How Many Beers Does it Take for Me to Suck at Math?

Math vs. Alcohol

Why Even Do This?

Something I’ve found going out to bars or restaurants with a large group of people is that it gets increasingly harder to calculate how much each person should pay (including tip, tax, etc.) after I’ve had increasingly many drinks. That really got me thinking just how much alcohol affects mathematical ability. And, so this experiment was born!

The Experiment

As a mathematician, I don’t get to design a lot of experiments, but given this chance, I wanted to do it as precisely as possible. The setup was pretty simple. I would start sober and take a random 28 question math test which I had programmed into my computer. This test consisted of 7 addition, 7 subtraction, 7 multiplication, and 7 division questions, each of which was timed. I would work out the answer on some scratch paper and then my results (correctness and time taken) was sent to a spreadsheet.

Then, I would drink 3 fluid ounces (floz) of beer, wait a couple of minutes, and then repeat the random 28 question test. All in all, I worked my way up through the night from 0 fluid ounces of beer to 60 fluid ounces of beer, taking the test each 3 fluid ounces (21 tests taken total).

A plethora of results follows.

Average Time per Question (seconds) vs. Fluid Ounces of Beer Consumed

Hover, Click, Select!

  • Without even considering the effects of the beer, it is clear that the difficulty in terms of time for the operations goes from Addition to Subtraction to Multiplication to Division where Division is much harder than the other three operations
  • For Addition and Subtraction, it doesn’t seem like the beer has any real effect, I personally didn’t find these to get harder as the night went on
  • With Multiplication, we see a slight upward trend
  • I can say right now that division DEFINITELY got harder as the night went on. The classic division algorithm started seeming longer and longer and towards the end, it was difficult to keep track of all the steps and make educated guesses about factorizing numbers

It wasn’t just that I was getting slower at answering some of the questions, it was also that I was getting less and less accurate. Here, I’m measuring drinks as each batch of 12 fluid ounces (basically each beer).

Percent Questions Answered Correctly vs. Number of Drinks

  • Division just gets worse and worse over the night until it springs back a bit at the end. Subtraction follows a similar downward trend
  • Addition is strange, it starts getting worse and then halfway through, springs back up and I get better at it
  • Multiplication actually seems to show an upward trend … then again it is really volatile compared to the others

Let’s take a look at the results in a scatterplot to see if there’s any correlation between fluid ounces consumed and time per problem.

Time per Question (seconds) vs. Fluid Ounces of Beer Consumed

  • Multiplication and Division definitely show upward trends: they get harder as I drank more beer, I can attest to that
  • Addition seems pretty stable, as we noted before
  • Subtraction actually seems to get easier in terms of time as I drank more beer but then again, my accuracy at subtraction was falling a lot over time too

Messiness of Scratch Work vs. Number of Beers

Well, no graph here, but just wanted to compare my scratch work sober (left) and after 5 drinks (right). Yikes.

So Why is Splitting the Check so Hard?

My biggest takeaway after all this is:

division skills crash fast and crash hard

which is probably why it’s so hard for me and let’s face it, you, to split the check after a long night of drinking with friends or family.

This made for a really interesting night and some pretty cool results. Still, the sample size as far as I know is 1 (me), so I’d love to see how this experiment fares for others (who carry it out safely).

As for me, I will resign for the coming weeks to the books and leave the beers behind.

Thanks for reading and please leave comments!

Written on January 21, 2017