The Math Smackdown

The Math Smackdown

I may lose my personal finance membership card for this, but I think math needs to be smacked right off its lofty pedestal. I know the personal finance community is full of optimizers and math evangelists, but please bear with me. You can judge me in the comments later.

Math is not the perfect, rational response to every personal finance question. Just because we’re dealing with numerical values doesn’t mean that they have to be rigorously and exclusively applied.

One of the reasons I think we use math to make decisions is that it’s relatively simple, in a big picture way – it’s input and output. It’s predictable, tangible, and universal. Math can be used to shut down a conversation, because how can you argue with ‘$10,000 > $5,000, the end’? 

Math is the easy way out, and it’s far from the whole story. When it comes to personal finance and other issues with a human element, math is only part of the equation. If the information we use is quantified in amounts of money, interest rates, investment yields, and savings percentages, what’s missing?

I don’t know, how about the entire range of human emotion?


Consider these common personal finance questions:

  • Is it better to make higher student loan payments or invest?
  • Should I pay off my mortgage early?
  • Do I settle a personal loan with a family member, or pay off my car?

The math favors paying off high interest debt and prioritizing investing over paying low-interest debt. The problem with this approach is that it does not take several major factors into account:


Many of the mathematical calculations for determining whether to pay debt or invest assume a certain percentage of returns, but the reality is that there are no guarantees in the investment world. Our normalcy bias causes us to believe that things will continue to function in the way that they have in the past.

To accurately weigh two choices, we need to seriously consider events like a market downturn, job loss, or other financial crisis. The additional money we’ve made by investing could be wiped out if we were forced to withdraw a portion of our portfolio in a down market.

We just saw the same biased behavior only a decade ago in the 2008 financial crisis, when we were gambling on the housing market, convinced that it would only go up for infinity.

When the tide goes out, you can tell who’s been skinny dipping. – Dave Ramsey

In a long bull market, confidence is at a high and we tend to discount the potential effects of a future bear market. What happens when the tide turns and you’re overleveraged?


As much as we’d like to think that we’re rational beings, we can still be easily swayed by our feelings. Advertisers know this, psychologists know this, behavioral economists know this. It’s time that we leveraged their research to benefit ourselves!

The standard investment advice is to buy and hold. If we objectively know this, why are there countless questions about timing the market on every personal finance forum?

I’ve heard that you’re not supposed to time the market, but everyone is talking about an imminent crash. Should I wait until it goes down to invest? – Everyone Always

I don’t know about you, but to me that sounds suspiciously like trying to time the f*cking market. We rationally know the answer, yet we ask these questions anyway because we irrationally perceive our own circumstances to be unique.

Why, if math tells us one thing, do we consistently do completely opposite things?

I’d like to introduce you to a little phenomenon I like to call the black box of human emotion.


A black box is a system which can be viewed in terms of input and output, without any knowledge of the internal processing. The human brain is the ultimate black box. We are constantly doing irrational things, no matter how rational we might perceive ourselves to be. In fact, perceiving ourselves as rational when we tend to act irrationally, is irrational in itself!

There are so many examples of irrational human choices that I’d have to start a new blog just to talk about them all. In the meantime, here are just a few examples of the mathematically inefficient choices we make with money:

  • loss aversion could explain why we buy things we don’t want, and why we fail to return unused things after we’ve purchased them
  • anchoring suggests an appropriate cost of something, even though a rational price might be much lower
  • hyperbolic discounting refers to our tendency to choose the smaller immediate gratifications over larger long-term rewards

For some additional reading on the subject, and many more examples of our flawed human mind, check out the books Predictably Irrational: The Hidden Forces That Shape Our Decisions by Dan Ariely, or Thinking, Fast and Slow by Daniel Kahneman.

The math only works to its full extent if we complete a number of transactions perfectly over a number of years. Are we perfect? Science says no.


There’s something inherently motivating about paying a debt off, especially a small one. The rational strategy is to tackle the high-interest debts first, but getting out of debt is actually more likely to happen using the snowball approach – paying debts from smallest to largest amounts.

A team of Kellogg School researchers has found that people with large credit-card balances are more likely to pay down their entire debt if they focus first on paying off the cards with the smallest balances — even if that approach doesn’t make the best economic sense. – The ‘snowball approach’ to debt, news article by Ray Boyer; research by assistant professors of marketing David Gal and Blakeley McShane.

The motivation factor is why Dave Ramsey’s baby steps are so incredibly successful for so many people, despite being mathematically inefficient – someone pays off a small debt, gets a quick win, and feels a push to keep going.

