Pure soaps, unlike "detergents", will soften water on their own, however this calls for using quite allot of soap depending upon water and soil conditions. As previous poster stated, forth is a good indication of a good balance between water softening, soil suspension and cleaning activity.
Many vintage laundry manuals would chide housewives about using too much soap for laundry as being wasteful, and would give various methods for testing how hard local water supplies were, and determining how much soap to use per load.
Also as previously stated, it is better to soften water using chemicals or even a whole home water system, than to rely purely on soap. It is also much cheaper than buying all that soap.
If you are using Ivory, or any other "floating" soap, remember a good part of those bars is air, which is why they float in the first place. Thus you may not get as much pure soap bang for your buck per bar, say versus using a harder bar of Fels or some other brand.
Again, if you are going to go this soap/homemade detergent route, your first rinse must be hot or at least warm water, and it is a good idea to add STPP, but not washing soda,or some such to the first rinse water.