Whether you are dealing with pipes for plumbing or a concrete slab poured in a basement or shower pan, the general minimum for any type of drainage is between an eighth of an inch to a quarter inch per linear running foot. This provides adequate drainage for any water, and can be used in a wide variety of construction protocols, such as bathtubs.
The reality with tubs is that the angle provided is directly up to the manufacturer of the tub. You, as a homeowner, have no control over the actual angle of the tub. As long as the pitch drains the water sufficiently, that is the only concern of the manufacturer. As a rule, they conform to the minimums for construction, which means your tub can be between an eighth of an inch to a quarter of an inch per linear foot.
Tubs are meant to be installed level and square within the framing of the overall house. This means the tub frame on top of which the tub is set needs to be completely level. This is so that when the tub has been installed and filled with water, the water (which is self-leveling) will not spill over the edge. If you attempt to add an angle to your tub during installation, the water will spill over when the tub is filled.
Almost all tub manufacturers request that you set your tub in a base of mortar or drywall mud. This is because the tub’s base needs to be installed on top of a base that conforms to its contours to protect the angle for proper drainage over the years. If mortar or mud is not provided as a base, the tub has the potential to crack out or warp over time, thus affecting the angle on the bottom of the tub.