I wasn't a user here when this was described but I wonder why the ratio is described as:

Grounds/brew weights?

To me, it would be easier math if the equation was switched to:

Brew/grounds weight.

If I wanted to brew 25 gm of liquid from 18 gm of grinds by the current equation that would be roughly 70% ratio. However, when describing parameters it is much harder for the user to figure out what, "I brewed 18 gm at a 70% ratio" means for the end product weight. If I tried to figure out in my head, what the end product should weigh, it would be much easier to have the equation say, "I brewed 18 gm at a 140% ratio" because I would merely multiply 18x1.4 which is easier to do in your head.

It's just a convention, with no intrinsic meaning. Someone or several someones did it one way and it stuck.

Don't let them bully you. You can do it your way if it's easier or has more meaning to you. if you want to share it with other people, call it an "inverse ratio" and let them figure out the reciprocal. Speaking of ratios, I'm comfortable with a ratio expression of "1.4," but not with "140%." There's something so wrong about any percentage greater than 100% (not that it isn't done).

Why do you think you find the mental math of multiplying by 1.4 easier than say dividing by 7 and adjusting the decimal point after doing the calculation? Per part of your hypothetical, 7 into 18 is 2, remainder 4; 7 into 40 is 5, remainder 5; 7 into 50 is 7, remainder 1. 25.7 is too many significant digits, so round up to 26g.

Or, do rough and ready "speed math." For instance, 70% is close to two-thirds, 18g is evenly divisible by 2 (2 x 9), simple inspection gets us to a brew mass of around 27g (3 x 9); but 70% isn't actually 2/3, so round down and call it 26g.

However, our 26g results tell us that your 70% wasn't accurate, even to two significant digits. Let's do some easy, mental long division. Temporarily forget the decimal point, use "place holder zeros" for convenience, and it goes like this: 25 goes into 180, 7 times with a remainder of 5. 25 goes into 50, 2 times. Readjust the decimal point and Ratio = 72%, on the nosey.

Speed math? Easier still. 25 (with the decimal point moved two places) is the reciprocal of 4. Multiplying by 4 will give you the same digits as dividing by 25. 4 x 18 = 72. Voila.

Some people find this easy, some excruciating. Me? I'd be an idiot savant if only I were a savant.

Lots of ways to skin the cat, not to mention the calculator on your phone. If your calculations tend to be inaccurate, that might be best.

BDL

Totally agree. I have had to do math in my head every time I work with it. I think VST calls it "brew formula" instead and defines it the way you suggest. Much more intuitive to me, but to each his own.

It's a great tool anyway. I think proposed by Andy S.

Grounds / Brew Weight has the advantage that the result is indicative of beverage intensity.

50% [15g coffee / 30g shot] is less intense than 150% [18g coffee / 12g shot]

Grounds / Brew Weight has the advantage that the result is indicative of beverage intensity.

Good point. In general a positive correlation (both changing in same direction) is more intuitive. A good example is the definition of pH, as many freshman chemistry majors will agree.

I guess it's an individual thing. I find it much easier to picture increasing beverage volume, which I can see, than increasing intensity, which I can't.

So much for the Identity Principle.

BDL

I thought I remember the brewing ratio for espresso being arranged that way to make it distinct and obvious that your talking about espresso instead of brewed coffee which already has it's own brewing radio that expresses the ratio by the weight of the water : weight of the coffee.

I find the coffee ratio, 16:1, counter-intuitive for some reason, even though I know and use it. Actually, I usually use 62.5 grams / liter instead which is less universal (the brewing ratio is unitless) and also mixes mass and volumetric measurements but allows me to calculate my metric extractions fairly well.