OK Ray, I've been talking about the fineness of the steps within the scale, and you're asking about the size of the scale itself. Re the latter, we're trying to relate the contrast ratio of the display with the dynamic range of the print. One can go about this mathematically, empirically, or both together. I simply haven't done the research to relate the numerical specs from one form of output to the other in terms of their impact on comparative appearance. That would be a considerable exercise. I'm not sure either how fruitful it would be.
Most of our displays probably have more potential or actual contrast than most printers and papers can reproduce, hence the challenge is to "dumb down" the former so that image appearance will be reliable relative to printed output. This is something I do with the calibration settings in ColorEyes Display, and then visually compare appearances between monitor and print. It's totally judgmental and totally non-mathematical (in my head, not under the hood where it is only mathematical), but it works pretty well. My waste ratio (discarded material out of the printer) is in the range of 10%, and more often than not this is a result of "pilot error" rather than miscues from the display. Pilot error usually arises because of that inherent difference between the appearance given from transmitted versus reflected light. This can be bridged with appropriate calibration settings and by soft-proofing to a great extent, but not totally, so depending on the image, stuff can emerge from the printer which appears to be less vibrant than it looked on display. Of course if I thought that by changing my calibration settings I could get the waste ratio down further I would do so, but there seems to be a rather narrow range which works for "most" images and reliability deteriorates once I move outside that range in any direction.