Be prepared to play the power law in start up valuations

?In general, most processes are assumed to originate from a normal distribution, where the deviation of any observation from the mean is symmetric. But this assumption, while often assumed to hold in social science may not hold as frequently as assumed. Xavier Gabaix. Professor of Finance at The Stern School at NYU once wrote an article about the fact that one fundamental law in economics, may well be the prevalence of “power law”[1], that leads to significant asymmetric distribution of phenomena in social science

POWER LAW RATIONALE

A “power law” is a mathematical relationship between Y (say income) and X, (e.g. population ranked in income from the highest to lowest), such that X = a.Y-β?, and?β?is the scaling exponent. Assume further that??β=1, then??probability that the income of a randomly drawn individual is greater than a certain income threshold is?inversely proportional?to this threshold.??Such a power law (also called Zipf or Pareto law)?exhibits a skewed distribution, with??a short concentrated head of 20% of population at the top ("the??few richs"), and?a long tail (or 80%) of the remaining population ("poor income earners").

As X. Gabaix has noted, power laws are visible in many situations such as wealth, education performance, or the size of cities[2]?, website and mobile apps traffic[3],??or still technology use diffusion among firms?[4],?[5].??Those power laws[6]??arise rather extensively because of the presence of feedback loops, contextual effects, or scale-free phenomena.??

A positive feedback comes from example from??preferential attachments, that is??new agents entering a system would prefer to connect to the node that is most easily recognized, (-which in practice is often largest node in a system). Think about how Google search ranks results that are the most popular on the first page, reinforcing their likelihood to be clicked on, thus reinforcing their popularity.??Business models such as platforms reinforce those loops, and creates power law, as a result of a “winners take all” mechanism.

Another explanation for power laws is contextual situations. Borrowing from??Crawford et al. (2015)?[7], think about a sandpile. Grains of sand, when dropped one-by-one may have radically differential effects—most grains that are dropped only move one or two grains on the pile, while a few grains have extreme cascading effects, moving hundreds of grains. The later case, while unusual, drive the power law.

One final driver of power law is what is called the multiplicative effect; that is, where the aggregate interactions that lead to a phenomenon are not additive but multiplicative. Think about someone who is good tennisman and is thus more equipped to play pingpong, or someone who is tall is thus more able to run fast, etc.

THE POWER LAW IN START UPS VALUATION

Looking at start up valuation demonstrates no exception to the power law.??Based on recent data by end of 2021,??we compute that the top 20% within non-unicorn start ups, or within unicorns, or still within decacorns concentrate close to 60% of the related universe value (see figures 1 to 3).

Taking further a full picture?of all funded start ups,?from seed all the way to the few octacorns such as ByteDance (figure 4), the regression fit leads to a rather precise estimate power exponent of??β=1,1 ( R-square of 92%), reminiscent of the typical Pareto law, with a split of 80-20 in value.

This statistical analysis (see?How to become a unicorn? | Fortino Capital?and?The rise of the decacorn | Fortino Capital) aligns with our own VC internal view that??start ups success comes from blending a set of interacting factors, that are multiplicative drivers to success.??E.g.., a start up that combines great team, large market size, strong products and competitive advantage, may be more successful that one with one exceptional market size, because great team will design more exceptional products, more competitive advantage will bring better inroads to broader markets, etc ,etc.

The preferential attachment is also present in startup: better performance along the life leads to more VCs attracted to fund those companies, or to more talents willing to join, providing them with more competitive advantage to succeed against competitors and consolidate their TAM for example. Finally, contextual effects may play a role too. This case happens at a certain critical time in the life cycle of start ups, like the chance to get introduced to a major VC that loves a POC, a significant event that opens large potential, like covid-19 opening the opportunity for significant remote interactions, or risk of war, leading to shift in cybersecurity demand.

START UP INVESTORS IMPLICATIONS?

The implications of the above are thus clear. Not only VCs should look at companies based on a set of filtering criteria such a team quality, product market fit, etc —but what really can discriminate between a good start up and the ones with a large call option of success is the presence of drivers to power law.?

In particular, one should look at how factors combination create positive externalities ( such as better product leads to large TAM), at what unique events can drive a context of flying wheel ( eg cloud leading to an explosion of SAS), at mechanisms of preferential attachments (BM such as platforms or marketplace, etc).??

Note finally that such an analysis is not only due to check on start up potential, but is a reality check against the possibility that competitors may benefit from them, - making any own investment stuck in the long-tail, and unable to advance with success in the funnel of valuation. Better be prepared for the power law to play in your favor.??