## Archive for February 18, 2013

### The Math of Maker’s Mark

Last week, Maker’s Mark announced that they would change their recipe. According to COO Bob Samuels, the company was planning to reduce the alcohol content of its bourbon from 45 percent to 42 percent by replacing the removed alcohol with water. But outcry from thousands of bourbon drinkers convinced them to abandon their new 84-proof recipe and continue stocking shelves with 90-proof spirits.

This morning, sports reporters Tony Bruno and Harry Mayes suggested that bourbon drinkers were opposed to the change because they want to get drunk faster.

This got me to thinking about math.

As you know, mathematicians know a thing or two about alcohol.

Where there are four mathematicians, you’ll likely find a fifth.

And so do mathematical objects.

A definite integral walks into a bar. “Ten shots of whiskey, please.”

The bartender asks, “You sure you can handle that?”

“Don’t worry,” says the integral. “I know my limits.”

In the U.S., a “standard” drink is one that contains 0.6 fluid ounces of alcohol, but a standard drink does not necessarily correspond to a typical serving size. In practice, a typical drink of bourbon is a 1.5-ounce pour.

So what does this mean for Maker’s Mark? Sticking with 90-proof bourbon means that a 1.5-ounce drink will contain 0.675 fluid ounces of alcohol, whereas the revised 84-proof bourbon would have contained 0.63 fluid ounces of alcohol. Does that extra 0.045 fluid ounces really make a difference?

A little bit, but not much.

As shown in the table below, a 200-pound man would need to consume 4.76 drinks of 84-proof spirits to reach the legal blood alcohol content limit of 0.08, yet he would only need to down 4.44 drinks of 90-proof spirits. The difference is small. Another third of a drink isn’t much when you’ve already downed 4½.

Number of Drinks to Become Legally Drunk (0.08 BAC) |
|||

Weight (lbs) |
Typical Spirits(80 Proof) |
Proposed Maker’sMark (84 Proof) |
Original Maker’sMark (90 Proof) |

100 | 2.50 | 2.38 | 2.22 |

150 | 3.75 | 3.57 | 3.33 |

200 | 5.00 | 4.76 | 4.44 |

250 | 6.25 | 5.95 | 5.56 |

Note that this chart is for men; women of the same weight would require fewer drinks to reach the same level of intoxication. In addition, time is not reflected in this chart. Because of normal body processes, a person’s BAC is reduced by 0.01% every 40 minutes.

Still, the data seems clear. The revised Maker’s Mark recipe would cause intoxication almost as quickly as the original recipe, so if bourbon fans reacted simply because they want to get drunk faster, well, that seems misguided.

Then again, how many sh*tfaced bourbon drinkers have done this kind of analysis? Probably very few. But that does remind me of a joke.

How many bourbon drinkers does it take to change a light bulb?

Just one. Have him drink an entire bottle, then hold the bulb as the room spins.

Or this one that’s a little more mathy.

How many math department chairs does it take to change a light bulb?

Just one. He holds the bulb, and the world revolves around him.