What’s your magic number?
If you’ve never heard this question or phrase, you’ve probably been living off-network or away from the developed world for some time. It’s a term used by people for different reasons and a variety of meanings.
We employ numbers in accounting to maintain financial accounts that assess our current balance among other purposes. We use numbers in educational institutions to assess relative performance levels of students and teachers. Numbers are used to design almost everything man-made and we use numbers to plumb the breadth and depth of the natural world around us.
What is the Magic Number?
But what is this “magic number” thing?
For a business manager it might be the backlog number. For a sales manager it might be the conversion rate, the forecast, and the quarterly “number” that’s finally posted upon which commissions are paid.
For a business owner it might be growth rate. For a CEO it might be earnings, return on assets, return on equity, the trading price of stock or the achievement of objectives established with the board.
For a customer service representative the magic number could be the number of calls serviced per hour, time spent on the phone per caller, or the number of successful close-outs per day.
For a lawyer the magic number may be billable hours. For an airline pilot the magic number is likely to be accident-free miles. For a truck driver it’s likely to be miles per day between required rest times.
For sports fanatics, the magic number may be the number of games remaining to be won until the home-town team wins a slot in the upcoming post season playoffs. The formula for this magic number looks like:
Magic number = total games – # of wins by 1st place team – # of losses by2nd place team + 1
In financial risk mathematics, Value at Risk became the magic number to express the total value of a portfolio that could be lost over a certain time horizon. We won’t both to include VaR calculations here; it would require an entire series of blog articles.
Magic Numbers: a reversion to the Mean
With the exception of teams remaining in contention for a playoff spot, almost all magic numbers reflect an arithmetic mean – the average – value for a series of numbers in a given population.
As an “average” value, most magic numbers aren’t really magic at all: they simply represent current consensus of the group. There’s really nothing “magic” about them other than the magic number is simply the current mean or average.
But, it’s the differences in the population – the deviations – at any given time that really are the interesting numbers. Most intriguing of all are the maximum differences between the outliers in a population and how far removed these are from average.
The outliers tell the story
It’s the outliers that are really the magic numbers, not the mean. I don’t mean the outliers that are so far away from any cluster, but the clusters of numbers that might be two, three, four or more sigma away from the mean.
The outliers tell the stories of “unexpectedly” super levels of performance or of sub-par performance. Or the outliers tell the story of overwhelming evidence of correlation between disease outcomes and causative agents.
Or the outliers reveal financial graft and corruption in the servicing of mortgages. Or outliers reveal the reasons why some organizations continue to be plagued by security breaches resulting in financial damage, public scrutiny and scorn, business downtime or other outcomes.
So the next time you hear the question, “what’s the magic number?”, think a bit beyond the comfortable box of average, and look for and then understanding what’s behind the fat-tails.
Going beyond average to find the magic numbers
The average is not the magic number. Instead it’s our way of saying this is the current level of average. For those who want to go beyond average, who want to understand how to improve results, or how to limit risk exposure, going beyond the magic number is necessary to going beyond the contextual level of acceptable mediocrity.
It’s the outliers that are really the magic numbers, not the average.
These are really the magic numbers!