This is the most widely known by the general public about publishing. All costs for editing, design, printing, and marketing are paid by the book publisher and royalties (certain percentage or commission) are paid to the author on the sales of each book.
This is the program that is most familiar to prospective authors because the media announces huge “advances” paid to celebrated authors. I equate this to the announcement of lottery winners of large amounts. It barely reflects the greater percentage of those that received little or nothing by doing the same thing.
The determination of giving someone an advance on future sales was made by the publisher as a business decision and given to the PR department to make the publisher look good and to create an anticipation for the upcoming book. The business decision to give the advance on sales probably met several criteria not announced with the PR campaign.
The author may have a huge following already from previous sales, a ready made market though his/her affiliations through public speaking or a great publicly recognized persona. Rarely is a huge advance paid just because it is well written. Every publisher knows that ultimately it is the public who decides the next best seller, not the desire of the publisher or the author.
Legacy Publishing does this type of publishing as part of the normal practice of publishing as we, too, are looking for the next “best seller” in the authors we publish. They, of course, will be under the same scrutiny as other publishers in that we need to be convinced, like anyone else you would approach to make a financial investment in a business venture.