The Hidden Power of Mathematics

We all want as much certainty as possible around our intended outcomes in life, but especially in business. Mathematical models have continued to evolve to create this often hidden certainty.

In baseball, with a man on first base and no outs, almost all managers will have their next batter bunt to move the runner to second base, placing him in scoring position. This decision had been figuratively engraved in stone for over 100 years. Then, Billy Beane and the Oakland Athletics hired a statistician to look at the hard facts — and everything changed. The data definitively showed that not bunting the runner to second base resulted in a far greater probability that the runner would be able to score from first base, by giving the team an extra at bat to drive in the runner. Only an in-depth mathematical analysis could uncover the certainty hiding under the gut- feel and intuition that previously dictated the decision making. Math can reveal what is not immediately obvious. But more than that, it has the power to change our perception of the world around us; rewriting thinking patterns that lead to an increase in efficiency, productivity and even home runs.

We all want as much certainty as possible around our intended outcomes in life, but especially in business. Mathematical models have continued to evolve to create this often hidden certainty. For example, regression models were developed to determine how independent variables can affect the dependent variables; by using the historical data fed to it, the model identifies the correlations between the independent and dependent variables. A more sophisticated example of this at work is the Black-Scholes model. Developed in 1972, the Black-Scholes model uses a unique a mathematical equation to create certainty around the pricing of an option.

Utilizing the implied volatility of the underlying stock, the current interest rate, the current stock price, the exercise price and the time to expiration as inputs, the model calculates the present value of all the expected future cash flows of the option. In other words, it analyzes the weighted probability distribution of continuous expected cash flows. The result is a price (present value) of an option at any point in time that is 95% accurate, contingent on the inputted implied volatility. This model became the foundation of the financial derivatives markets. In situations where one does not have sufficient historical data to estimate the probability distribution of an underlying variable, another mathematical tool was developed: “Monte Carlo Simulations”, which provide a substitute for the historical data by running thousands of possible outcomes, off of which a probability distribution is based.

While these equations have been developed to take the guesswork out of potential value creation, one area in business that has continued to be dominated by gut-feel or knowledgeable guesswork is sales projection. Most companies have to live through multiple sales cycles to realize the need for recalibration, forcing them to lose valuable time to reach their goal. Sales projections are very similar to bunting in baseball. Without the correct mathematical tools, we have to rely on our experience, even if it is qualitative rather than quantitative.



P3rceive is the first company to build a software using parts of the Black Scholes model and Monte Carlo Simulations to create certainty in the probabilities of an expected revenue outcome from a company’s sales process. While similar models have been created for supply chain processes, the sales process has been, up to now, very difficult to model. Whereas, the Black Scholes model is able to access large amounts of historical data to correlate its inputs to outputs, P3rceive uses the historical inputs of the company’s actual sales numbers and “Monte Carlo Simulation” mathematics to map out 10,000 probable outcomes for each change in a sales variable. Similar to the Black-Scholes model’s calculation of the present value of an option, P3rceive builds a probability distribution around the 10,000 simulated potential outcomes resulting from the change in a sales variable and identifies the probability that the desired revenue outcome will be reached.



Projecting future sales or bunting with a runner on first were dictated by long standing traditions that are difficult to drop without the factual support of probability. What P3rceive reveals through machine learning are the “hidden opportunities” that businesses have been missing out on due to long standing traditions or lack of data. Through this simulation process, P3rceive provides companies with a simple tool that grants access to actionable facts in the face of historical “maybes,” ultimately, giving businesses the green light to hit their ball out of the park.