The Startling Convexity of Expertise

Byrne Hobart
Jul 24, 2019 · 14 min read

There’s this meme that you shouldn’t work more than forty hours per week. Don’t believe it. It’s just laziness apologetics. If you’re reading it on Twitter or Hacker News, it doesn’t apply to your job.

There are studies showing that productivity per hour drops after forty hours per week, and turns negative at higher levels — but these are studies of dangerous factory jobs, or monotonous call-center work. And I don’t doubt it. If I spent a hundred hours a week on the assembly line at a munitions factory, I’d probably end up dropping a missile on my foot or something, which would do a number on my productivity.

But there aren’t that many factory jobs in the developed world that require such long hours, and even the call center jobs are moving offshore. In other words, if you have the kind of job that allows you to use your work computer to argue with people on reddit about the length of the optimal workweek, it’s likely that neither you nor your interlocutor work in the jobs being referenced in those studies.

It’s hard to measure productivity for white-collar jobs. Alan Greenspan famously, then infamously, argued that productivity statistics understated growth because they ignored the obvious efficiency gains computers gave knowledge workers. Many of us have a sense of who at work is most productive, and who is least, but it’s exceptionally hard to actually quantify. If a clever coder finds some hack to make a complex problem trivial, it’s probably a net saving — unless their hack introduces an obscure edge case, and its conciseness makes it hard to debug.[1]

In general, I take the view that the clever solution is a win. But if I had to quantify how much of a win it was, I’d demand a wide confidence interval.

And that’s for comparatively structured questions, like “What is the optimal way to convert input X into output Y?” It’s even harder for uncertain jobs, like “What should input Y be?” Was the team that designed the “like” button more productive than the team that produced Slack’s “emoji react” feature? We can argue indefinitely. Maybe the “like” tightens the feedback loop between creating content and knowing what’s appealing; maybe emoji-reacts are a higher-resolution version of the same. Or maybe both of these are bad for productivity by crowding out more thoughtful replies.

As a rule, if you couldn’t write a standardized test for it, it’s not amenable to direct productivity measurement. You can test someone’s knowledge of arithmetic or their vocabulary, but if you made a standardized test for art, Picasso would fail and Thomas Kinkade would get an A+.[2]

Since it’s hard to measure relative productivity in knowledge work — and since it gets harder as the work gets more valuable — we’ll have to go back to the old standbys: anecdotes and first principles.

On the anecdotal side, I know very few successful people who don’t work exceptionally hard. There’s some variability — plenty of poor people put in long hours, and there are still idle rich people who were in the right place at the right 409(a) valuation. But mostly, it’s striking just how much effort successful people put into their chosen fields. Ramit Sethi has a wonderful story about this:

My first experience with this was with my super-ripped friend, who used to tell me, “All you need to do is work out 3 times a week.” What a fun and easy-to-implement tip worthy of a magazine! So imagine my surprise when I spotted him doing some light cardio at the gym one Saturday. “Hey dude,” I said, “don’t you normally work out Mon/Wed/Fri?”

“Yeah,” he admitted. “This is my off day.”

BOOM. It blew my mind that he was still at the gym on his “off” day.

I see this with good investors: one friend of mine has had a very successful career working at big hedge funds. His favorite hobby is — investing in companies that are too small for his fund. When he was CEO of Microsoft, Bill Gates once took a vacation with his wife and brought along half a dozen biographies of Henry Ford.

I’m not entirely sure if writing counts as “work,” but if it does I work a lot. But it’s not a be-seen-in-your-seat-at-7am kind of work; it’s a background process. Probably 10% of my topic and conclusion sentences are things I type up wearing only a towel because I wrote them in the shower. If your work is not something you find deeply engaging and interesting, this is a nightmare. But if you like what you’re doing, it’s great.

If there is a Secret To Productivity, that’s probably it: cultivate an antsiness for progress. There are a few ways to do this. One is to be born lucky; some people seem to have some gene that just lets them flip a switch and devote 100% of their conscious effort to the task at hand.[3] The rest of us have to work harder. There are three tricks, which compound:

  1. Work on interesting problems
  2. Find friends who are working on parallel problems and will challenge you
  3. Use the Convexity of Expertise to stay engaged and make faster progress

The Convexity of Expertise

Convexity is a finance term that approximately means the extent to which your financial exposure to something changes as it moves in the direction you want. Consider a ten-year bond yielding 4%. If rates rise to 5%, your bond loses about 8.2% of its value. If rates fall to 3%, your bond goes up 9.1%. The lower rates go, the more responsive it is to changes in rates. So if you bought the 10-year yielding 4% (congrats!) your exposure to your bet rises as you get more correct. Buying options has the same trait: if a stock’s at $50, your $20 puts don’t move very much when it drops, but as it gets closer to $20 they start to move a lot.

But it applies in more abstract ways, too: if you work at a company whose product has network effects, you get a lot of convexity from additional user adoption; as Slack went from a product used by a handful of startups to a product used by tens of thousands of customers, Slack became more of a bet on the shift from email to IM — a shift Slack helped catalyze and accelerate.

Currencies have a lot of natural convexity: if a the currency of a developing country with dollar-denominated debts starts dropping, it can lead to a run-on-the-bank effect that pushes the currency down further, causing economic disruption that further weakens the currency. Conversely, Bitcoin hyper-optimists can argue that Bitcoin owners are smarter than governments, so any regulation is a sign that the regulators are too late to stop it. (Hence the classic call and response: “Bitcoin banned by X” “Actually, this is good for Bitcoin.”)

Nothing in life demonstrates the same level of convexity as expertise. It really never ceases to astonish. Pick a topic, read a book, and you know something. Pick a topic, read every book ever published on it, and you’ll find yourself inside the OODA loop: you’ll start reading a chapter, know which study the author is citing, quickly figure out that the author either didn’t read or is choosing to ignore a contradictory study, and zip right through.

When I read The Man Who Knew, I kept thinking about The Prize and The Box. Central bank policy in the 80s and 90s only makes sense in the context of suddenly-cheap oil and relentlessly cheaper shipping. And the next time I read up on the 80s LBO boom or the Internet Bubble, I’ll have all three books in mind.

If you read Uber’s S-1, you get a decent understanding of the business. If you read it after you read Lyft’s, you just wonder: where are all the cohort analyses? Isn’t that the whole story? It’s a business that acquires users and gets a little more out of them each year — or, based on what Uber omitted, maybe it’s not.

If you’re a programmer, this happens with programming conventions and libraries. When I first learned Python, the fact that it was len(x) and not x.length() was just something to memorize; years later I read Fluent Python and was enlightened. Now I’m more likely to see differences like that as indicative of meaningful design choices rather than random noise — and the fact that there’s meaning behind them makes them easier to remember.

This convexity pays off when all the information is in your head, so you can draw as many connections as possible. And those connections actually improve your retention. As you read more, more details and omissions stand out.

And it pays off in another sense: over time, you get better at developing expertise and getting the attendant convexity. It took years for me to get fluent in my first intellectual obsession, with value investing, and took a similar time to know what I was talking about in online marketing. I’ve picked up the pace since then. Although my fluid intelligence has probably peaked — if you’re over 30, expect to get slightly dumber every year, forever — crystallized intelligence can more than compensate.

Work and “Work”

My last post was about the push notification-enabled tyranny of Total Work, so where do I get off lionizing long hours? I’d draw a distinction between the kind of work an always-on system enables and the kind that actually helps people produce accomplishments of lasting value.

Slack, email, status meetings, etc. — these all enable “ping-pong” work, in which you get an input and immediately bounce it to somebody else. A certain amount of this work is unavoidable. Sometimes the only way to make progress is to get the right five people in a room for thirty minutes, and if those people are busy it may take more total time to schedule the meeting than it takes to complete it.

But at the other end of the spectrum is “sniper-shot” work: one mostly solitary person with exactly one goal, painstakingly lining up their shot, and taking it. If you’re hitting “reply” at 11pm, there’s a good chance you’re doing ping-pong work; if you have Excel, iPython, and your text editor of choice open at 11pm, you’re hopefully lining up your kill shot.

Both of these kinds of work are time-consuming, and there’s an interesting symmetry to them: busywork expands because you have an imperfect mental model of the people you work with, and they have an imperfect model of you. If you’re in the middle of a company hierarchy, you’re going to invest a lot of effort in figuring out what your boss wants, and another big chunk of effort in figuring out how to articulate these goals to your direct reports.

