Crappy friends at crappy burger joints: A statistical analysis of 10 million meals

 

[NOTE: I wrote this blogpost ages ago to pitch to another website, for whatever reason it fell through but I feel the need to point out a couple of things:
1. Since writing this, it turns out that Byron is a really nasty company, so if you take anything from this it is DO NOT BUY FROM BYRON, the burgers ain’t that good anyway. As a result I have replaced all use of the word byron with CRAPPY BURGER JOINT.
2. Since I was expecting it to be on another site, the style of it is a bit more sweary, probably just a one off.
3. My friends aren’t crappy and actually I don’t know anyone who does this so don’t think this is aimed at y’all.]

It is 2016 and we still have major issues dealing with the restaurant bill. Too many times you have 10 people sat around a table in Zizzi who each either have to rationalise that “£20≈£18.95 with a tip right?” or sit there for several excruciating minutes waiting for the card machine to go around each person while the dad from the next family up angrily catches your eye from the “Please wait to be seated” sign. Then, in this time crisis enforced upon you by the social pressure of being in eyesight of ‘the sign’, you have a major decision to make: either try and relearn how to use your calculator app to work out how much your meal was or split the bill evenly. What I’m here to show you is that because of this option, its very easy for your crappy friends to take your money.

What I’ve got: The ability to simulate random meals drawn from the CRAPPY BURGER JOINT menu
What I’m going to do with it: Prove that having a bad friend can cost you money

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A crappy friend can be a lot of things, but in this case its the crappy friend who will make a rough judgement about whether they’ve spent more or less than the average in the group and then decide their position on splitting based on that. If they’ve spent more than the average they’ll want to split it evenly and if they’ve spent less they’ll want to pay for their own. What we’re going to do is use computers to work out how much money your terrible friends are costing you.

How much does a meal cost?

Just above I was complaining about how long it takes to pay by card at a restaurant, so you can probably assume that I don’t have the patience to go through every one of the mid-range theoretically-better-than-nandos chain restaurants’ menus and get their prices, so I just picked CRAPPY BURGER JOINT. I wrote a program which will randomly choose a burger, a side, a dessert and a drink from the CRAPPY BURGER JOINT menu and return you the price.

This is the great thing about computers, in a few seconds we can see what the distribution of prices from 1,000,000 different CRAPPY BURGER JOINT meals would be:

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Well there you go, its probably not a coincidence that the average price of a meal at CRAPPY BURGER JOINT’s is about £20, attempting to avoid the struggle to find change.

Now we’re here though, lets take a brief detour to talk about something cool called the ‘central limit theorem’. The theorem states that as soon as you add up a load of different numbers which aren’t directly dependent on each other, their distribution will always end up being the same shape, something known as the normal distribution – also known as the bell curve.

So lets make 100,000 theoretical people buy 100 theoretical CRAP BURGER JOINT meals each and then look at how much they spent:

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This is a normal distribution, and this is a cool gif showing how this comes about. If you want to find another normal distribution, take each phone number in your phone book, knock off the ‘07’ from the start and take an average of the remaining numbers, the sum of those numbers will form a normal distribution (as long as you have enough friends).

Anyway, back to your crappy friends, lets use this program to simulate some thursday evening meals.


How much do your friends cost?

What we can do is take this CRAP BURGER JOINT meal price generator and make some fake bills. To work out how much money you lose, we generate a number of meal prices, randomly assign one to your crappy friend and one to you, then if the crappy friends’ meal price is higher than the average everyone splits the bill so you lose the price of your meal minus the average price of a meal, and if the crappy friends’ meal is less expensive than the average everyone pays their own so you don’t lose anything.

This is called a ‘biased random walk’. This comes from a branch of statistics which is concerned with systems such as when someone gets way too lit at a party and tries to walk home, but each step they take they forget which way they are meant to be going so there’s a half chance they’ll go left and a half chance they’ll go right. That’s a random walk, however a biased random walk like this one is different in that if the person tries to go the wrong way someone will stop them. That’s a simplified version of what’s going on with your crappy friend, except in this system your friend is walking all the way to the bank.

Firstly lets imagine you and this friend go out for meals on your own and every time they decide whether to split or not. The amount of money you lose is random so to get a full grasp of whats going on we should simulate many different sets of nights out to see what the full range of outcomes could be.

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So say you went out once a week with your crappy friend to CRAP BURGER JOINT for a year, by the end you may have lost over £50 just because you’re too polite to call them an asshole.

An interesting point that hadn’t occurred to me before starting this is that if you add more people into the equation with your crappy friend, you might actually win out. If we look at the same thing but with three people:

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The purple and green lines at the bottom are actually making money by having a crappy friend. This is because they have managed to luck into having cheap meals when the crappy friend is having cheap meals, and expensive meals when the crappy friend is having expensive meals.

Again though, even diluted your crappy friend is still probably costing you like £30 over the whole of the year.


Some people might tell you not to have crappy friends, or if your friend is being crappy maybe you should just mention it to them instead of writing a whole blogpost about it and wasting hours of yours and your computers time simulating it. I’m personally shocked that anyone could take anything from this post besides joining my campaign to boycott all restaurants that don’t use the superior system of paying before your meal, á la Spoons or Nandos. All you gotta do is check the number of your table, eat, and then walk out. No awkwardly beckoning someone over, no trying to work out if you had the “BRGR CHS” or the “CHEESE n P”, just a faceless and dystopic future where everything is cold and exact.