I had a scare. A simple application of number sense dispelled my worry

A family member alerted me recently to the Medium article with the above headline. Knowing I have a long-adopted European lifestyle habit of having a glass (sometimes two) of wine with a meal, she was concerned about what seemed to be a significant health risk.

The article led off with this paragraph:

It was so comforting to think that a daily glass of wine or a stiff drink packed health benefits, warding off disease and extending life. But a distillation of the latest research reveals a far more sobering truth: Considering all the potential benefits and risks, some researchers now question whether any amount of alcohol can be considered good for you.

As a scientist, I am always open to being convinced by hard data. So I read on. The article rapidly became more alarmist:

For years, moderate drinking — typically defined as one drink (such as regular beer or a glass of wine) per day for women and up to two for men — had been billed as a way to reduce the risk of stroke, in which a vessel carrying blood to the brain bursts or is clotted. But a study earlier this year, involving more than 500,000 men and women in China and published in the Lancet, refutes that claim. “There are no protective effects of moderate alcohol intake against stroke,” says one of the study’s co-authors, University of Oxford professor Zhengming Chen. “Even moderate alcohol consumption increases the chances of having a stroke.”.


While not for a moment doubting the validity of the science and the conclusions the researchers stated, I nevertheless wondered if there were really any cause for alarm. Just how significant is the risk I am being exposed to as I sip my Pinot Noir? After all, from a scientific standpoint, a well-established increased risk of 0.5% can merit publication in a professional journal, but most of us would discount such a low increase when it comes to deciding to give up an activity that gives us a great deal of pleasure. Maybe the article writer was being unjustifiably alarmist.

In the case of moderate wine drinking, there is certainly a well-established correlation between countries where that is common practice and countries with longer life-expectancy—though as is often the case, establishing any causation is a tricky challenge. (I tend to think that the pleasure I get from a glass of good Pinot, together with the relaxed sensation is produces, has a net beneficial effect on my overall health. That’s a plausible assumption, but did the new study show that effect was outweighed by negative consequences?)

In fact, the article quoted far more alarmist figures:

The study, published in the Lancet, found a “strong association between alcohol consumption and the risk of cancer, injuries, and infectious diseases.” Among other findings, just one drink daily was linked to a 13% increased risk of breast cancer, 17% increased risk of esophageal cancer, and 13% higher risk of cirrhosis of the liver.

Those percentages definitely grab the attention. But again, while not for a moment disputing them as valid scientific findings, I wondered how significant they are in making a life decision. 

Time to do some quick calculations.

According to the article, 88,000 people in the United States die each year from alcohol-related causes. Let’s assume the bulk of those are adults (i.e., legal drinkers). The total population of people over 21 in the United States is about 200,000,000. So according to the figure quoted, the proportion of American adults who die from alcohol each year is 88 out of 200,000.

To simplify the calculation, let’s assume the situation is worse, and 100 out of 200,000 die each year. That’s 10 people in every 20,000. I dropped down to 20,000 because that’s something we can visualize, as many stadiums and arenas have capacities of around that number. A quick Google search revealed that the Amway Center in Orlando, Florida has a stated capacity of exactly 20,000.

The Amway Center in Orlando, Florida, seating capacity 20,000

I can now get a visual representation of the annual risk of death from drinking alcohol as 10 people in the crowded stadium. (Other well-known examples I came up with are Madison Square Garden in New York City, with a capacity just over 20,000, and Meadowlands Arena in New Jersey that comes in just under 20,000. Imagine ten individuals in either of those facilities.)

Personally, I don’t find that particularly scary. If it were not for the degree to which a glass of wine with my meal gives me significant pleasure, it would absolutely make sense to avoid the risk of being among those ten people in the stadium. But in my case, I’ll take that risk. Not least because I suspect that most of those deaths are from people who drink a lot more than I do. (The writer of the buzzkill article responsibly alludes to the far greater risks associated with excessive alcohol consumption and binge drinking, where to my mind the data cannot be dismissed.)

But the focus of the article was not on the base-level risks, rather the increased risks of one drink each day. That has me right in the crosshairs. What is the significance of that particular risk?

Again, let’s look at a scenario worse than the one reported, to make the math simpler. Assume there is an increased risk of 20% — bigger than those reported increases of 13% and 17%. That would mean 12 people in the Amway Center; 2 up from 10. Now I can visualize, and hence understand, my increased risk as follows. (I’m assuming I were not already in the danger group, but become so as a result of my daily glass of wine. Again, my goal is not to produce accurate risk data, but to visualize, and hence understand, the data presented. I am making simplifications that, if anything, create a picture showing greater risks than the actual data indicate.)

In any one year, 10 of those people in Amway Center will die as a result of alcohol. If you don’t drink, you will not be one of those 10. The increased risk as a result of having one drink daily enlarges that danger group of 10 people to a group of 12 people. At least to my eyes, the difference between 10 people and 12 people in that massive Center is nothing like enough to convince me to give up my daily glass of wine. I’ll accept the risk.

In my scenario, those two additional people in the audience are the ones who get there as a result of one glass of wine a day. Becoming one of those two individuals in the Amway Center are the ones the buzzkill article is warning us about.

Just to be doubly sure I’m being sensible, however—after all, I have a vested interest in convincing myself my wine habit is not unwise—I decided to google common causes of accidents and deaths. 

According to my search, taking a shower turns out to be a dangerous activity. (For my entry “accidents in the bathroom”, Google returned over 22 million hits.) But what are the figures? In the U.S., roughly one person per day dies in the shower, mostly adults. In an adult population of around 200 million, that’s a low risk. But that’s the risk of death. Statistically of more significance, around 250,000 people aged 16-or-older per year have an accident in the bathroom that requires a visit to the emergency room (with 14% requiring hospitalization). That represents 25 people in Amway Center. We all accept the risk of being one of those 25 every time we step into the bathroom.  

None of this is to say we should ignore the valuable evidence science provides when it comes to risks. On the contrary, I went through the above exercise because I habitually try to maximize my length and quality of life. Every action we take carries risks—including inaction. We just have to make wise decisions that balance the pluses and minuses of everything we do. 

To do that, it helps to visualize the risks in some real-world scenario we are familiar with. I tend to go for movie theaters, sports stadia, and the like. It usually doesn’t require any complicated calculations; it’s number sense rather than arithmetic. Grab a few relevant figures from the Web and make gross simplifications that if, anything, make things worse than they really are. 

In the situations described in the article, that “20%” figure refers to a 20% increase in size of the risk group. But if that risk group is already small, the increased risk group will still be small. In the case of moderate alcohol consumption, it corresponds in going from ten people in the vast Amway Center to being twelve in Amway Center.  

But the question I asked—and everyone faces questions like this all the time—is this: Will I accept the risk if there is a personal cost to me. Once I had a clear way to visualize that risk, I found the decision easy. Pass the Pinot!

That’s not an endorsement or a recommendation. It’s my personal decision arrived at from a good understanding of the risks, based on hard data. (Hence no photo of a glass of wine.) Comparable data on risks persuades me to always fasten my seat belt in a car and never go out on my bike without a helmet. Why take a risk—however small—when there is no personal cost to avoiding it?

And that’s what this post is about: Applying number sense to make sense of numerical data in order to reach personally significant decisions. Once I had a good image in my mind to visualize the risks, I found the decision was easy.

But that was not the focus of the buzzkill article, where I found the complete absence of important contextual information to help readers understand what the data actually represents resulted in a story that I think is unduly alarmist. To repeat a recurring SUMOP theme, number sense is a critical mental tool in today’s data-rich world.