# How many drinks were consumed by each test subject in this study?

I was reading this study and came across the following line:

...subjects consumed either 500 mL of whey protein (25 g; PRO), alcohol (1.5 g·kg body mass⁻¹), 12±2 standard drinks) co-ingested with protein (ALC-PRO)...

Does the 12±2 translate to 10-14 drinks? This seems like a lot, so I went to the equation, 1.5 g·kg body mass⁻¹, but I'm not sure how to go about calculating that. Is "body mass" just bodyweight in kg here?

This is probably very wrong, but, if I take a bodyweight of 87kg and plug it in:

87kg⁻¹ (191lbs) = 0.01149425287
0.01149425287 * 1.5 = 0.0172413793


What am I doing wrong here?

"1.5 g·kg body mass⁻¹" can be equivalently written "(1.5 g)/(1 kg body mass)" or read "1.5 grams per kilogram body mass".

So, a 87 kg person would be given 130.5 g of alcohol. The units work out as:

(1.5 g EtOH)/(kg body mass) * 87 (kg body mass) = 130.5 g EtOH

That is, you have (kg body mass) in the numerator and denominator, these cancel and you end up with just the g EtOH. When working with units, it's always a good check to write out the units you have and see that the units you end up with make sense for the answer you're trying to get.

Written out another way, you have the dose per weight; you want to multiply that dose per weight by the actual weight to get the dose.

Does the 12±2 translate to 10-14 drinks?

A standard drink in the US is about 14 grams, but these authors aren't in the US. A UK standard drink is 8 grams. Australia is 10 grams. However, they write in the paper:

The alcohol ingestion protocol (1.5 g·kg−1 BM; 12±2 standard drinks) began 1 h post-exercise and was consumed in 6 equal volumes of 1 part vodka (∼60 mL) to four parts orange juice

So if they are taking a standard drink to be 30 mL vodka (approximately 1 fluid oz) and giving 12 of those. 30 ml vodka is going to be just under 10 g ethanol, so by the Australian measure that all works out.

And, yeah, that's a lot of alcohol to drink, especially over just 3 hours. The paper begins "The culture in many team sports involves consumption of large amounts of alcohol after training/competition" - they're targeting the binge level of drinking observed around team sports.

• The term "standard drink" seems to be particularly used in Australia. Here in the UK we'd use "unit" in the same contexts Commented Oct 21, 2021 at 14:43
• @ChrisH My understanding is that "standard drink" is used everywhere except the UK, though you'll also find "standard drink" and "unit" used interchangeably for the UK measure. en.wikipedia.org/wiki/Unit_of_alcohol reads "Standard drinks were referred to in the first UK guidelines (1984) that published "safe limits" for drinking, but these were replaced by references to "alcohol units" in the 1987 guidelines and the latter term has been used in all subsequent UK guidance." Commented Oct 21, 2021 at 14:50
• Maybe so - "standard drink" is certainly never used here in public-facing material. Perhaps my reading is biased in such a way I've mostly seen the term in an Australian context, or perhaps it's discussed more there even if it's the correct term in more countries Commented Oct 21, 2021 at 14:57