How to calculate snowfall probability

Calculating probability of various snowfall totals is not all that complicated, although not quite as easy as calculating the average seasonal snowfall for your market(s).

Probability is the likelihood of occurrence in terms of a percent. While there are different ways to calculate probability, one of the easiest is to sort your list of seasonal snowfall totals from smallest to largest. (For background on how to gather that information, read the May 2014 Snow Strategy column, “How to use weather data for sales, renewals.”)

For example, in my home market of Detroit, the smallest seasonal snowfall total is 12.9 inches and the largest is 93.6 inches. With 132 years of data at my fingertips, I can say with confidence that there’s a 99.99 percent probability that next winter’s snow total will fall between 12.9 and 93.6 inches. I’m not a mathematician, but this seems apparent to me.

Divide the total number of years by two to determine the midpoint of your data set. For my market, I have 132 years’ worth of data. The midpoint is 66 years, or 40 inches. In other words, 50 percent of seasonal snowfalls are above this total and 50 percent are below this total. Note that the midpoint is not the same as the average (40.5 inches for my market).

Next, split each half of your data set in half again. Do this by dividing the number of years below the midpoint by two and by dividing the number of years above the midpoint by two. By doing so, you have created quartiles at 25 percent, 50 percent and 75 percent. For my market, the 25 percent quartile is at year 33 and the 75 percent quartile is at year 99. Without any further understanding of statistics, you can now accurately say that there is a 75 percent probability of seasonal snowfall totals being below the 75 percent quartile. In my market, this amount is 49.6 inches.

You can also accurately say there’s a 25 percent probability of seasonal snowfall totals being above the 75 percent quartile and a 25 percent probability of being below the 25 percent quartile. In addition, you know there’s a 50 percent probability of being between the 25 percent and 75 percent quartiles.

How to use this data

For example, if a customer wants to understand the differences between a per-event (or visit) agreement and a seasonal agreement, the use of snowfall data and probability is a critical component of this discussion. The customer needs to realize what his or her costs may be under different snowfall scenarios and the likelihood of such a scenario happening. Only then will he or she be able to make an educated decision.

From the snow professional’s perspective, the risk/reward equation is simply reversed. Just as the customer needs to understand his or her risk under different scenarios, so does the snow professional. This is critical both in terms of the individual proposal and in terms of the portfolio as a whole. There’s no reason for a snow business operator to be in the dark when historical weather data are readily available.

A more advanced approach is to link probabilities to estimating and proposal programs. By making this entire process formula-driven, a savvy salesperson could sit with a customer or prospect and run various scenarios to see the impact on risk, liability and pricing. Alternatively, a sampling of these scenarios may be run prior to the sales meeting and presented as options in the proposal. Again, the use of charts and graphs will greatly increase the attractiveness and understanding of your proposal.