Percentage Terminology

Our teminology for percentages really sucks.

Say the current mortality rate for an operation is 10%.

If you say "survival increased by 10%" what does that mean?

• 10% => 20% - this is "absolute"
• 10% => 11% - this is "relative to success"
• 10% => 19% - this is "relative to failure" - the "failure area" of 90% shrunk by 10% relative.

In this case, "relative to success" makes most sense, since the use case for the sentence is in evaluating a policy change.

But imagine the current success rate was 99.9%. In that case an improvement to 99.99%, reducing deaths to 1/10 as many as before, could be described in these ways:

• My opponent's lazy policies only increased survival by 0.01%
• Death rates dropped by a factor of 10x
• Death rates dropped by 90%

So where do you draw the line between these cases?

Sociological effects

This has real effects: In meetings with both execs and technical/stats people, there is usually a lot of hand-waving when the stats people hand-off of the analysis to execs. The stats people explain the results using some percentage-related terms, and then the execs internalize the numbers. When they then repeat the number, they usually have just guessed which percentage variant was meant, and frequently have switched it.

That goes into their slide deck to present onward, and meaning is lost. Then the C levels naturally become suspicious and generally don't believe stats as much as they could, because their business knowledge occasionally tells them something went wrong. If we believe in the meaning of numbers, this is a problem. This also backs up skepticism about numbers - "you can prove anything with statistics"

Similar Terminology Problems

The situation

Imagine seeing a map with dots on cities, with this voiceover:

"Larger dots indicate indicates cities where the coronavirus is more widespread"

• "Small" is a city of 100k people where they all have coronavirus
• "Big" is a city of 10m people with 110k cases (1.1%).

Descriptions of the situation

• Big has more coronavirus infections. (strictly true)
• Coronavirus is more prevalent in Small
• Coronavirus is more common in Small
• Coronavirus is overwhelming Small
• There is a larger Coronavirus infection in Big. (this one is on the edge)
• Coronavirus is a bigger problem in Small
• The Coronavirus problem in Big | Small is huge.
• More people have coronavirus in Big, so it's a bigger problem. (easy mistake to make)

The problem here is that the word "more" clearly denoting an additive or multiplicative difference. We do have lots of words which inherently include the sense of ratio.

Simply adding in a sense to existing words would solve the problem.

There is more crime in New York than Boston

What does this mean? Is it additive or multiplicative? I want to qualify the word more into two senses:

• More (absolute)
• More (per capita)