## Monday, November 9, 2015

### Measurement Granularity

Answering a question on StackExchange, and I came across some very nice little articles by the Six Sigma system people on Measurement System Analysis:
Establishing the adequacy of your measurement system using a measurement system analysis process is fundamental to measuring your own business process capability and meeting the needs of your customer (specifications). Take, for instance, cycle time measurements: It can be measured in seconds, minutes, hours, days, months, years and so on. There is an appropriate measurement scale for every customer need/specification, and it is the job of the quality professional to select the scale that is most appropriate.

I like this because this issue comes up a lot in issues of the mathematics of game design: What is the most convenient and efficient scale for a particular system of measurement? And what should we be considering when we mindfully choose those units at the outset?

One key example in my D&D gaming, is that at the outset, units of encumbrance (weight carried) were ludicrously set in tenths-of-a-pound, so tracking gear carried by any characters involves adding up units in the hundreds or thousands, frequently requiring a calculator to do so. As a result, D&D encumbrance is infamous for being almost entirely unusable, and frequently discarded during play. My argument is that this is almost entirely due to an incorrect choice in measurement scale for the task -- equivalent to measuring a daily schedule in seconds, when what you really need is hours. I've recommended for a long time using the flavorfully archaic scale of "stone" weight (i.e., 14-pound units; see here), although the advantage could also be achieved by taking 5- or 10-pound units as the base. Likewise, I have a tendency to defend other Imperial units of weight as being useful in this sense (see: Human scale measurements), although I might be biased just a bit for being so steeped in D&D (further example: a league is about how far one walks in an hour, etc.).

The Six Sigma articles further show a situation where the difference in two production processes is discernible at one scale of measurement, but invisible at another incorrectly-chosen scale of measurement. See more below: