# The Success of Startups & Power Laws

We know from historical records that startups have a high failure rate (i.e. many startups do not produce any profit at all) and that the few that do tend to win big. It’s no surprise that venture capitalists choose to model this relationship by a power law—meaning “a relative change in one quantity results in a proportional relative change in the other quantity” (Wikipedia). In the case of startups, this means the chance of providing 2x return to your investors is, say, 70% as likely as providing 1.5x and that 1.5x is 70% as likely than 1x, and so forth.

This number, 70%, both explains the decaying likelihood of success—the decay rate—as well as the proportion of startups that generate 0x return to investment—the failure rate. In other words, if we know one, we know the other; if we know that 1.5x is 70% as likely than 1x, we know immediately that 30% of startups generate 0x. Similarly, if 1.5x is only 10% as likely as 1x, then 90% of startups generate 0x.

Perhaps you have noticed the pattern already: Decay Rate = 100% – Failure Rate

Why are the decay rate and failure rate tied together by such a simple equation? That concept may be a bit advanced. Suffice to say that, probabilistically, in order for all possible outcomes to sum to 100% (as in the chance that a startup returns either 0x or 0.5x or 1x or … must total 100%), the decay rate and failure rate must be related as such.

If this seems too simplistic, then so is assuming that power law can model startups’ returns.