. (2017), Mainali et al. (2017), Verhamme et al. (2017), Sobral et al. (2018), Hutchison et al. (2019), Cassata et al. (2020), and Matthee et al. (2020a,b), shown by the small dots. To prevent cluttering the figure the estimated uncertainties are not shown. The median errors on the magnitudes and Δv_Lyα are 0.2 mag and 50 km s⁻¹. The dashed curves present the predicted median Δv_Lyα as a function of UV magnitude for a range of redshifts (according to the color coding) from Mason et al. (2018b, corresponding to the black curve in their Fig. 2 from their Eq. (2)). This is based on an abundance matching model relating the absolute UV magnitude to the galaxy halo mass (Mason et al. 2015). Points and curves are color-coded according to object redshift and the color gradient highlights the importance of halo mass, that is available gas reservoir, in producing and determining Δv_Lyα. The solid histograms show the distribution of objects from our study, whereas the dotted histograms include the sample of measurements from the literature.