# Schwarzenegger Bandit Success Formula

In “Does Luck Matter More Than Skill?“, Cal Newport writes

<success of a project> = <project potential> x <serendipitous factors>,

where <project potential> is a measure of the rareness and value of your relevant skills, and the value of the serendipitous factors is drawn from something like an exponential distribution.

and

If you believe that something like this equation is true, then this approach of becoming as good as possible while trying many different projects, maximizes your expected success.

Indeed, we can call this the Schwarzenegger Strategy, as it does a good job of describing his path to stardom. Looking back at his story, notice that he tried to maximize the potential in every project he pursued (always “putting in the reps”). But he also pursued a lot of projects, maximizing the chances that he would occasionally complete one with high serendipity. His breaks, as described above, all required both rare and valuable skills, and luck. And each such project was surrounded in his life by other projects in which things did not turn out so well.

If success is measured in dollars, then I bet the distributions of <serendipitous factors> have fat 1/polynomial tails because there are a lot of people with great skills, but the wealth distribution among self-made billionaires is something like C/earnings^1.7.  For many skills, like probability of hitting a baseball, the amount of skill seems to be proportional to log(practice time) plus a constant.  For other skills, like memorized vocabulary, the amount of skill seems proportional to (study time)^0.8 or the Logarithmic Integral Function.  Mr Newport emphasizes the “rareness” of skill also.  Air is important, but ubiquitous, so no one charges for it despite it’s value.  In baseball, I imagine that increasing your batting average a little bit can increase your value a lot.  I wonder what the formulas for <project potential> are for various skills.  If we could correctly model Newport’s success equation, we could figure out the correct multi-armed bandit strategy for maximizing success.  (Maybe we could call it the Schwarzenegger Bandit Success Formula.) You may even be able to add happiness into the success formula and still get a good bandit strategy for achieving it.