Data Analyst · #051 · September 12, 2026 · 1 min read
Why is down 50% then up 50% not back to even? Percentage traps explained
Asymmetric drops, percentage points vs percent, tiny-base explosions, why you never average percentages, and the CAGR line: the percentage traps that lie on dashboards, on one page.
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The dashboard says recovered. It has not. Percentages are the most quietly dishonest numbers in analytics, and the traps repeat so reliably you can learn them once. One page. The print-ready A4 PDF is at the bottom.
The classic
start 100
down 50% 50 -- 100 x 0.5
up 50% 75 -- 50 x 1.5
net move -25% -- 0.5 x 1.5 = 0.75
to recover +100% -- 50 needs to double
- Percent changes multiply, they never add.
- -20% needs +25% back. -90% needs +900%.
Points vs percent
- 10% to 12% is +2 points AND +20% relative.
- Say which one, every single time.
Small bases
- "+300%!" can mean 1 user became 4.
- Show the counts next to the percentage.
- CTR moves lie the hardest.
Averaging
- Never average percentages: weight by the base.
- Simpson's paradox: splits can reverse the total.
- Rates travel with their bases, always.
Growth
- CAGR: (end/start)^(1/n) - 1.
- MoM vs YoY: seasonality picks the window.
- Compounding: about 26% MoM for two years is a 10x.
The trap: the headline number
| The claim | The reality | Honest version |
|---|---|---|
| conversions +300% | 1 sale became 4 | show counts with rates |
| churn only +2% | 5% to 7% is +40% | give points AND percent |
| avg conversion 25% | one tiny segment at 90% | weight by traffic |
If a percentage looks amazing, ask for the base. If it looks small, ask for the relative move. Same trick, both directions.
Frequently asked questions
Why does a 50% drop followed by a 50% gain leave you down 25%?
Because percentage changes multiply, they do not add: 100 x 0.5 x 1.5 = 75. After a drop, the gain applies to the smaller base. The general rule: after a drop of d, recovery needs d/(1-d), so -20% needs +25% and -90% needs +900%.
What is the difference between percentage points and percent?
A conversion rate moving from 10% to 12% went up 2 percentage points AND up 20% in relative terms. Both are true, and headlines pick whichever sounds better. Always state which one you mean, and ideally give both: churn 5% to 7% is +2pp and +40% at the same time.
Why should you not average percentages?
Because rates carry different bases. Averaging a 90% conversion rate on 10 visits with a 2% rate on 100,000 visits gives a meaningless number: weight by the base, or recompute the rate from the summed numerators and denominators. Splits can even reverse the overall conclusion, which is Simpson's paradox.
How do you calculate CAGR?
(end / start) ^ (1 / years) - 1. It is the constant yearly growth rate that turns start into end, which makes multi-year growth comparable. For monthly cadence the same formula works with months, and remember compounding: roughly 26% month over month sustained for two years is a 10x.
Get the free PDF
One page, print-ready, free to share. No signup needed.