AndyS: Very late getting in on this post, but excellent idea! I only wish I had stumbled upon this before. I love your idea of the Brewing Ratio!
As a home baker I frequently use a very similar term called baker's percent, which is the relative weight of various ingredients to that of the flour. By understanding various bread formulas based upon their baker's percent, one can immediately appreciate differences in hydration, yeast, salt, or any number of ingredients without having to do any calculations. (Many bread formulas are simply published in baker's percent...) The system, being essentially normalized, allows for the direct comparison of vastly different styles of bread.
In the same way I can see your idea as doing the same for coffee. It already has provoked quite a bit of discussion on the basic (water+coffee) drinks; now add-in milk, foam, and perhaps even sweeteners (god forbid!), and imagine what an explosion of discussion that can generate. (Which I see as all good...) With your BR numbers we now have a "scale invariant" means to approach the discussion.
Forgive a small diversion, and perhaps proposal/consideration, here. Most reader's can simply skip this part!
There's an interesting difference in the baker's percent system vs. the one you propose. Perhaps rev. 2.0 of your brewing ratio might consider redefining the percentages in a similar manner?
In the baker's percent system, the percentage shows each ingredient as a ratio of the total flour weight, so it not a true percentage in the sense that it does not represent the percentage of the part vs. the whole. Thus flour weight (read dry coffee weight) will always be 100%. This actually ends-up being very convenient, though not immediately being the most intuitive choice. The value of doing it this way becomes particularly apparent when evaluating multiple-ingredient "recipes" (read multiple-ingredient drinks).
If we applied this approach to your concept the coffee will always be the 100% ingredient, and all other ingredients (e.g. water) will be relative to the dry coffee weight. Since the coffee will always be represented by a value of 100% "barista's" percent, any single or multiple combination of ingredients can immediately be appreciated with respect to the dry coffee weight via simple addition of their "barista's" percent - no division is required as in a conventional percent system.
For instance in a milk-based espresso drink one would simply calculate: barista's % water + barista's percent milk. In the traditional system one would have to calculate (% water + % milk)/%coffee.
Since all ingredients are always normalized with respect to the coffee (flour), all constituent ingredients just simply add without losing the "meaning" of the "barista's" percent, which is the ratio of the ingredient with respect to the coffee...
Also one often characterizes breads by their (baker's) percent water (hydration), yeast, salt, etc. This works well even across vary different styles of bread. The same would hold true for espresso drinks, in all of the various forms it now is found on the street. From the Char$'s Frappucino (argggh!) to the 3rd wave cafe's ristretto, they can all be understood, or at least contrasted, by their "barista's" percent of water, milk, or wet ingredients, or by their "barista's" percent of sweetener.
Another advantage is that since one knows (at least in principle) up front the dry weight of the coffee but not necessarily the total weight of the drink they will eventually pull and build, the "barista's" percent can easily be measured for every component as the drink is being built. (To do this in standard percent one would have to "know" the total drink weight before it is even built!) This requires a simple digital scale with a tare and counting function. (I frequently do the same for my breads where I will first always determine up front how much total flour I will use...)
This is done by simply weighing the coffee (I actually pre-dose all of my coffee right after roasting in tiny single-shot tuperware-like containers) and then switching to counting mode, normalizing the beans weight to a count of 100 "pieces". Thereafter all weights will automatically be in "barista's" percent. The nice part is that the tare function will continue to work, so one just tares the scale before each ingredient is added and simply reads-off each ingredient directly in "barista's" percent as the drink is built-up...
So now how to add the variable of extraction time? Now that we have normalized the water and coffee weights, they no longer have to take "2 dimensions" of an x-y chart, but rather just 1, the BR number. So the second dimension/axis can be freed up to represent the extraction time.
I can now picture a map wherein shaded areas are drawn out on such a field of BR versus extraction time, sort of a topological map of sorts, except that in this "map" the peaks will be the "sweet spots" for the respective drink, the mountains would be the variations in the respective drink as it is practiced from cafe to cafe, barista to barista, and the "elevation lines" would be degrading levels of quality.
So each drink type will be a sort of "mountain", and each "mountain" will probably have a ridge line whose "verticality" (assuming BR is on the X-horizontal axis and extraction time on the Y-vertical axis) represents the particular drink's relative resistance to degradation with respect to the effects of extraction time. (I'd expect these ridge-lines to tilt /-way vs. \-way, indicating that a higher BR [more coffee; less water] can somewhat compensate for a higher extraction time...)
Furthermore drinks that are very similar (i.e.: drinks that are often debated) will have shallow valleys between their respective mountains, while very different drinks (i.e.: drinks that are not easily confused) will have very deep valleys between them.
No doubt every single person will draw up such a map quite differently due to it's subjective nature, but perhaps some generalities can still emerge from map to map?
Will have to put together a sample/illustrative plot when I find the time...
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