The percentage change methodology can be applied when comparing two values to each other. Consider two competing bike shops: Spin Cycle with sales of $2,000$ bikes this year and Bike World with sales of $2,200$ bikes.

Which shop has the most sales and by how much?

The first question is easy, as Bike World clearly sold more bikes this year.

The second question depends on your perspective $($or base value$).$ Look at how these two measurements of percentage change can offer different results:

$\%=\frac{2,200-2,000}{2},000=10\mathrm{.}00\%$

$\%=\frac{2,000-2,200}{2},200=9\mathrm{.}09\%$

In the first calculation, Spin Cycle's sales are used as the base value. The first calculation is interpreted as: Bike World has $10\%$ higher sales than Spin Cycle.

In the second calculation, Bike World's sales are used as the base value. The second calculation is interpreted as: Spin Cycle has $9\mathrm{.}09\%$ lower sales than Bike World.

Both statements are correct and describe the same event, but they do so from different perspectives. When comparing values, the base value used is important to understanding the percentage comparison.

Paradox of Percentage Stock Returns

The importance of changes in base can be illustrated by looking at percentage stock returns.