Show Your Work
On the math nobody explained and why that wasn't an accident
If you ask most people around you, they’ll tell you they hate math. Now, whether this is an issue with the education system or not is a conversation for another time.
For now, let’s just focus on why math can be difficult.
It is literally a different language.
Arabic numerals (also known as Indo-Arabic), combinations of digits from 0-9, originated in India somewhere between the 1st and 4th centuries. Famous mathematician Leonardo Fibonacci popularized the usage of this system in 1202. Before this, abaci were used to help count. These numerals were introduced to assist merchants with keeping track of sales.
Somehow we got from counting on our fingers to utilizing symbols in addition to numbers.
Even though it can be incredibly difficult to understand, math is literally everywhere around us. Whether you look at chances of winning the lottery or your next parlay, how your credit score is calculated, or even how insurance companies use the probability of you dying to determine how much to charge you, it is all math.
So instead of throwing formulas at you, we need to talk about why you’re bad at math in the first place.
Show Your Work.
You’re not bad at math because you’re not smart. Our brains were built to survive, to make fast decisions with a limited amount of information. They weren’t built to calculate winning percentages at casinos.
Psychologists Daniel Kahneman and Amos Tversky identified a concept known as the availability heuristic in 1973. (A heuristic is just a mental model we use to solve problems.)
The availability heuristic is the tendency to judge how likely something is based on how easily you can think of an example.
It’s easy to see all the people who’ve won the lottery, but we don’t think of the millions and millions who have played and won nothing.
You are more likely to become a saint than win the lottery. The Vatican canonizes roughly 1 in 250 million Catholics.
But lottery ticket sales in the US exceed $100 billion a year.
Expected value is the average outcome of a decision if you made it thousands of times. It’s the math that answers the question: is this actually worth it?
Powerball tickets costs $2. The odds of winning the jackpot are 1 in 292 million. If you bought one ticket per draw, three times a week, you would need to play for an average of about 2 million years to win.
But forget the jackpot. Even accounting for all the smaller prizes, the expected value of a $2 Powerball ticket is roughly $0.32 on a standard draw. Meaning for every $2 you spend, you can expect to get back about 32 cents. That’s an 84% loss rate on every single ticket.
Casinos understand this math better than anyone. Every game on the floor is designed around the house edge or the built-in mathematical advantage the casino holds on every bet. American roulette has a house edge of about 5.26%. That means for every $100 you bet, the casino expects to keep $5.26. Over thousands of spins, the law of large numbers guarantees the casino makes money. Always.
The gambler believes in hot streaks and cold streaks. The casino believes in math. That’s why the casino always wins.
Discount Double Check.
Insurance companies figured out the same thing casinos did, just with higher stakes and the appearance of being less scummy.
Actuarial science is the discipline behind every insurance premium you've ever paid. At its core, it uses the same principle as the casino house edge, the law of large numbers. The more you spread the risk across a lot of people, the less any one unpredictable individual affects your outcomes.
Let’s say an insurance company insures 10,000 people against a risk that has a 1% chance of occurring such as a house fire or a car accident. Statistically, about 100 of those people will make a claim in a given year. If each claim costs $10,000 to pay out, the total expected payout is $1,000,000. Divide that across 10,000 policyholders and each person owes $100 just to cover claims. Add administrative costs and profit margins and your premium goes up from there.
You are not being priced as an individual but as a member of a group that looks statistically similar to you.
This is where mortality tables come in. Actuaries use tables that show the probability of death at every age based on decades of historical population data. They predict the likelihood of policyholders dying at each age and therefore when the company might have to pay out a death benefit. A 30 year old male non-smoker in good health is in a different row of the table than a 55 year old with a history of heart disease. The premium difference between those two people isn't a guess:
It is math.
All of your insurance, all priced using variations of the same math. Factors like your age, zip code, credit score, and driving history feed into risk models before you've spoken to a single agent.
The insurance company has been running this math on people like you for decades. Their models are built on millions and millions of data points. You’re negotiating with a spreadsheet that already knows the answer.
The least you can do is understand what’s in it.
No Calculators.
Your FICO score runs from 300 to 850 and is built from five categories:
Payment history is 35% - the single biggest factor.
How much you owe relative to your available credit - 30%.
Length of credit history - 15%.
New credit inquiries - 10%.
Credit mix (having different types of accounts) - 10%.
Two things control 65% of your score. Pay on time and keep your balances low.
Credit cards ruin people’s lives.
Imagine you have a $5,000 credit card balance at 22% APR:
Your minimum payment starts around $100.
In month one, $92 of that $100 goes straight to interest, and only $8 goes to your balance.
If you only ever pay the minimum, it takes:
9 years and 7 months to pay off that $5,000.
By the time you’re done, you’ve paid $6,520 in interest. Your $5,000 purchase cost you $11,520.
But what about math that can help you?
$10,000 invested at 5% simple interest for 3 years earns $1,500. The same $10,000 at 5% compound interest earns $1,576.25. Not a huge difference at 3 years, but if we stretch that out to 30 years, the gap becomes enormous.
Compound interest works for you in investments. It works against you in debt. Credit card interest compounds daily. Your retirement account compounds too, which is why starting early matters more than starting big.
Math is everywhere and everything is Math.
So next time you leave a tip (and if you don’t, quit being stingy) don’t pull out your phone. Do the math.
Who knows, next time you see me, I might pull out one of these and give you 60 seconds:
