Top: histogram of the precision of the eccentricity for all of our 118 binaries. For models where an eccentricity is favoured it is the 1σ error bar. For models where a circular solution is favoured it is the upper limit, which is equal to the fitted eccentricity value plus the 1σ uncertainty. The vertical red dashed line is the median precision of 0.0025. Bottom: histogram of the precision of the binary period, in seconds. The red dashed line is the median precision of 1.4 s. We emphasise that the period precision is obtained purely by the radial velocity fit, not from the eclipse timing.