The Art of Approximation
A case for estimation in a world that rewards accuracy, and how rough approximations lead to better decisions faster.
From the moment we enter the school system, we're trained to value precision above all else. When asked to multiply 21 by 19, the only acceptable answer is 399. Say “about 400,” and you're marked wrong. There's no credit for being close.
Coincidentally, many machine learning models are also trained this way. Take cross-entropy loss, for example: the model gets rewarded only when it predicts the exact target, not when it gets close. Close doesn’t count.
And yet, in many real-world contexts, particularly in business and investing, this obsession with precision is often more of a hindrance. That’s why I’m here to make a case for approximation. It takes me about a second to estimate that 3,400 times 1,800,000 is roughly 6.1 billion. Sure, some dork might chime in that the exact result is 6,120,000,000. Great, but they took five times as long to get there. By the time they finish calculating, I've already moved on to the next problem. In domains like investing, that kind of speed and directional thinking can be invaluable. You don’t need to know that something is worth exactly $6,120,000,000. You need to know whether it’s closer to $6 billion than $3 billion. That difference is what determines whether you act or move on.
In the investment world, especially on X, we see a lot of analysis paralysis, where people run elaborate models to prove a stock has 15% upside. But that’s not what great investors like Warren Buffett or Charlie Munger are looking for. They’re not trying to eke out a 10% gain based on some spreadsheet voodoo. They’re looking for sheer, outrageous value, as Michael Burry calls it.
If a stock is trading at 0.2x its intrinsic value, you buy it. Whether it’s actually 0.17x or 0.21x doesn’t matter.
Approximations allow you to quickly screen for opportunities worth investigating. For example, when evaluating mining stocks, a quick back-of-the-envelope P/NAV or P/NPV calculation can help you discard most of the candidates immediately. After you identify a compelling value proposition, you then dig deeper. Identify the reasons why it might be cheap. Estimate the political risk discount. Background check on the management. Etc. But there is no need to do this work for a 10% gain.
To further support our case, here is an excerpt from Ray Dalio’s Principles:
Understand the concept of “by-and-large” and use approximations. Because our educational system is hung up on precision, the art of being good at approximations is insufficiently valued. […] “By-and-large” is the level at which you need to understand most things in order to make effective decisions. Whenever a big-picture “by-and-large” statement is made and someone replies “Not always,” my instinctual reaction is that we are probably about to dive into the weeds—i.e., into a discussion of the exceptions rather than the rule, and in the process we will lose sight of the rule. To help people at Bridgewater avoid this time waster, one of our just-out-of-college associates coined a saying I often repeat: “When you ask someone whether something is true and they tell you that it’s not totally true, it’s probably by-and-large true.”
He describes how getting bogged down in edge cases often distracts from the big picture. At his firm, Bridgewater, they encourage focusing on what’s “by-and-large” true. According to him, that’s where the real leverage in decision-making comes from.
Of course, approximation has its limits. When you’re designing a bridge or calculating doses for chemotherapy, do not approximate. This should go without saying. But in the early stages of business analysis or investment screening, getting directionally correct answers fast is far more useful than slowly arriving at perfection. Hence, we hope that our point has become clear: not everything needs to be calculated to the cent. Doing so might actually slow you down. In fields like investing, efficiency often matters more than decimal-point precision.
So next time you find yourself tempted to fine-tune every input to the last decimal, ask yourself whether the potential upside justifies this effort.
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Anti-Thesis