The Power of Power Laws and Impact

I trained in Mathematics, not Physics, so I tend to despair when I see physicists presenting their results and focusing on power laws. I used to think, “So what?” Unless you link this data point to some greater insight about the underlying process, “Why should I care?” But I’ve been revising my perspective recently.

Power laws are an unreasonably relevant piece of information to know about a process. I will still reserve the right to despair at a physicist who doesn’t know why (s)he’s telling us that their pet process represents a power law distribution. But I can no longer deny that knowing that a process, in which I am interested, follows a power law distribution gives me a hugely powerful insight.

I used to work in neuroscience. I never really cared that certain frequencies in the brain appeared to follow power law distributions. The network has a wiring which is pretty much guaranteed to induce such frequency distributions. So knowing that it really does, never seemed to add much for me.

However, in other fields, knowing that the system obeys a power law distribution means that you know that certain elements have outsized effects.

• Nate Silver argues, in The Signal and the Noise, that prediction markets effectively follow power law distributions. He advocates entering immature prediction markets, in order to have an outsized impact. The basic curve on return-on-effort mean that early members of the market, who apply an average level of ability and effort, gain outsized returns relative to the market. In contrast, in a mature prediction market even incremental gains require oversized investments of effort.

• In Zero to One, Peter Thiel makes a powerful argument for what kinds of project you choose to spend your life working on, and a related point about what types of companies are actually creating value. I find his thinking quite reminiscent of an application of my power laws insight. i) Working on certain challenges comes with outsized returns in terms of impact. ii) The only kinds of companies which make real profits are monopolies.

• When you look at businesses and entrepreneurs, what is it that justifies the outsized returns that founders are in line to make? Their returns clearly follow another power law – most just about break even, whereas a few make a ton of money. The most coherent argument I have heard so far is that their level of risk is much higher. They are taking on a project involving their time, their network, and the great unknown. All of the other participants are dealing with known risks and better defined returns on their investments.

When I combine all of the observations above, I come to a point where I see that recognising that a system obeys power laws leads me to conclude that I should i) choose the project which is most likely to take less effort to achieve a significant return, ii) is trying to become the only solution in a given space, iii) will reward my effort in terms of both time and risk appropriately.