The ball bearing race characteristic you seem to be asking about is called "osculation". Osculation is the relationship between ball diameter (D) and race track radius of curvature in a plane transverse to the rolling direction (r). Osculation is typically defined as a ratio (r/D) or percentage. For example, if you have a 1.000" dia ball and a race track radius of curvature of 0.530", that would be an osculation of 0.530 or 53.0%.
Ball bearings commonly use different osculation for the inner and outer race tracks. This helps provide a better balance of contact fatigue life between the inner/outer race track surfaces, and more optimized ball/race rolling contact conditions for improved efficiency. The osculation used for each race is basically a compromise between efficiency and contact stress levels. A typical good quality ball bearing might use an osculation of 51% to 52% for the inner race and 53% to 54% for the outer race. I don't know of any rolling element bearing standards that specify tolerances for osculation or race track curvature transverse profile/radius. I've had some custom aircraft ball bearings made using an SCD specifying an osculation tolerance of +/-0.50% (ie 52.5% to 53.5%), and the FAI reports showed all osculation values were well within spec. So meeting that osculation tolerance must not have presented a problem for this particular vendor.