Percentage points or percentage change?

A rate moving from 20 percent to 25 percent has increased by five percentage points. The rate is also 25 percent higher than it was. Those statements describe the same change using different comparisons.

The first subtracts one percentage from the other. The second measures the difference against the earlier rate. Keep that starting point visible before deciding what a headline says.

Two descriptions of one change

Consider an invented shop reporting two thirty-day periods. In the first, it receives 100 orders, of which twenty come from customers who had bought before the period began. In the second, it receives 100 orders, of which twenty-five meet that same definition. Each order is counted once.

The repeat-order share rises from 20 out of 100, or 20 percent, to 25 out of 100, or 25 percent. Here are two ways to describe the movement:

Five percentage points

Subtract the earlier rate from the later rate: 25 percent minus 20 percent. The difference is five percentage points.

A 25 percent increase in the rate

The five-point difference is one-quarter of the earlier 20 percent rate: 5 divided by 20, multiplied by 100, equals 25 percent.

Eurostat's percentage-point definition uses the difference between percentage levels. Its percentage-change explanation compares the later value with the earlier one. Naming the measure avoids making the reader guess which calculation was used.

Saying the share increased by 25 percentage points would give a different result: from 20 percent to 45 percent. Saying it increased by five percent would give 21 percent if that means a five-percent relative increase from 20. Neither describes the supplied move to 25 percent.

The count can change at a different rate

Now change the second period. Instead of 100 orders with twenty-five repeat orders, suppose the shop receives 200 orders with fifty repeat orders. The first period stays at 100 orders and twenty repeat orders.

The repeat-order share still moves from 20 percent to 25 percent. Its change is still five percentage points, or a 25 percent relative increase in the rate. But the repeat-order count rises from twenty to fifty, an increase of thirty on an earlier base of twenty: 150 percent.

The total order count has doubled, increasing by 100 percent. Three different statements are now available: total orders rose 100 percent, repeat orders rose 150 percent, and the repeat share rose five percentage points. Each names a different thing that changed.

A claim that repeat business rose 25 percent would therefore need a clearer label. In this variation, 25 percent describes the relative change in the share, not the growth in the number of repeat orders. Nor is this a customer-retention measure. The case counts orders, including any separate orders from the same person; it does not count how many earlier customers returned.

Going back changes the starting point

If a rate falls from 25 percent back to 20 percent, it has fallen five percentage points. Relative to its new starting point of 25, the decline is 20 percent: 5 divided by 25, multiplied by 100.

The same five-point distance therefore corresponds to a 25 percent increase in one direction and a 20 percent decrease in the other. The direction changes the earlier value used in the calculation. With an earlier rate of zero, this relative-change calculation would require dividing by zero; report the levels and point difference instead.

The numerical passages in Infinite Upside: Building Wealth With Room to Live repeatedly attach a percentage to its base. Chapter 9 defines what customer receipts a fee applies to. Chapter 13 keeps the owner's full contribution visible when comparing a later cash amount. The same habit helps when the number being compared is itself a percentage.

Before repeating a change claim, name the quantity, the earlier value and the later value. If the quantity is a rate, distinguish its point difference from its relative change. Then bring back the counts and definitions. A precise percentage still needs to describe the thing the reader wanted to understand.