How do doctors determine whether I need a hard cast or a soft cast for my hand?

Type of fracture. Whether you are placed in a splint ("soft cast") or regular hard cast depends upon the type of fracture you have, and the length of time you will need to keep it on. If the fracture is minor, stable and will heal in a short period of time, a splint is easier and often more comfortable. If your fracture requires 3-4 weeks or more to heal, then a cast is more durable and more practical.
Type of fracture. If the fracture is stable and not at risk of displacing, a soft cast may be adequate. Conversely, if the fracture is at risk of displacement and hard cast is needed to provide the stability needed for fracture healing and to prevent it from shifting into an undesirable position.