Probability, uncertainty and inanity with the coronavirus

The very bad polling outcomes from the 2020 U.S presidential election pointed out the key differences between two often-confused topics. Pre-election polls are measured in percentages and look like probabilities, but they are really trying to quantify uncertainty, and there is a very big difference between the two that the public largely does not understand.

The same confusion has bled over into the subject of coronavirus risks and mitigations. I contend that if you understand the difference, then you improve your real chances of survival. Unless you are in the third category, which I call inanity, where you intentionally “don’t do math or science” and put other people besides yourself at risk of disease and death.

Frank Knight, one of the founders of “the Chicago School” of economics, wrote a seminal text in 1921 called Risk, Uncertainty and Profit. His theme was that classical economics was stuck in the assumption that “risks” in the world were measurable probabilities, and then he introduces the reality of uncertainty, where key elements of the problem remain unmeasurable. [1] The existence of the latter complicates the problem significantly.

As we have lived for over nine months with this new dangerous coronavirus, I suggest that we started with almost everything being uncertain, and we made a lot of mistakes. However, many mitigations are moving on a continuum toward the firmer ground of probability. Even if they have not reached that firmer ground, some mitigations are more worth betting on than others. Ignore them, as far too many people continue to do, and you are, as I called it early on in the crisis, “driving drunk in Coronavirus World.”

Probability continuum

The dice versus the voter

Probability defines the risk of alternative outcomes when the basic conditions are well-known and quantifiable. Throwing two dice is the classic example here:

Probabilities of 2 dice

Probability of outcomes when throwing two dice.

I may throw a two, or I may throw a seven, but the odds of the latter occurring are six times the former. For any one throw, any of the eleven outcomes might occur, but thanks to “the law of large numbers,” I can start to place intelligent bets on outcomes if I throw the dice enough times. [2]

With vote projections, however, the basic underlying population is always changing. The sampling methods are always flawed (e.g., cell phones versus land lines). Voter preferences on the margins are more akin to shifting restaurant loyalties rather than reflecting committed party voters. As a result, there are many more “degrees of freedom” jerking outcomes around than in a dice throw or a game of blackjack. Purported accuracy ranges for vote projections are typically understated because of this squishiness. And the predictions are not getting any better.

Back to the virus

And so, are the various recommended coronavirus mitigation strategies based on probabilities, or are they still uncertainties? In real life, probability and uncertainty exist on a continuum. Weather forecasts are a good example of this. Through the application of Bayesian statistics, every new hurricane improves the many storm forecasting models by analyzing the error of “posterior probabilities” and feeding them back into the equation, but altered by the new data. My Weather Channel app now gives me a decent rain forecast in fifteen-minute increments. It is not reliable as 1000 dice throws, but it is close enough to the “probability” end of the continuum most of the time for planning a day out.

Bayes Theorem

Mask wearing as a coronavirus mitigation is a good example of this shift from uncertainty to probability over time. Most medical professionals recommended mask wearing early in the pandemic solely based on reasonable “prior probabilities” from other medical practice. The medical team performing that heart procedure on you all wore masks and gloves, as much or more to protect you as to protect them. Assuming this new virus was (ahem) virulent, it made “Bayesian sense,” even without new data, to assume benefits from widespread masking. Much of the early caution against the public rushing out to purchase masks was due not to doubt of the benefit, but rather to address a very scary depletion of the medical-grade mask supply chain. Many months later this supply chain has not yet stabilized, especially for N95 masks.

New data on mask effectiveness coming into the Bayes calculator “bubble” shown above has always been partial and incomplete, but that is the nature of new data. Attacking the reality on the ground from different directions of data, just like we do with weather forecasts, continues to move mask wearing in net toward the “probability” end of the spectrum. For instance, you can compare new Covid cases in counties with mask orders to those without or compare the party affiliations of Congress members with Covid. Partial information, both for and against, will net out in the Bayesian decision-making process. Other touted mitigations, on the other hand, are still hanging in the “uncertain” end of the spectrum for that very reason, or have even fallen off that end, such as with hydroxychloroquine.

