NORTHERN ROUTE
And the expected value will be:
E = (0.9 x 6) + (0.09 x 2) + (0.01 x -4) = 5.54
This analysis produces an expected value on the northern route of 5.54 points compared to 5 points on the southern route. So, any decision based on expected value would be in favor of the northern route, supporting the earlier conclusion.
Now, maybe others would score the probabilities of damage differently—and it’s worthwhile to play around with the numbers to see how the outcome changes—but there’s no doubt that the analysis helps to clarify the choices. We’ve swapped hand-waving for assigning probabilities, and that has to improve any discussion and any decision made.
An expected-value analysis can help in other areas of our complex sport. One of the big problems facing any race-boat campaign, be it an America’s Cup team or a small keelboat shooting for top 10 at the national championship, is there are more ways to improve performance than time or money to pursue them. It’s always hard to make decisions about where to put limited resources when the outcomes are uncertain, and expected value provides an analytical approach, calculating an expected cost for each unit of performance gain.
The process starts by creating a list of the performance projects that are under consideration. For example, practicing for a weekend, buying new sails, or hiring a coach for the season. A simple version of the calculation would be to assess the potential speed improvement (this would be V) for three cases: the best outcome, worst outcome and most likely outcome for each option being considered. We would then assign a probability (P) to each of these possible outcomes and use these three pairs of numbers [speed improvement (V) and probability (P)] to calculate the expected value just as we did for the route choice ahead of the storm.
In this case, we can go a step further: By dividing the monetary cost of each option by its expected value, we can generate a cost-effectiveness ratio. This allows us to tackle the issue of balancing resources in a parallel way to balancing risks—and expected value can be just as useful in revealing the trade-offs. There are limitations to the approach; for instance, there is no allowance for how these gains will degrade with time. Nevertheless, it’s still a great way of tackling any problem where resources are being assigned in uncertain circumstances—just one of the many tough calls in sailing that the concept of expected value can help to illuminate.