Calculating Odds and Probabilities

1986 Liberty Half Dollar Tossed on Grass (Heads) (Image on Photoshelter)


A team will have an opportunity to call “heads or tails” for a coin toss at the beginning of a football game. If the call is successful, heads in the case of the coin pictured above, the team will have the opportunity to chose to take the ball (go on offense) or defend a particular goal. The choices are non-trivial as a team’s defense may be superior to their offense, or the wind may determine the choice of the goal defended. These choices represent the team’s expectations of their success, given their strengths, weaknesses and prevailing conditions.

The coin toss, for a fair coin, will give a probability (p) of .5, or 50% that the call (either heads or tails) will be successful. Coins flipped successively will tend, over a period of time to “revert to the mean”, or tend towards their expected value of 50% heads and 50% tails. The odds ratio for the coin toss is 1:1. Odds ratio is calcuated as the ratio of the probability of the event happening (p) to the probability that it won’t happen (1-p). Thus, out of 2 possible outcomes (heads or tails), one outcome (out of 2) is successful, one outcome (out of 2) is unsuccessful, for a ratio of 1:1.

While the coin toss is random, there is a balance of risks involved in the result. For example, a team with a superior offense can choose to go on offense, sputter on three downs, punt, and turn the ball over to the other team in good field position, despite their expectation of offensive success.


Two Sixes Dice Toss (infrared digital effect) (image on Photoshelter)

People use probabilities and odd ratios in their daily lives, consciously and unconsciously computing expectations and making decisions based on those expectations.

Some may choose to gamble on the roll of the dice. In this case, the probability of rolling two sixes is (1/36) while the odds are 1 to 35 (1 good outcome, 35 losing outcomes). When gambling in an establishment, the house will include a margin in for themselves, to cover expenses and profit. Given fair dice, the underlying odds (and the probabilities) will tend towards their mathematical expected value (1 to 35 and 1/36), thus giving over time a margin to the house.

Mathematical models can calculate the odds that there will be a city rivalry World Series this year, the odds of a particular candidate winning the 2012 election, and many other events.

Of particular interest are the mathematical models that deal with environmental issues, such as weather and climate change, given the emergence of extreme weather events.

Albert Einstein was quoted as saying “I, at any rate, am convinced that He does not throw dice.” (paraphrased as “God does not play dice with the universe”). However Stephen Hawking is quoted as saying “So Einstein was wrong when he said, "God does not play dice." Consideration of black holes suggests, not only that God does play dice, but that he sometimes confuses us by throwing them where they can't be seen”.

The National Oceanographic and Atmospheric Administration (NOAA) has sophisticated climatological models which forecast the weather, and they are continually improving these models in order to provide the maximum amount of warning possible to the populace. Through their efforts, NOAA is seeking to minimize the amount of risk, and maximize the information provided, seeking the “load the dice” in the publics favor.

We rely on weather forecasts in our daily plans. Should we call off the company picnic with a 70% chance of thunderstorms? How about that outdoor wedding? Do you pack the rain slicker or umbrella or leave it behind? Governments and businesses rely on weather forecasts for their daily operations and long term plans. Seasonal hurricane forecasts are looked at with interest by many sectors in planning ahead into the coming hurricane season.

Two United States Coast Guard Cutters monitoring the Westport, Washington Bar entrance (image on Photoshelter)

Nowhere is the issue of balance of risks and weather forecasting more apparent than in the maritime arena. When is the storm predicted to arrive? Is there a confidence interval around that arrival time, as well as its expected intensity? Sailors will balance the risk of venturing out and making headway to their destination versus the risk that the weather will take an unexpected turn for the worse, making for difficult, or hazardous headway, or worse.

The United States Coast Guard (USCG) is a branch of the U.S. Armed forces and is charged with maritime safety, security and stewardship. In this image, the two Coast Guard Cutters are monitoring the closed Westport Bar / navigational entrance from the Pacific Ocean to Westport, Washington. The USCG monitors ongoing conditions and weather forecasts to decide whether or not to close the bar, thus managing safety for mariners. The United States Coast Guard, in its decision-making, relies on the concept of balance of risk, as it makes decisions that affect the public. The public, in turn, makes decisions using balance of risk as it relies on NOAA guidance, the actions of the Coast Guard, and other factors.

It is human nature to calculate probabilities, calculate odds, consciously or unconsciously assess balance of risks. We do so continuously in our daily lives and rely on others to help us do so. We need to expand that awareness to include the risks we face due to environmental changes, consider the balance of risks inherent in the evolving situation, and find a way to meet the considerable challenges head on.