If our motivation stumbles and we spend a portion of the amount we should have been investing, we slowly eat away at the financial benefit, potentially even losing it altogether. Staying motivated throughout the process is key, and it’s more difficult than we think. We assume that our financial knowledge will insulate us, but this assumption is often biased as well.

Humans are notoriously bad at self-control, regardless of our knowledge, so we need all the help we can get. Ever wonder why you see so many doctors and lawyers and finance majors in poor financial health, despite a higher intelligence or financial experience? They’re human!

In the area of financial decision-making, self-control issues are significant (e.g. Raab et al. 2011; Rick et al. 2008) and can plague even the most financially literate (Brown, Chua and Camerer, 2009. – Small Victories: Creating Intrinsic Motivation in Task Completion and Debt Repayment by Alexander Brown and Joanna Lahey.

So willpower isn’t very effective, and more knowledge doesn’t help us? It’s not looking good for you, math!


If our net worth was the ultimate consideration, why aren’t we all living in a van drinking meal replacement shakes? Why do we make accommodations in the math for things like a home and delicious food, but not for our mental health?

Chronic stress caused by volatile finances or a high debt load can start to interfere with your life in major ways. Stress can lead to fatigue, inability to concentrate, irritability, or even physical ailments. For a risk-averse, debt-averse person, owing hundreds of thousands of dollars while investing in an unpredictable market can take a particularly high mental and physical toll.

If we’re so concerned about being financially healthy, why are we not more concerned about our mental (and physical) condition too? Can’t enjoy our fat portfolio to the full extent if we’re in poor health as a result of worrying about it for decades!

We are not perfect. We are emotional and irrational, and pretending that we aren’t can actually be detrimental. Instead of worshipping at the altar of math, we should be considering psychological efficiency as well as mathematical efficiency.

If you’re choosing to pay down your mortgage instead of invest, or pay back a personal loan from family before tackling your other debt, know that there is science behind your choices. Just because math provides a concrete answer, doesn’t mean it’s the correct one. We shouldn’t be so quick to discount mathematically inefficient choices – they could very well be the best option!

Are you Team Psychology or Team Math?

20 thoughts on “The Math Smackdown”

  • Excellent points – I love this post and have a draft half-done that talks about many of the similar issues.

    I’m definitely Team Psychology, for many of the reasons you’ve outlined. I think in particular the whole ‘pay off the mortgage early’ debate is overrated. If you’re investing or paying down your mortgage, you’re making good progress. Sure maybe on average the market out-performs the interest rates on a mortgage. Interest is tax deductible. There’s a lot to say for investing.

    But like you said there’s risk involved. Things can go down; a paid off house is a guaranteed thing. Imagine life without having to pay for where you live, with an exception of upkeep, insurance, and taxes. What opportunities does that open for you?

    The key is to weigh the pros and cons of the situation, figure out what your individual risk tolerance is, and proceed in a way that supports your goals. For that reason, we’re paying down our mortgage at an accelerated rate, but also investing; because we want the freedom from a mortgage, but not at the cost of our nest-egg.

    It’s about finding a balance that’s right for YOU. That’s why they call it PERSONAL finance. If I wanted Team Math I’d read a text book; not blogs.

    • Absolutely! It’s all about weighing it out – math isn’t THE answer, it’s only one factor. If math worked for everyone, the credit card companies and payday lenders would go out of business. We wouldn’t have most of the population living paycheck to paycheck, unable to come up with $1,000 in an emergency. If you can do basic elementary school math you can stick to a budget, so why are so many educated people with sufficient incomes still struggling? We focus on math and willpower, and we leave the real efficiency on the table.

  • Great point! It’s all about balancing your emotions and the cold, hard facts. For example, we plan to pay off our mortgage before FIRE. Does that mean our FIRE date will be delayed? Sure. But we’ve made the emotional decision that we want to own our house. There’s a lot of pride in owning a home outright, but we also want something to pass on to our future kids and love the security of a paid-for home.

    • Nice! Owning your own home can be particularly motivating in itself! It’s all about knowing the landscape and being comfortable in your own choices.

  • Great post – lots of food for thought! Like you, I think it’s all about striking the right balance.
    When I need to make a financial decision, I tend to start with a math-based approach because I’d prefer to begin with a rational baseline for any decision. But there are plenty of times that I’ll override what math would tell me to do because of some emotional or psychological reason. I think the key is recognizing that a decision contradicts the mathematical solution and carefully analyzing the pros and cons for choosing an alternative option.

