When the “Expected Value”, isn’t

A core concept in uncertainty-based decision making is the “Expected Value”.  Simply stated, if an uncertain trial is repeated many, many times, the Expected Value is the average result you would experience across all of the trials.

A simple illustration can be constructed using a coin.  Image a game where heads wins the player $100 and tails returns $0.  For each flip, the player either gets $100 or $0.  If the player repeats the game a hundred times or so, he or she would receive on average $50 for each trial.  The Expected Value for this game is then $50.  But what’s the chance of the player winning $50 playing the game once?  0% of course.  They will always win $100 or $0 on a given flip, but NEVER $50.

Crystal clear right?  Couldn’t be simpler you say.

But here’s where the problem arises.  For complex projects, businesses often construct uncertainty-based business cases.  We consider many uncertainties and model the range of their values, resulting in a ranged value for the business case.  We can see the distribution of possible outcomes and calculate the average of their values.  Invariably we label this the “Expected Value”.  

What’s the chance of actually getting this outcome?  Once again, it’s practically 0%.  It is but one point on the curve of possible outcomes.  However, when we place a grand label on this data point, suddenly everyone forgets the distribution of possibilities, and expects this value to be achieved.  For most assessments, if the Expected Value is about in the middle of the distribution, there is roughly a 50% chance you won’t get that good of a result.

Uncertainty-based business analysis is more about exploring the distribution of outcomes and their drivers, and taking action to improve the results based on these Insights, and far less about a single point on the outcome distribution. Comparing only the Expected Values of project alternatives is not a valid approach to selecting which project to promote, and if the Expected Values are close, they should be ignored completely.  Examining the breadth (or risk) of the outcome distributions, their key drivers, and the probability to experience disaster or wild success is far more insightful and will make for better decisions, stronger projects, and more successful companies. 

If only we had called the point something other than “Expected Value” all of this confusion could have been prevented.  I suppose we could have simply called it the “Mean Value”, but then we probably would have to devise an additional analysis to find the “Nice Value”.