For five years my wife and I lived in a house that was at the base of the lee side of a small mountain range in Northern Nevada. When a storm would come through the area it would have to make it over a couple of small mountain ranges and valleys before getting to our house, and as a result we experienced less precipitation at our house than most people in the Reno/Sparks area. Now my wife and I live in a house higher up on a different mountain that is more in the direct path of storms coming from the west. We receive snow at our house while my parents and family lower in the valley barely get any wind. At both houses we have learned to adjust our expectations for precipitation relative to the probabilities reported by weather stations which reference the airport at the valley floor. Our experiences with rain and snow at our two places is a useful demonstration that probability (in this case the probability of precipitation) is multifaceted – that multiple factors play a role in the probability of a given event at a given place and time.
In his book Risk Savvy, Gerd Gigerenzer writes, “Probability is not one of a kind; it was born with three faces: frequency, physical design, and degrees of belief.” Gigerenzer explains that frequency is about counting. To me, this is the most clearly understandable aspect of probability, and what we usually refer to when we discuss probability. On how many days does it usually rain in Reno each year? How frequently does a high school team from Northern Nevada win a state championship and how frequently does a team from Southern Nevada win a state championship? These types of questions simply require counting to give us a general probability of an event happening.
But probability is not just about counting and tallying events. Physical design plays a role as well. Our house on the lee side of a small mountain range was shielded from precipitation, so while it may have rained in the valley half a mile away, we didn’t get any precipitation. Conversely, our current home is in a position to get more precipitation than the rest of the region. In high school sports, fewer kids live in Reno/Sparks compared to the Las Vegas region, so in terms of physical design, state championships are likely to be more common for high schools in Southern Nevada. Additionally, there may be differences in the density of students at each school, meaning the North could have more schools per students than the south, also influencing the probability of a north or south school winning. Probability, Gigerenzer explains, can be impacted by the physical design of systems, potentially making the statistics and chance more complicated to understand.
Finally, degrees of belief play a role in how we comprehend probability. Gigerenzer states that degrees of belief include experience and personal impression which are very subjective. Trusting two eye witnesses, Gigerenzer explains, rather than two people who heard about an event from someone else can increase our perception that the probability of an unlikely story is accurate. Degrees of belief can also be seen in my experiences with rain and our two houses. I learned to discount the probability of rain at our first house and to increase my expectation of rain at our new house. If the meteorologist said there was a low chance of rain when we lived on the sheltered side of a hill, then I didn’t worry much about storm forecasts. At our new house, however, if there is a chance of precipitation and storm coming from the west, I will certainly go remove anything from the yard that I don’t want to get wet, because I believe the chance that our specific neighborhood will see rain is higher than what the meteorologist predicted.
Probability and how we understand it and consequentially make decisions is complex, and Gigerenzer’s explanation of the multiple facets of probability helps us better understand the complexity. Simply tallying outcomes and predicting into the future often isn’t enough for us to truly have a good sense of the probability of a given outcome. We have to think about physical design, and we have to think about the personal experiences and subjective opinions that form the probabilities that people develop and express. Understanding probability requires that we hold a lot of information in our head at one time, something humans are not great at doing, but that we can do better when we have better strategies for understanding complexity.