    • Balance is key! I make all kinds of decisions that contradict the math.. but I’m willing to bet that I’ll come out ahead anyway just because of the psychological boost. If you know your options, and choose the mathematically disadvantageous one in favor of other factors, I can’t fault that!

  • I like your “Black Box” metaphor in the dynamic tension between Math/Logic and Emotion/Psychologic. You catch alot of attention with your f*cking word choice that may work in a short term marketing angle, but it will become old and dilute/distract from your spot on messages.

    • Thanks for the feedback! It probably comes down to individual style, but I didn’t even think about the marketing aspect or that some people might find it distracting! I can’t imagine people are reading just for that – I don’t even notice it when I’m reading other blogs. I appreciate your perspective though!

  • Yes! We’re in the pay-off-the-mortgage club even if investing might make more sense just looking at the numbers. The thought of having a paid for house just gives me so much joy that it motivates me more than just investing as much as possible.

  • This is spot on! The balancing act is definitely something I’ve thought about a lot, and like any other balance in life it takes some soul searching.

    What I’ve found that works for me is setting minimum automatic transfers to my goals – right now this is paying off student loans, saving for retirement, and saving in the house fund. So I’m doing minimum student loan payments, 15% to 401k, and a set amount to savings. After that, I use whatever is leftover for whichever of these goals I feel the most inclined to work on. Lately it’s been the house fund, so extra savings is going in to that. Earlier this year it was student loans, so I made extra payments on that.

    By doing this, I’ve been able to get past the desire to constantly tinker with my budget and expenses and start thinking about how to increase my income, which at this point will be a more efficient trade off for my time. So now I focus that energy on building and creating, rather than analyzing and projecting. I’m also more content – I know whichever option I choose that month for my extra money, even if it’s based on emotion, is going to increase my net worth.

    After a couple years of doing this, I’ve realized that even with “switching it up” every month, over the course of the year I tend to spend those extra funds on all my goals pretty evenly.

  • Hey Veronika, I’m on the psychology team all the way. We’re aggressively paying off the mortgage on a 2.625% loan. The math says we should be putting our money into the market instead. But I might be truly math team driven since the cash flow we’ll recover is huge after the thing is paid off…

  • I love this post. I’ve been thinking a lot about this lately. I’m so tired of the canned responses from team math. They like to ignore the fact that they’re making many assumptions. Past performance is not an indicator of future results. While personally I have no intention of paying off my mortgage early. I definitely understand why people do. We shouldn’t ignore the fact that having large piles of accessible money will make us more likely too make less than optimal choices. I’ve seen this in myself, when I have more than $12,000 lying around I feel like I have to do something optimal with it. At the same time I’ll start looking at what kind of car I can buy for $12,000. It’s nice not to feel like you have to make frugal choices, but I find my frugal willpower fades at that point. As long as you keep a decent amount on hand for emergencies, I believe keeping money away from your flawed self can be beneficial.

    Another observation about myself, I find debt to be extremely motivating. I carry debt intentionally( at 0%) simply because it motivates me to pay it off. I don’t like to bust my hump all week just to throw another hand full of money on top of the my large pile of money that I’m not spending anyway. I would never admit this in the many personal finance groups I participate in.

    Math provides the framework, but the framework should be adjusted to fit our lives, not the otherway around.

    Thanks for this post. I love it!

    • Very true, past performance doesn’t mean much! Debt motivates me quite a bit as well, and I’m interested to find out if I can keep that motivation going once I’m switching to throwing handfuls of money on the pile..

  • In Maslow’s hierarchy of needs Security comes way before Esteem or Self Realisation: Psychology makes me pay down my 3.47% mortgage.

  • Human fallibility is definitely something personal finance folks don’t seem to want to talk about to much. I would say I’m team math, with a touch of scandalous double-dipping into psychology. I know the math is right, and I know what my heart wants me to do, I just try to strike a balance.
    I heard a while back (can’t remember where, of course) about someone who was trying to use the same psychological rewards to better themselves that video games use to keep people playing. They would give themselves a motivational reward when they accomplished a goal. For example, if the goal was to lose weight, they would set themselves a tangible and realistic short term goal. Say, lose two pounds in one month. Once they reached that goal, instead of treating themselves with a slice of cake, they would buy themselves three new pieces of clothing. Two would fit properly, but the third would be just a bit tight, thereby prompting them to feel motivated to continue.
    I haven’t yet found a good way to implement that for myself and my financial goals, but if someone were to come up with some method involving those reward triggers, I think they would help a whole lot of people achieve their finance goals.
    Thanks for the insightful piece, really got me thinking!

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