Most people are bad at thinking about low probability events and their eyes can glaze over as they think about very small or very large numbers. Further, how the data is framed has a big impact on how your react to them.

To take a personal example, I’m about to go in for surgery to donate a kidney next week. [Update: My surgery has been postponed, but that doesn’t affect this analysis.] The chances of me dying are very small, only about 0.02%. I guess that seems very safe. Now let’s frame it differently. There are about 6,500 live kidney transplants a year, which means on average one or two donors die each year. Now my surgery seems a lot more dangerous. By changing from a percentage to an actual count, the number seems more personal. I can image that the person who dies is me.

Here’s another example. According to the United Network for Organ Sharing (UNOS), as of June 24, there are 85,512 kidney patients in the U.S. waiting for a kidney transplant. It seems like an impossible task to find enough donors to help them all. Assuming no other additions or removals in the next week (which isn’t quite true), that number will drop to 85,511 after I complete my donation. It seems my contribution is insignificant. But I can frame the problem in another way. The Univ. Washington Medical Center, where my surgery will take place, has 416 people on the waiting list. After my donation, it will be 415. This makes the impact of my one donation seems a lot bigger.

To make the task more general, there are 249 transplant centers in the U.S. that perform live donor transplants, meaning an average of 341 patients per hospital. Finding 341 more people (per year) to donate seems like a solvable problem. This isn’t an unachievable task. I just need to find a group of live donor champions at each hospital, probably previous nondirected donors. Then I need to convince them that they just have to help each of the 341 patients (on average) at each hospital find a donor and the waiting list will go away. To make the task seem even smaller, I can state the problem is to find one donor for each patient on the waiting list. Now it really seems easy. Small integers have a concrete aspect to them. Very large numbers or very small fractions do not because you just can’t picture them in your mind.

Keeping this smaller goal in my head should help keep me motivated as I prepare my outreach efforts to help kidney patients find live donors. (Yes, I’m fooling myself, which violates my Real Numeracy credo. So what?)

Choice A Choice B
Which option seems riskier? A 0.02% chance of dying from surgery (outcome per patient) 1 to 2 deaths per year (outcome per population)
Which task seems harder? Find 85,510 donors for the kidney patients on UNOS waiting list (count per population) Find 1 donor for each kidney patient on the UNOS waiting list (count per patient)