Water is essential for most of the soaping reactions people discuss here. Different types of recipes use differing amounts and ratios of water, but they pretty much all require water. Once the soap reaction has finished, though, the water becomes less important and much of it evaporates from the bars over time - they shrink.
The recipes I use all account for water, with its amount depending largely on: The amount and nature of the oils used, the amount of superfatting; the type of alkali, and whether I'm using water as % of oils, lye of a specific concentration, or a particular water:lye ratio. With the exception of liquid soaps that amount of water contributes only a fairly small amount towards the final weight of the soaps. It's the weight of oils that does that.
Here's a recipe from the calculator I use. I have specified the amount and type of oil, zero superfatting, and the water:lye ratio I want to use and it has told me I need 115.15g of water and 67.74g of sodium hydroxide.
When you're doing the reaction this mixture will weigh around 680g. If you left the soaps to cure for, say, 90 days then you're likely to have a weight of around 600g … some 10-15% of the soap bar weight will have evaporated away during the cure*.
* The curing of soap is more than just evaporation, although evaporation is a major part of the process. Curing also allows the bars to harden, albeit mostly dues to evaporation. Curing also allows some moderation of the alkalinity of the soap by reaction with carbon dioxide in the air.
