One of the problems with statistics and numbers is that we trust them as if they’re always trustworthy. But the problem with those numbers is that they depend on which domains and which sources they’re using. Averages are even trickier than that.
One concept that blew my mind recently is the Will Rogers phenomenon.
A Simple Example
Let’s say you’re a sales manager.
You have two groups of salespeople.
Group A
- Person 1 sells 1 item per week.
- Person 2 sells 2 items per week.
- Person 3 sells 3 items per week.
Group B
- Person 4 sells 4 items per week.
- Person 5 sells 5 items per week.
- Person 6 sells 6 items per week.
Now your boss comes to you and says, “Hey, you need to sell more items per week in both groups.”
Here’s the interesting part.
If you move Person 4 from Group B to Group A, you’re moving the lowest performer from the best-performing group into the least-performing group.
What happens?
Group A sees an increase in average performance because you’ve added someone who performs better than everyone already there.
Group B also improves because it lost its lowest performer.
Both group averages go up, even though nobody actually became better at selling.
Numbers are tricky
This example is obvious once you see it, but the same thing happens whenever you have two groups that are separated and you move lower performers from the better-performing group into the worse-performing one.
That can happen intentionally, or it can happen unintentionally.
One of the most controversial examples is around cancer.
Stage 1 is the “entry level” group for when you’re diagnosed with cancer. The cancer is still early-stage and confined to the original site.
The problem is that 50 years ago we didn’t have the same ability to detect cancer that we have today.
Some cancers went unnoticed. Some of them probably weren’t even risky, so people simply continued living their lives with a normal life expectancy.
Over time, though, technology evolved.
Some of the people who previously belonged to the best-performing group, the people who lived a long and healthy life, are now included in the Stage 1 cancer group because we can detect those cancers today.
Out of the blue, Stage 1 cancer group appears to have a higher life expectancy, even though there may have been no improvement in treatment, at least as far as this phenomenon is concerned.
There may, of course, be genuine improvements in treatment, but that’s not the point.
The point is that the average improved, even though nothing necessarily improved.
Why? Because people moved between two groups, removing the lowest performers from the better-performing group and adding them to the worse-performing one.
Every average and every statistic can be tricked.
Treat numbers with caution, always.
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