March 6th 2017
Guess Anything for Fun and Profit
Estimation is very hard. More often than not we'll do some simple extrapolation or "gut feels" and multiply by a known number. Sometimes we'll get more technical with a spreadsheet. We will do some averaging and summation, toss in some extra excel functions. This is otherwise known as the technical term: bullshit.
In this post we're going to learn how to do powerful estimation. The same methods that SpaceX and the Department of Defense use when making decisions. They hire statisticians and use expensive tools, we'll get comparable results without it. (Disclaimer: If you are building rockets, hire a statistician.)
When making complex estimations we should be using probability distributions. WHOA WAIT, don't stop reading, we're not going to be doing any complex maths please bear with me. A probability distribution can be as simple as "The worst case is 0, the best case is 10." Thinking about our problems this way lets us make stronger estimations.
When we make simple estimations we will take the "most likely case" and call it our estimate. For the example above of 0 to 10 we'd most likely use 5. By doing that we ignore the outliers which can end up having an outsized effect on our outcomes.
Real World Example
Lately I've been watching Twitch streamers play some of my favorite video games. A huge chunk of their income comes from donations through PayPal. Usually they show a little "sell out bar" that shows how much they've earned that day.
Over the course of a year I've taken some mental notes on how much my favorite streamer makes in a day. Roughly the lowest they earn is $50 and the highest is $2300. Typically its in the $50-$200 range. They stream roughly 2 to 6 days a week.
Question: How much does this streamer make per year on donations?
First lets use the basic simple estimate. Roughly they earn $100 every time they stream, they stream about 5 days a week so using basic math:
$100 * 5 days * 52 weeks = $26,000
And because we know they sometimes earn way more lets "fudge it" to $35,000.
Now lets do it using using distributions. My tool of choice is Guesstimate which gives an easy to use, excel like, interface for doing this kind of analysis.
Let's first fill in our variables: https://www.getguesstimate.com/models/7961
Number of Streams per week = [2, 5]
Notice how I used [2,5] this is our way of saying that 2 is lowest, 5 is highest.
Number of Streams a year = Number of Streams Per Week * 52
Notice how the result of this is also a distribution even though I multiplied by a constant 52.
Donations Per Stream = [50, 2300]
Earnings per year = donations per stream * streams a year. And the final output looks like
Our output is $10k to $520k with the most likely case of $110k.
For number of donations per stream and streams per year in my example I chose a lognormal distribution. This is like saying "the distribution of values falls on the left side". Or in the context of my example "the streamer, for the most part, had days in the $50-100 range". If you play with these distributions you can see how they affect the final earnings a year.
Guesstimate takes our distributions and then runs 5000 random simulations for each distribution. This is a Monte Carlo Simulation. Typically Monte Carlo simulation software packages don't have public pricing and run in the thousands. We just did it for free and in the browser. If you'd like to see how these simulations ended up just click on a box and click "expand".
You can also analyze how sensitive a result is to changes in variables by clicking the sensitivity button.
This shows you how much a result would change if a variable changed. In our situation the donation amount they earn per stream has the largest effect. Streamers might want to really appease their biggest donors OR attract a ton of small donations.
Both analysis used the same basic information but came to very different conclusions. Using a simple average we are only able to account for a single case. Using Guesstimate we are able to simulate 5000 realistic cases about our problem.
Being able to simulate the scenarios gave us insight into all possible cases. Even ones where the streamer only earns $50 a stream, or even $2300 every stream.
I hope you learned a little bit about statistics, and a ton about making Guesstimates. If you're interested in learning more ways you could use this tool feel free to reach out, we'd be happy to help.