There exist two websites,

What's less obvious is what drinks are allowed if we want to meet both these objectives: to spend less money and consume fewer calories all while holding the amount of alcohol imbibed constant. As best I could, I combined the data from the two sets to give us a comprehensive look at each drink along both dimensions.** Here's a scatter plot of the 78 candidate drinks:

I've marked some outliers:

What one can notice here is that this view gives us a sense in which one drink is "better" than another. If all one cares about is (a) consuming ounces of alcohol while (b) minimizing caloric intake and (c) minimizing dollars spent, then Bailey's is plainly a better choice than O'Doul's. It's both less costly and has less calories, per ounce of alcohol. Similarly, Kahlua dominates both Bailey's and O'Doul's.

You can't, however, necessarily say that Patron Silver dominates

If we carry this to it's logical conclusion, we should imagine that there are only a few drinks in our dataset which are not dominated by any other drink. If we zoom in on our above plot, we'll see:

Like I mentioned earlier: the three undominated beverages are Everclear, Mad Dog (20/20), and Olde English High Gravity 800.*** It's pretty neat that these three just so happen to be: a terrible tasting hard liquor, a terrible tasting approximation of wine, and a terrible tasting beer (malt liquor, but close enough). We've covered all the major booze food groups!

You noticed that I've added to the scatterplot a rectangle for each of these three drinks. These rectangles represent the "zone of domination" for our final three: any beverage caught in, for example, the dash-dot rectangle is a beverage both higher in calories and more expensive (when normalizing for alcohol content) than Olde English High Gravity. Anyone who believes exclusively in (a), (b), and (c) should strongly consider trading their

So far, we've considered only whole beverages, standing on their own. But if we now allow ourselves the possibility of mixing two beverages, a new opportunity arises. Since we know at this point we can ignore any drink but Everclear, Mad Dog, and Olde English High Gravity (these three dominate all the others), let's consider combining Everclear and the OEHG.****

If we mixed these two, we'd have effectively drank a beverage which, on balance, cost less than pure Everclear but had fewer calories than pure OEHG. (The pessimist rightly points out by the same token that the concoction would also cost more than the OEHG and be more fattening than the Everclear.) Here's what mixing would mean for our scatterplot:

Any OEHG/Everclear mixture would wind up somewhere on that dotted blue line between them. The point I've marked "MIXTURE" here asks that the ratio of ounces of alcohol obtained from the OEHG to ounces obtained from the Everclear be about 2.5:1. I've given this point it's own rectangle to make it clear: the mixture now dominates the Mad Dog -- the Mad Dog 20/20 is no longer undominated.

Given that they can be combined, Everclear and Olde English High Gravity 800 are the only two drinks a believer of exclusively (a), (b), and (c) would ever need. Together they form a dominant pair. I think this is pretty strong evidence for why (a),(b), and (c) are together pretty infrequently exclusively believed.

Brian Gawalt

bgawalt@gmail.com

September 24, 2010

http://gawalt.com/brian/

http://www.twitter.com/bgawalt/

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* At first I thought maybe the classy thing to do would be to throw up a link to donate to Alcoholics Anonymous, but then I discovered on page 17 of this PDF that donations aren't accepted from non-members. It's not often that I learn things that leave me less cynical, and I tend to want to pass them on.

** Unfortunately, there's not a perfect matchup between the two sites. Not all the beverages for which I found calorie information also had pricing information. It's possible that a fuller dataset would produce a different set of undominated drinks. Who knows where Franzia would land in our scatterplot? All the same, these 78 still represent a strong sampling of the world of low- to mid-range booze. You can look at the raw numbers here.

*** With the scale of all the data values, it's hard to show that Everclear, Mad Dog, and OEHG are all left undominated. You can check it easily numerically; here's a Python script which does just that in conjunction with the datafile above.

**** Mixing isn't meant necessarily in the sense of pouring both in the same cup; the old standby of shot-and-a-chaser would work just as well, so long as the proportions were kept on the level.