Two different things
A percentage is a way of expressing a part of a whole out of 100. A percentage point is the unit used when you subtract one percentage from another. The two are easy to mix up, and mixing them up is one of the most common sources of confusion in reported statistics.
If a player’s win rate goes from 50% to 55%, the change is 5 percentage points. It is also a 10% increase, in relative terms, because 5 is a tenth of 50. Both statements are accurate. They describe the same change in different ways.
Absolute and relative change
The percentage-point change is the absolute change: simply the difference between the two percentages. The relative change expresses that difference as a share of the starting value.
Some examples with checked numbers:
- A shot conversion rate rising from 10% to 12%: absolute change 2 percentage points, relative change 2 ÷ 10 = 20%.
- A win rate rising from 50% to 55%: absolute change 5 points, relative change 5 ÷ 50 = 10%.
- A pick rate falling from 8% to 6%: absolute change 2 points, relative change 2 ÷ 8 = 25% fall.
- A rise from 40% to 60%: absolute change 20 points, relative change 20 ÷ 40 = 50%.
Notice that the same absolute change of 2 points gave a 20% rise in the first example and a 25% fall in the third. The starting level determines how large the relative change looks.
Why headlines choose one or the other
Relative changes tend to look larger when the starting value is small. “Doubles the chance” sounds dramatic, but if the chance goes from 1% to 2%, the absolute change is a single percentage point. A source who wants to emphasise an effect may report the relative figure. A source who wants to play it down may report the absolute one. Neither has to be false, which is why it is useful to ask for both.
The same issue appears when reporting rare events. A 50% increase in a very unlikely event can still leave the event very unlikely. Understanding the starting rate, the base rate, is crucial, and ignoring it is the mistake described under base rate neglect.
Percentage changes do not cancel
A frequent trap is assuming that a rise and fall of the same percentage cancel out. Start with 100. A 50% fall takes it to 50. A 50% rise on 50 is 25, so you reach 75, not 100. To get back to 100 from 50, you need a 100% rise.
The reason is that each percentage is taken of a different base. In a game context: if a character’s win rate bonus is cut by 50% and later raised by 50%, it ends up at 75% of its original size, not back where it started.
Percentages of what?
A percentage is meaningless without knowing what it is a percentage of. A few common ambiguities:
- “Up 30%” could be up 30% on last year, or on last patch, or relative to a different group.
- “Accuracy of 40%” might be shots on target as a share of shots, or goals as a share of shots on target.
- Combining percentages. If one group has a 60% rate and another 40%, the overall rate is not necessarily 50%. It depends on how many are in each group. This is related to the way Simpsons paradox arises, where a trend can reverse when groups of different sizes are combined.
- Adding percentages. Probabilities and percentages cannot always be simply added. Adding probabilities wrongly is a standard error, particularly when events overlap.
When a report quotes a percentage, look for the count behind it. “100% of players” may mean three players, which brings back the problem of small sample sizes.
Rounding and precision
Reported percentages are usually rounded, which can create small oddities: three categories that each show 33% add to 99%, and a rise reported as “from 10% to 11%” may hide a real change of anything between a little more than zero and almost two points. It is a mild point, but it matters when comparing numbers that differ by a point or so.
The connection to chance is worth remembering too. A difference of a couple of percentage points in a small sample could be pure noise. Even a quoted percentage with no uncertainty attached is an estimate, a point the idea of confidence intervals makes concrete.
Habits that help
- Convert to counts. “A 2 point increase” feels more concrete as “2 more wins in every 100 games”. This approach is related to using natural frequencies for risk.
- Ask for both numbers. If you are given the relative change, look for the starting and ending values. If you are given the points, think about the base.
- Check the base. Percentage of what, and compared to when?
- Do the arithmetic. Subtract to find points, divide by the starting value for relative change.
- Watch the wording. “Percent” and “percentage points” are not interchangeable, and a good report uses them carefully.
A small amount of care here goes a long way. Many dramatic-sounding statistics turn out to describe modest changes, and some modest-sounding ones describe changes that matter. The only way to tell which is which is to look at both the absolute and the relative figure.