Dick Hinch

New Hampshire House Speaker Dick Hinch, now-deceased from Covid-19, demonstrates a high-risk technique for wearing a mask.(Washington Post)

My inbox continues to receive specious claims both against mask-wearing and in favor of “natural” coronavirus cures and preventions. How should we know whether to put some mathematical credence on a claim or study, and when should we reject it?

Having worked in both academia and industry, my observation is that most academics would not risk their reputation on a $50,000 research grant funding their lab, which the anti-science community often claims to happen. Real science has its own competition methods that tend to root out bad and unreplicable studies over time, especially on urgent topics. “Pseudoscience” studies are more typically those that persist being touted even when they cannot be replicated or have failed to demonstrate scientific and mathematical rigor.

In contrast, a multi-million-dollar profit opportunity will bend far too many investors and turn them into scam artists, especially when so much of the public is easily bilked. If you want to know why we reportedly have over 60 million doses of hydroxychloroquine stockpiled, despite warnings virtually from day one of its use, I suggest that you “follow the money.”

And there is certainly “big money” in the competitive vaccine push. We have just begun a risky large-scale experiment on vaccine rollout to the public. From a scientific viewpoint, we are certainly rolling out this vaccine much sooner than most would have preferred. This is a moral dilemma from classical ethics that I will address in a subsequent post. The big difference here, however, is that we will be gathering a lot of good data in a very short amount of time, which will be analyzed by virtually every reputable virologist on the planet.

In effect we are watching the move up the continuum from uncertainty to probability in real time. It is likely (i.e., probabilistically moving away from uncertainty) that by the time you get to the front of the line, we will see the shape of the probability curves for both effectiveness and complications flesh out. Sometimes the urgency of people dying around us requires some good people to, as Martin Luther said, “sin boldly.

What about the other mitigations?

The “six foot rule” of social distancing has been harder to move toward the “probability” end of the spectrum due to real-world controlled tests, but it at least does sit on the solid math of the inverse square law, which suggests that infectious particles from you are 1/36th as likely to get to me if you are six feet away as opposed to one foot away. That is less than 3%, which is a pretty good risk reduction. Ten feet would be 100 times safer than a one-foot separation. Outside air dispersal improves those odds even more.

Time limits for exposure are also good bets for moving toward the probability end of the spectrum. Evidence suggests that the body fights off small invasions of the virus far better than sustained, large doses of exposure. Long-standing studies of viruses and air circulation also push toward time-limited exposure threats.

There is no single “magic bullet,” including the new vaccines on the horizon, which may not halt the spread of the virus even as they prevent infection. However, the interaction of multiple, high-probability mitigations working in conjunction with one another, often called the “Swiss Cheese Defense,” remains the best strategy for most people who need to leave the house and interact with others as a matter of necessity.

Unfortunately, we are in a time when political and religious leaders are demanding that people ignore the science and the math regarding this virus in order to pledge fealty (and money) to their cause. If I may use religious language myself, let me say that God gave you a “Bayesian Brain” that is really good at plotting your survival if you do not let others take over your reasoning abilities.


  1. Here was how Frank Knight described the problem in his 1921 text:

Our preliminary examination of the problem of profit will show, however, that the difficulties in this field have arisen from a confusion of ideas which goes deep down into the foundations of our thinking. The key to the whole tangle will be found to lie in the notion of risk or uncertainty and the ambiguities concealed therein…[U]ncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated…The essential fact is that “risk” means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomenon depending on which of the two is really present and operating. [p. 11]

  1. Of course, casinos pay off on dice bets at lower odds than the physics dictate, shaving a bit of cash off each throw and, in the end, always coming out the winner (unless your casino owner is Donald Trump).

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