How Statistical Analysis Revealed a Bet Worth Taking

A client had to dispose of a pile of sandblast grit left over from cleaning a dry dock. If classified as special waste, the disposal would cost $500,000 more than removing “clean fill.” Testing by a procedure which washes the grit in acid and measures the dissolved metals showed that lead concentrations for three of the five samples did not meet environmental standards for clean fill. But a statistical analysis simulating an additional fifteen random samples predicted a 7% probability that the grit would be designated clean. What to do?

In effect, our client could gamble $10,000 (the cost to obtain and test 15 more samples) against a payoff of $500,000.

If you play this game one hundred times, you’ll lose 93 times. But seven times, you’ll win back $500,000. So, while one hundred attempts at a cost of $10,000 each results in a million dollar loss, the payoff (7 x $500,000) produces a net gain of $2.5 million.

From experience, we knew one other critical detail that made our client’s decision much easier: few environmental consultants obtain samples via procedures that guarantee lack of bias. In fact, most take samples where there’s the greatest chance of finding contamination. When a medium is generally clean, this practice results in an unfair portrait.

We used quantitative analysis to determine that fifteen was the correct number of samples to take. Determining the chance of success also required more than textbook formulas, which give a false answer. To arrive at the correct answer, we developed a sophisticated computer simulation.

Our advice to our client, based on statistical and financial analysis and decades of experience: though the odds are against you, take the bet. Our client elected to play, and won. Within two weeks, his $10,000 investment delivered a $500,000 return.

In other cases, our clients have taken similar gambles and lost. But like the principle behind the success of casinos, while playing once is always a gamble, playing many times is a sure thing.