Several factors...
First of all, here is another vote for Earl Hinz' book. It is required reading, in my opinion. Two important issues are type of anchor and depth. A Danforth, for example, looses almost all of its holding power on short scope, and may not even set. 7-1 scope is pretty well mandatory. A CQR fares a lot better in this regard. I don't know about a Delta, but a Bruce looses only a proportional amount of holding power. For example, it will hold about half at 3-1 scope as it does at 6-1. With regard to calculating loads on an anchor, an important factor is the surge load. Since this is distributed over the length of the chain or road, it becomes less of a factor in deep water. In other words, a ten foot wave is proportionately much less of a surge in fifty feet of water than a ten foot surge in twenty feet of water.Consequently, a smaller scope ratio will work in deeper water. Of course, chain lies much flatter along the sea bed than rode, up to a point at which it becomes as taught as line. Until that point, however, a chain rode needs much less scope to achieve the same pull angle as line.In practice, I use a storm anchor sized Bruce as a main anchor. This allows me to have acceptable holding power at short scope, if necessary. But, if a storm comes up, I need only to let out more rode for the anchor to gain its full holding power and function as a storm anchor. I seem to spend a lot of time anchoring in depths of between thirty and fifty-five feet, which helps. My goal is to generally have about 5-1 scope, but I will go with 3-1 on occasion, and sometimes go as high as 7-1 or 8-1 or a bit more. The bottom is generally good sand and I have gone as much as eighteen months between visits to a marina. I sleep well, and don't mind leaving the boat to herself during the day as this system seems to work pretty well. My observation of cruisers is that, for whatever reason, Europeans seem to use less scope, 3-1 or 4-1 being thought of as quite acceptable. On the other hand, they do seem to slide around quite a bit, particularly French and German boats. Sorry about that!I use 220 feet of 1/4 inch Hi-Tensile chain backed up by 300 feet of line. Used to be the recommended 1/2 inch, but 5/8 is much easier to handle and chafe resistant, if less stretchy. In uncrowded anchorages of thirty feet or deeper (plus four feet of freeboard), I will typically lay out all the chain plus a little less than the depth in line. My scope will be appropriate for whatever depth I am in (up to about 85 feet), I have a snubber already in place, the line never touches bottom, and I will let out as much line as I need in stormy conditions. We last dragged in 1986 (TOUCH WOOD!!!)