Iterating your UI on paper saves time in the long run because doing iterations in code later on typically takes longer since there is more connected functionality.
It’s also harder to throw away and change code once a site is built. However, it’s common for developers to skip the design stage and dive right into a build.
Paper generally refers to sketching, wireframing, and mockups; sequentially, each of which is more time intensive. Getting your ideas visualized quickly helps others respond to them. Low fidelity can encourage more feedback and modification, if needed, since high fidelity looks complete and expensive.
The design portion of a code-heavy project is typically the smaller portion of a project, so iterating early based on the team’s ideas and user feedback is not only better for the product, it saves money. In The User Experience Team of One, Leah Buley relates that sketches are cheap, encourage exploration, forstall perfectionism, invite conceptual feedback, and engage others.
Often, the best experience comes from combining more than one option. Exploring a large number of options on paper is a great way to iterate quickly, something harder to do at the code level. In the process, burning through the bad ideas quickly is also important. The more ideas that are available to respond to, the more information is gathered about which solution might be most appropriate and effective. User testing can be done off of paper as well.
Bottom line, design starts to build form and function around your ideas and options in a deeper way than coding typically can, and prioritizing and starting a rapid UI/UX prototyping process on paper can go a long way toward saving time and money in the long run.