Where we left off#
- Week 1: a production cost, measured before any tax or margin in dollars per litre
- One litre of beer and of spirits are not the same product!
Unit that makes them comparable?
Treating the standard drink as a serving suggestion is a public health decision. Treating it as a unit of account is an economic one, and the two have been conflated in the literature for thirty years.
The Standard Drink as a Unit of Account (Journal of Beverage Economics, 2020)
Learning objectives#
By the end of this lecture you should be able to:
- explain why raw volume cannot be compared across beverage categories
- convert any shelf price into a price per standard drink
- state what a standard drink is, precisely, in grams
- describe how one bad conversion propagates through an entire dataset
The problem with litres#
| Product | Volume | ABV | Litres |
|---|---|---|---|
| Full-strength beer | 375 mL | 4.8% | 0.375 |
| Bottled wine | 750 mL | 13.5% | 0.750 |
| Vodka | 700 mL | 40.0% | 0.700 |
Ranked by litres, the wine wins. Ranked by what is actually being bought, it does not come close.
The unit#
One Australian standard drink is exactly ten grams of pure alcohol.
Not a glass. Not a serving. A mass.
standard_drinks = (volume_ml × abv_percent × 0.789) / 1000
index = standard_drinks / price_dollars0.789 is the density of ethanol at 20°C. The /1000 collapses the percentage and the ten-gram division into one constant.
The same three products, converted#
| Product | Standard drinks | Price | Per drink |
|---|---|---|---|
| Beer, 375 mL | 1.4 | $2.20 | $1.55 |
| Wine, 750 mL | 8.0 | $11.00 | $1.38 |
| Vodka, 700 mL | 22.1 | $42.00 | $1.90 |
The ordering has changed, and it will change again once weeks 4 and 6 add the tax each of these carries.
A currency, not a serving suggestion#
Why the distinction is load-bearing#
- a serving is advice about consumption
- a unit of account is a denominator for comparison
- this course only ever uses the second sense
- week 11 is where the first sense is dealt with properly, and it is dealt with as economics rather than as advice
One wrong conversion, one hundred wrong answers#
The scraping exercise asks for 100+ SKUs. If the conversion is wrong:
- every index in the dataset is wrong by the same factor
- the ranking may still look plausible, which is the danger
- nothing downstream will announce the error
- week 10’s optimiser will happily return a confident wrong answer
Check the conversion on three products by hand before trusting it on a hundred.
Common errors#
- multiplying by ABV as a decimal and by 100 in the same step
- using 0.789 as though it converted millilitres to grams directly
- reading a multipack’s total volume as a single container’s
- rounding standard drinks before dividing, rather than after
Where this connects#
- week 3 applies this unit to cask wine, where the result is furthest from what the shelf suggests
- weeks 4 and 6 express two different taxes in it, which is the only way those two structures can be compared at all
- the Data Scraping Exercise is marked hardest on getting exactly this conversion right across every row
Next week#
Cask wine: the first product whose measured cost-efficiency and shelf reputation point in opposite directions.