Lets look into decision making as it might apply to weather routing.
I have a forecast that says the wind is going to veer by 30º overnight. Suppose if I jibe now and the wind does veer 30º by tomorrow morning I will gain. But If I jibe now and the wind does not veer 30º by tomorrow morning then i will lose.
What do I need to know to decide if I should jibe?
We need numbers, or estimates of numbers, on all three factors involved.
P = probability of the wind veering as forecasted.
Gain = how much you gain (in hours or miles) if you jibe and the wind shifts as forecasted
Risk = how much you lose (in the same units) if you jibe and the wind does not shift as forecasted.
We can figure the Risk and Gain numbers from our polars.
We are left with computing a take point probability P for the forecast. In other words, we calculate how big does P have to be so that the chances of gaining are higher than the chances of losing.