The battle of the shifting base: why only zombies can have a tenfold decrease in mortality

Beware percentages of increase and decrease. They don’t behave in an intuitive way — because of the “battle of the shifting base.”

According to a tweet by our president, we’ve had “A Tenfold Decrease In Mortality” from COVID-19.

While there’s a lot wrong with this tweet — here’s a fact check on why the statement about mortality rates is wrong — we can start with the tenfold decrease. Here’s a thought experiment.

You have $10,000 in your bank account. Due to hitting the lottery, you see a tenfold increase in your balance. Then you make a number of poor spending decisions and see a tenfold decrease in your balance. How much do you have in the bank now?

Seems like you should be back to the original $10,000, wouldn’t you think?

But you haven’t reckoned with the shifting base. A tenfold increase in $10,000 will get you to $100,000. But a tenfold decrease in $10,000 implies that you reduce the balance by 10 times $100,000, or $1,000,000. So your balance is now negative $900,000. Your creditors will be repossessing your Maserati and foreclosing on your McMansion. You’re not back where you started, you’re far worse off.

Anything that cannot go negative cannot have a tenfold decrease. Since there is no such thing as negative mortality (except in zombie movies), mortality cannot have a tenfold decrease.

The statistic that Trump is quoting shows that deaths, which were at 2,500 per day, are now at around 250 per day. This is a 90% decrease, not a tenfold decrease.

(In case that makes you optimistic, just wait. With the surge in infections, ICUs in places like Florida and Texas are filling up. Without ICU beds, many more will die. This tweet will age poorly, as the surge in hospitalizations starts to overwhelm the healthcare system. I hope I am wrong about this, but we’ll know in a few weeks — in any case, it’s a little soon to declare victory here.)

The battle of the shifting base

This problem with percentage change is a common fallacy; in his incredible 1954 book How to Lie With Statistics, Darrel Huff called it “the battle of the shifting base.”

Here are some examples.

Due to poor sales, you take a 20% pay cut on your $50,000 per year salary. The next year, sales are better, so you get a 20% increase. What’s your salary now?

20% cut = 20% times $50,000 = $10,000. Your salary drops to $40,000.

20% increase = 20% times $40,000 = $8,000. You’re only back up to $48,000.

You lost $2,000 somewhere.

I face the same problem with agencies. One agency that refers business to me takes 15% of what the client pays. I want to clear $4,000 for a writing job. How much should they charge the client?

Obviously, $4,000 plus 15% extra, or $4,600, right?

So we charge the client $4,600 and the agency takes 15% of that, or $690. And I’m left with $3930. Hey, how did I end up $70 short?

It’s my own fault. I should have charged $4000 divided by 85%, not $4000 times 115%. The correct fee to the client is $4705.88. Then when they take the 15%, I’m left with the $4,000 I should be getting.

Similarly, if the stock market goes up 10%, then down 10%, you’ll end up 1% in the hole. ($10,000 will appreciate to $11,000, then shrink to $9,900).

Unless statistics are calculated on the same base, you can’t compare them.

And unless you expect to see the bodies of thousands of COVID-19 victims spring back to life, there is no such thing as a tenfold decrease in mortality.

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  1. Don’t even get me started about jounalusts and headline writers who think that “Unemployment rate drops 2 percent” means “Unemployment rate drops by 2 percentage points.”

    1. As a special education teacher I’ve had to submit Student Growth Indicators, to “prove I’m effective”. (simplified example) If I had a student that performed a skill at 40% at the start of the semester and was up to 60% at the end. I reported it as 50% growth. My administrator said, no that’s 20% growth. After debating it I said fine. A week later I resubmitted it. I stated that the student performed the skill 40 times at the start of the semester, then 60 times by the end. I basically factored out the percent sign, then put it back in the end: 60 – 40 = 20, 20/40 = .50, .50 x 100 = 50%. He said, okay, looks good. Now I always wait to convert to a percentage until the end. It’s difficult accepting him as my boss. BTW, he always talks about incidences when referring to multiple events, not rates.

  2. Math isn’t Orange’s strong suit.

    Nor is English, morality, fidelity, and just about any other quality you’d want in any leader, much less the President.

  3. I’m always happy to see someone mention “How to Lie with Statistics.” It’s a great little book that should be required reading for any writer! It’s short and fun and humbling to realize how much basic math I never learned.

  4. Awesome Article!
    Very clear and consice, and conscious breakdown.
    Perfect example of easy and common math mistakes.