(There’s a famous story about a successful executive who was able to minimize his delegation time relative to his strategizing time, from Ogilvy on Advertising: “On the night before a major battle, the first Duke of Marlborough was reconnoitering the terrain. He and his staff were on horseback. Marlborough dropped his glove. Cadogan, his chief of staff, dismounted, picked up the glove and handed it to Marlborough. The other officers thought this remarkably civil of Cadogan. Later that evening, Marlborough issued his final order: “Cadogan, put a battery of guns where I dropped my glove.” “I have already done so,” replied Cadogan.”)

The cool thing about sniper-shot work is that, rather than retail-level mental modeling, you’re doing wholesale mental modeling: you’re working on a mental model of reality, not of your coworkers. This distinction helps keep things fine-grained: a detailed strategy memo is not fake-work, because rather than incrementally managing people’s mental models you’re asking them to reframe them; replacing the email-and-IM API with a software library that can be imported wholesale.

And, like software libraries compared to API calls, the stakes are higher and the rewards to perfectionism are correspondingly greater.

So both kinds of information work are fundamentally about improving a mental model. It’s just that one of them has diminishing economies of scale, and the other is arbitrarily scalable.

There are people who have long and prosperous careers that consist disproportionately of ping-pong work: lawyers and investment bankers, for example. But there are countless deals in which the bankers and lawyers make millions from their hundred-hour weeks, while the principals of the deal make billions instead. (From time to time, a practicing attorney or i-bank exec makes the Forbes 400–usually a good bubble indicator — but the richest bankers and lawyers on the list are the ones who did a couple years of i-banking or biglaw and decided that charging by the hour just didn’t have the convexity they wanted.)

Where to Start

Start by having arbitrary strong opinions. Expect them to be wrong. But they’ll keep things interesting. Strong opinions, weakly held, are a cheap call option on information.

There are a couple themes I keep coming back to in my writing (and investing, and my career broadly):

  • Western standards of living will stagnate or decline during my lifetime. This is mostly due to a freer and fairer global market, which allows talented people from places with a low cost of living to compete with relatively rich and lazy Westerners like me.
  • Americans consume too much housing, healthcare, and formal education. In the case of housing and education, we lever up and treat consumption as an asset; in the case of healthcare, we’re uncomfortable facing tradeoffs and bad at aligning incentives.
  • The world is full of mispriced options. Endless dating means constantly overpaying for future opportunity; marriage means selling that overpriced option and collecting the attendant risk premium.
  • More broadly, many phenomena can be modeled quite well as options: any choice you make generally involves an upfront cost or benefit in exchange for a skewed bet on the future.
  • Mainstream politics are an intellectual dead end. Absolutely nothing of value will come from debates among NeverTrump Republicans or Obama Nostalgia Democrats. If you’re not losing friends over your completely insane views, don’t even bother.

I’m confident that some of these opinions are wrong. I’m equally confident that they’re all instrumentally useful — if I have to change my mind, it will be for some unique reason that makes me smarter.

When I tell my techno-utopian friends that my kids will only have a better standard of living than I do through some combination of luck and a nice inheritance, I get an earful about the latest advances in asteroid mining, quantum computing, and CRISPR. When I talk about how high housing prices are destroying San Francisco’s tech network effects, I hear about fascinating new counterexamples I’ll wish I had gotten into the seed round for. When I mock the search for optionality, I hear about all kinds of plans that people could put in motion any day now (though that day doesn’t ever seem to come). And when I tell someone a career decision is a call option on the online ad market or equivalent to writing puts against the status quo, I hear all about how the vanilla trade I have in mind is interestingly exotic.

When I share my political opinions on social media, I get blocked, which is a good reminder to spend my time better.

By having a random-looking collection of strong views, I’ve outsourced a lot of research to the people who disagree with me. At the same time, I’m making a reputational bet, so I have an incentive to actually do my own research to make sure I’m right.

Convexity has a Cost

It’s the fate of anyone who gets really into modeling the real world in terms of optionality to fall in love with one of the Greeks:

  • Delta: I can take idiosyncratic risks but continuously hedge them in conventional ways (as long as the market is liquid).
  • Gamma: I can get overpaid to take pretty much any risk (although unless I’m exceptionally careful I’ll get wiped out).
  • Vega: I don’t even have to bet directionally; I can bet on the degree of uncertainty.

