confusing espresso brew ratio: 1:1 shot, 1:2 shot and a 1:3 shot

first of all the brew ratio is not same brewing ratio in SCAA

from SCAA :

The ratio of coffee grounds (mass) to water (volume): how much coffee is used for a given quantity of water. This may be expressed in units of either grams per litre

this is mainly used for unpressurised brewing, eg drip, pourover or french press brewing.

This can be simply called as coffee-to-water ratio

it is recommended to be 55 g /L +/- 10%.

    The brew ratio ( or simply ratio of coffee grounds (mass) to water (volume)): how much coffee is used for a given quantity of water. This may be expressed in units of either grams per litre or ounces per US half gallon.

These are related as follows:

    Strength = Brew ratio × Extraction

which can be analyzed as the following identity:

    dissolved solids/water = grounds/water × dissolved solids/grounds

So Brew ratio = Strength / Extraction
or                    = (dissolved solids/water) / (dissolved solids/grounds)

if you have TDS meter, brew ratio
                       = measured TDS / Extraction




somewhere on internet, some simplified it to be used in espresso making:

1:1 shot as ristretto
1:2 shot as normal espresso
1:3 shot as lungo

This causes trouble.

without considering the grind setting, yield extraction, you can make a very weak ( or very strong ) drink with same 1:1 shot.

From Scott Rao:

One of the stickier trends in the past couple of years has been the near-religious adherence, at least in the US, to the 2:1 espresso-brewing ratio.  I’d like to discuss what an espresso-brewing ratio (EBR) is, why it’s relevant, and why it’s a little silly for so many cafes to latch on to this suspiciously harmonious ratio.

What is an Espresso-Brewing Ratio?

Simply put, it’s the ratio of an espresso’s beverage weight to the weight of the dry grounds used to make the shot.  For example, if a barista pulls a 36g shot from 18g of grounds , the ratio would be 2:1. 

Why EBR is relevant

I suspect most baristas do not realize this: if you have exact targets for extraction % and TDS, there is only one EBR that can produce a shot that achieves both targets. For example, let’s say you desire a 20% extraction and 10% TDS.

Using a slightly simplified calculation, the only EBR that can produce a 20% extraction/10% TDS shot is a 2:1 ratio. 

For example, with a 20g dose and 40g shot:

10% TDS = 4g of coffee solids (10% x 40g shot = 4g)
4g of coffee solids extracted from a 20g dose = 20% extraction

A 2:1 EBR can yield a spectrum of extraction/TDS combinations; for example
8% TDS / 16% extraction or
9% TDS / 18% extraction

But no other EBR can produce any of the combinations mentioned above.

It's a combination of:


dose

yield extraction ( grind size)
time (or flow rate )
brew temperature


From Jim Schulman's Espresso 101 , (red arrow is what you want to achieve):

Espresso Compass from Matt Perger:

fivesenses

SCAA protocol