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.

Mt St Helens 31st Anniversary of May 18, 1980 Eruption

Aerial View of Steam Eruption, Mt St Helens, May 20, 2006, taken from Johnston Ridge Observatory, Mt St Helens National Volcanic Monument, Washington (image on Photoshelter)

Thirty-one years ago, at 8:32 am on May 18, 1980, Mt St Helens erupted, in a cataclysmic eruption, that would change the face of the environment and sow the seeds of future renewal. Nature has its way of promoting renewal, through cycles of creation and destruction, and nowhere is this more evident than at Mt St Helens, where the volcano and environs continue to emerge in their new environment shaped by the vehicles of geological change.

Mt. St Helens National Monument can be reach from I-5 southbound at Toledo, SR 505, or from I-5 northbound at Castle Rock, SR 504 (Spirit Lake Highway). I took the latter route, visiting Washington State’s Silver Lake Visitor Center, 5 miles east along SR 504, and took in their presentation on the Mt St Helens Eruption “Cycle of Chaos and Creation”.

I entered Mt St Helens National Volcanic Monument, stopping at Hoffstadter Bluffs Visitor Center, enjoying a view of Mt St Helens in the distance and an excellent Elk Burger in their dining area before heading up to Johnston Ridge Observatory. As you drive towards Johnston Ridge Observatory, there are opportunities to pull over and enjoy differing views of the mountain as you get closer, including at the Elk Rock and Loowit Viewpoints.

The sense of closeness to the volcano becomes more than distance as you become more and more aware of the impact of the blast area on the landscape. Even as it is being transformed, being renewed, you are aware that there are thirty-one years of renewal, and that contrasts with the age of the landscape you left behind.





Mt St Helens Steam Eruption, May 20, 2006, viewed from Hummocks Trail showing renewal of vegetation, Mt St Helens National Volcanic Monument (image on Photoshelter)

The road heads downward before the last ascent to the Johnston Ridge Observatory. The Hummocks Trail provides an opportunity to hike amongst the hummocks, created by the Mt St Helens debris avalanche. The debris avalanche created by the eruption of Mt St Helens offered geologists an opportunity to learn about and identify such formations elsewhere.

From the Hummocks Trail, the road then climbs upwards towards Johnston Ridge Observatory at 4,255 feet. As you hike up an incline from the parking lot towards the Visitor Center, you are greeted with a marvelous view of Mt St Helens, looking right down into the throat of the volcano. It is up close and personal, looming as a reminder of the blast impact, as the crater opens up its giant maw to the visitor, you are struck by the awesome power that so forcefully reconstructed the landscape in the wake of its eruption.

As the clouds dance across the crater and the lava dome inside it, you are reminded that Mt St Helens, the youngest of Cascade volcanoes, has not been quiet since it’s May 18, 1980 eruption. Eruptive activity continued into 1986 and then resumed during 2004-2006, including dome building activity.

A visit to the Visitor Center gives the opportunity to explore exhibits, view a movie, “Message from the Mountain”, and attend ranger-guided talks. In one talk, the ranger used still photographs to illustrate various stages of Mt St Helens’s activity leading up to and including the eruption events. We saw Mt St Helens’s pre-eruptive recreational splendor as a near-perfect volcanic cone and glimpses of pre-eruptive awakenings.

As explained by the ranger, volcanic activity beneath the surface of the volcano eroded and weakened the rock structure on the side of the mountain, turning it to clay. This weakened area provided an opportunistic path for the upwelling magma to take, versus the hardened rock plug at the top of the volcano. The side of the mountain bulged with pressure and structural weakening. The landslide and accompanying 5.1 earthquake triggered the event that would unleash the power and fury of Mt St Helens, with resultant lateral blast, pyroclastic flows, lahars (mud flows) and an ejection of ash that would circle the globe.

It is sobering to realize that volcanism can eat away at a mountain’s rock structure from within, weakening it and exposing the mountain to risk of collapse. It is yet another example of a “tipping point” where a marginal change can have a result out of proportion to its own magnitude.

Geologists and volcanologists study volcanoes and other geological system and we are all continually learning from their experience. Johnston Ridge Observatory was named in memory of geologist David Johnston, volcanologist, who witnessed the May 18, 1980 eruption from what is now Johnston Ridge, and radioed in the message “Vancouver, Vancouver, this is it” before perishing in the blast.

The Mt St Helens 1980 eruption has resulted in a continued expansion in knowledge and monitoring tools for understanding the behavior of volcanoes.

In one study, the impacts of volcanic hydrothermal systems on Cascade volcanoes is being studied by the United States Geological Survey.

A wide range of information about Cascade Volcanoes can be found on the Cascade Volcano Observatory (CVO) site.