Belts & Belt Loops

I got a belt on that’s holding up my pants, and my pants have belt loops that hold up my belt. I don’t know what’s really happening down there. Who is the real hero? — Mitch Hedberg

Great question, let’s give it a shot.

Who is the real hero?

Hmm, not so simple. A pie chart doesn’t really make sense here.

This is because belts and pants are complementary goods, things that are more useful when they’re together. Complements are all around us: Pencils and erasers, peanut butter and jelly, shampoo and conditioner. Some complements are so tightly coupled that either would be useless without the other, like a lock and key, or left and right shoes.

Substitute goods, on the other hand, are things that are more or less interchangeable. Common examples: Coke and Pepsi, umbrellas and raincoats, regular and electric toothbrushes, bar soap and liquid soap. If you use more of one, you’ll use less of the other, so a pie chart actually makes sense.

Econ 101 usually stops the lesson here. But the mental models behind complements and substitutes extend far beyond simple consumer goods.

Hidden Complements in an Apple

Different nutrients in food are complementary, but most of us have been trained to think about nutrient sources as substitutes instead. Take a look at any nutrition facts label. Everything is in terms of “% Daily Values” — exactly the type of pie-chart thinking that misses all the interaction effects between nutrients. This packet of Emergen-C has 1,000mg of vitamin C. Wow, 1667% daily value? That means I’ll be sixteen times healthier!

Emergen-C nutrition facts

It’s far better to eat a whole apple than take a vitamin C supplement. It turns out that vitamin C doesn’t do much on its own, but when paired with other chemicals in an apple called phenolics and flavonoids, the whole team kicks into gear. Of course, the supplement’s nutrition label makes no mention of this. While vitamin supplements are not harmful by themselves, they can fool us into thinking they’re valid substitutes for real food.

Luck vs Skill

I am a great believer in Luck. The harder I work, the more of it I seem to have. — Coleman Cox

Ideas can be complements too. How much of success is luck and how much is skill? Fatalists say luck is more important, free-will believers lean toward skill, and others split it half-half.

Of course they’re both important, but you can’t split them like splitting a pie. Asking “How much of success is luck?” is like asking “What percentage of my-pants-not-falling-down is caused by my belt?” Complements just don’t work like this. In a positive feedback loop, it’s impossible to attribute a percentage contribution to one factor because it affects and is affected by other factors. Plenty of often-debated pairs have this relationship: Luck vs skill, attitude vs skill, luck vs hard work, talent vs hard work, ideas vs execution, nature vs nurture. It’s both. It’s always both. And it’s that special kind of “both” where one boosts the effectiveness of the other.

The Simple Math

You’ve seen those motivational posters that say something like SUCCESS = PLANNING + EXECUTION. But that little + sign is misleading. Addition implies that substitutes are acceptable: If you don’t have enough execution, just do more planning. 100 can be expressed as 50 + 50, or 80 + 20, or any split of the pie. As long as it adds up to 100, we’ll have success, right? Not quite.

A more accurate formula is SUCCESS = PLANNING × EXECUTION. If you do zero planning, it doesn’t matter how good your execution is — zero times anything is zero. Multiplication captures the idea that both planning and execution are needed and that they’re not substitutes.

With our new formula for success, we can take derivatives. If S = P × E, then dS/dE = P and dS/dP = E. What does this mean? dS/dE is the marginal productivity of execution, and it’s equal to P. That is, the more planning you do, the more success any additional execution will bring. Likewise, the more execution you do, the more success each additional minute of planning will bring.

These formulas are examples of production functions, mathematical descriptions of how inputs turn into to outputs. S = P + E is an additive function, while S = P × E is multiplicative. Of course, success, planning, and execution are not directly measurable quantities and the multiplicative formula is still dramatically oversimplified, but it’s a little closer to reality.

Cultivate Complements

I imagine the word leverage (despite being overused to the point of meaninglessness today) originally emphasized multiplicative rather than additive effects. A lever multiplies a force, and that lever can be a crowbar, a computer, or a credit default swap. Has your computer ever been so slow that you just turned it off in frustration and went to bed? Have you ever used a knife so dull that it felt like sawing through brick? A good tool will multiply any effort you put in. Good craftsmen know this and take great care of their tools.

A product team and a sales team are complementary, and can use each other as levers. A great product makes the sales team more effective by making the product easier to sell, and a great sales team makes the product better by using on-the-ground feedback to identify problems and opportunities in the product. Teams who think of themselves as complements will work together to multiply the size of the pie. Meanwhile, teams who think of themselves as substitutes will fight each other for bigger slices of the pie.

It’s easy to fall into the substitute trap. We might mistakenly call it “focus.” But we live in a wildly interconnected world, where the whole is greater than the sum of its parts. Let’s cultivate complements in the same way we’d put on left and right shoes.