Inbreeding, done with thought and care, is what is called "creating a line" in animal husbandry. To stabilize a genetic trait in a line of creatures, it is common to take the young and cross them back to the parent with the most important trait. The resulting young are then separated into various groups and cross bred. Each subsequent generation can be crossed back to another group of young - for, kept "separate", you have essentially created two "families" that are very very close in genetic makeup, but not exact.
I have hopes of creating a line of Broadtail Ryukins that breeds successfully with most individuals. Goldfish genetic makeup is extremely complicated - thus you will ALWAYS have a fair number of "bad" fry in a spawning. The goal is to reduce those "bad combinations" to the absolute minimum.
When you cross two unrelated fish you can get a tremendous number - or only a lot. I recently crossed 4 "like" Ranchu. If I had to guess, I would have thought that they were somewhat related. REgardless of their potential relations, their genetic makeups were NOT compatible with each other. I have well over 90% that are really NOT good at all. I crossed two good Broadtail Ryukin together last year and got over 4000 fry to work with over the year. Of those, I selected 2 male and 2 female. This year, I crossed the females back to their dad- the better of the two original parents. These fry are the result. I was lucky. I got at least 75% that are fairly good broadtails. I expect to find more than 4 in this group that I would show or breed.
Next year, (or after) I will split this group and create at least 3 "lines" that, properly bred (and with a LOT of luck) should give me a reliable spawn of good fry each time.