Titration is a process used to measure the unknown concentration of a known reagent in a given solution. In this case, it is used to measure the concentration of a specific chemical (
soap) in your water. For this reason, you would not necessarily measure a difference in titration level (concentration) between a soft and hard water sample.
The basic reason to use soft water vs hard water is efficiency of the chemical. All things being equal, the
soap does not have to "clean" (react with) soft water before reacting with the organics on a vehicle as it does with hard water. Therefore, a given concentration (titration level) will not clean as well in hard water as it will in soft..