If you’re betting on convexity, the big risk you run is model risk: you need to be exceptionally certain about the slope of an intrinsically unknowable curve. If you’d spent the last five years getting up to speed on nuclear power, you’d be a very well-informed person — but it turns out the debate over nuclear is not defined by cost or risk but by how hard it is to make a compelling HBO miniseries about the incremental effects of air pollution.

Since the whole point of the convexity of expertise is to learn things, you’re necessarily subject to Knightian/Rumsfeldian uncertainty: the unknown unknown is whether or not the topic you’re interested in actually has skewed upside. Some subjects lend themselves to endless debate but will never be resolved — in economics, philosophy, and lit crit, you can end up getting slightly better at arguing but not any better at understanding the world.

There are two rubber-meets-the-road tests here: one, do the experts affect the real world? And, two, do any of them get really, really rich?

If you learn how DC works, you might conclude that it basically doesn’t. There are some government agencies whose headcount is so large relative to their responsibility that it’s clear that everyone involved just works full-time managing or thwarting other people — famously, there are more Department of Agriculture employees than farmers [Edit: a reader points out that this is not, in fact, true. Not by a long shot: 100k D of Ag. employees vs about 1.2m farmers. My mistake.]. So expertise in American agricultural policy might be a waste of time.

In the US, the two fields that produce a disproportionate share of rich people are software and finance. These are, not coincidentally, two very meta fields — if you said you worked in either industry, it would sound kind of evasive. Software is meta because it leads to the question “What kind of software?” It’s odd that there are people who got rich in processing payments, doing payroll, advertising, and media — all of whom really got rich running software companies that automated these fields. Finance is meta because it’s the exchange of a certain amount in the present for an unknown amount in the future. Every industry has a finance layer, just as most have a software layer. So if you’re in either software or finance, you’re really in the business of converting some other industry’s output into either a) a stream of symbols that can be manipulated according to logical rules, or b) a stream of cash flows which can be traded.

But while both fields are meta, they lend themselves to an arbitrary level of specialization — there are programmers who work with one special-purpose language for one specific piece of enterprise software, and there are programmers whose mandate is “Increase a company’s sales through some combination of a modicum of business knowledge and the use of some arbitrary scripting language.” I’ve met investing generalists with long positions in Mongolian currency and American community banks, and a few people who specialize in just analyzing the constellation of companies around one guy.

Even then, “generalists” are just opportunistic specialists who can’t succinctly describe what their interests have in common. And a dyed-in-the-wool Maloniac can’t help but get a sense of how the broader media business is doing, and what tax plays the IRS is just barely willing to countenance, which they can apply outside that narrow set of stocks.

In a meta field, you can consistently benefit from moving to a slightly adjacent topic. I’ve spent the last seven years primarily using alternative data to analyze tech stocks, which has given me a very handy frame of reference for my macro hobby — the preference cascade into and out of Snapchat is not exactly distinct from the preference cascade out of and back into peripheral European sovereign credit.

I didn’t know that ex ante; I only got into this industry because my hobby intersected with my day job at exactly the right time. But that’s the beauty of the convexity of expertise coupled with interestingly argumentative friends: at first, you’re just flailing around at random. but eventually you end up — by default — making a big bet in exactly the right direction.


Thanks to Jonathan Libov and Alexey Guzey for edits.

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[1] Brian Kernighan: “Everyone knows that debugging is twice as hard as writing a program in the first place. So if you’re as clever as you can be when you write it, how will you ever debug it?”

[2] The people most keenly aware of this are failed artists who assume they’re just misunderstood. But many artistic geniuses had an earlier career phase in which their work was relatively conventional and really good. Before saying you’re virtuous because you never sold out, you have to prove it by selling out.

[3] Richard Feynman’s second wife, in her divorce complaint: “He begins working calculus problems in his head as soon as he awakens. He did calculus while driving in his car, while sitting in the living room, and while lying in bed at night.” Feynman’s wife literally made him choose between math and her. He solved for ex.

Byrne Hobart

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I write about technology (more logos than techne) and economics. Newsletter: https://diff.substack.com/

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