Monte Carlo Without the MathZach ScottBlockedUnblockFollowFollowingFeb 15Okay, maybe a little mathMonte Carlo Casino and Garden, MonacoMonte Carlo simulations are extremely common methods in the world of data science and analytics.
They can be used for everything from business process optimization to physics simulation.
Unfortunately, the math of Monte Carlo simulations is often unwieldy and can be intimidating for people without strong math backgrounds.
More importantly, the actual implementation of Monte Carlo methods is very difficult to explain succinctly, especially in a meeting with senior leaders.
The goal of this article is to explain Monte Carlo simulations using an analogy that is approachable for non-technical readers without resorting to dense math or coding that is difficult to explain to non-mathematicians.
Before we discuss Monte Carlo methods themselves, we need to do a little background work to establish a basic statistical framework, and the best way to do that is with a dart board.
Darts is a game of skill (or maybe chance if you’re really bad at it).
If you have a dart board with values from 1 to 5 and you throw a dart at it, you’re going to earn a certain number of points based on where the dart lands in the dart board.
Circular dart board with labeled point valuesIf you throw 10 darts at the dart board and add up all the scores, you’re going to have some amount of points between 0 and 50.
For a casual player who doesn’t play darts very often, this point total will probably add up to something around 25.
If you’re really bad at darts, that total may be around 10, and if you’re good at darts, your total points will probably be higher.
Let’s say 40.
Dart board and chart showing example number of darts landing in each region by player skill levelNow let’s say you’re rich and want to buy out the whole bar so you can have all the dart boards to yourself.
It’s probably not much of a stretch to say that throwing 10 darts at one board is probably going to be very similar to throwing 1 dart each at 10 identical dart boards.
If you score about 25 points throwing 10 darts at one board, you’ll probably also score about 25 points throwing 1 dart each at 10 identical boards.
Ten identical dart boardsIf you do much work in data science, you can probably see where this is going.
Since you’re rich and have bought out the whole bar so you can have a party, you decide that having 10 identical dart boards is kind of boring.
You decide to make each dart board a different shape with different points.
Because you have different shapes with different points now, it’s unlikely that every single stall will have the same average score.
If one dart board is a quarter of the size of the original, point totals are going to be lower.
A board with a giant bullseye is going to have higher score totals.
Ten different boards of various shapes, layouts, and sizesNow your darts party is really taking shape.
The veterans will have the added challenge of more difficult boards, the beginners will have some boards that are easier to help them learn, and some of the boards are so weird that you have no idea what the distribution of scores will be.
To add a bit of incentive, you’re going to have a tournament.
Every person who attends gets 10 darts and gets to throw one dart at each of your weird boards.
They’ll add up their scores from each of the boards, and they’ll submit their total to you.
Score sheets for 7 players including points per board, total score, and total per boardNow it’s much harder to predict the average score.
Each board is different, and each person has a lot of variables contributing to their ability to hit any given board.
You can’t really say what someone’s total score will be.
You might have a gut feeling based on what you know about the person, but that’s all you can have.
Without Monte Carlo simulations, this is the situation many decision-makers find themselves in.
They are faced with a very complex system, and they might have some gut feelings about the potential likely outcomes (e.
g.
, better players will have higher scores on a smaller dart board), but they don’t know how to integrate their intuition about individual variables into a complex system.
So they go with their gut, maybe with minimal experience related to somewhat similar situations, and it might work out or they might be in for a surprise.
Going back to the game of darts analogy, say your darts party is a huge success.
Everyone loved it.
There was a party planner there.
A representative from some new sports television station was there.
They both loved it.
They want this game concept to go big, really big.
Now your multi-board darts competition goes international.
There are hundreds of Monte Carlo darts competitions.
Millions of people play, and you have all of their score totals.
Now you’ve got some real data.
Based on the scores of millions of people throwing darts at the same 10 boards, you have a pretty good idea what a “good score” is per board.
You know what the average score is per board.
You know the average and standard deviation for total score.
You can predict the basic statistics of the game.
This is the power of Monte Carlo simulations.
Each dart board represents a variable, and the values of those variables combine into an aggregate outcome.
If you know the general distribution of possible scores for each variable, you can use Monte Carlo simulations to predict aggregate scores across multiple variables.
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