Two ways of describing the same change
Slot machines and other games of chance have a built-in house edge, and no strategy, system or timing changes the odds. Most players lose money over time, and nobody should gamble money they cannot afford to lose. This article is about reading risk statistics in general. The examples are hypothetical and are not medical, financial or gambling advice.
News reports and advertisements often describe a change in risk in relative terms: “twice as likely”, “50% higher”, “cut by a third”. These phrases sound weighty. But without the starting level they say very little, and a big relative change in a tiny risk can still be tiny.
The two definitions
Absolute risk is the plain chance of something happening, such as 1 in 1,000 or 0.1%.
Relative risk compares two absolute risks as a ratio, or as a percent change from one to the other. If a risk goes from 1 in 1,000 to 2 in 1,000, the relative risk is 2 (a doubling, or a 100% increase), while the absolute risk has risen by 1 in 1,000, or 0.1 percentage points.
A worked example
Imagine a hypothetical risk that affects 1 person in 10,000. A new factor is said to “double the risk”.
- Before: 1 in 10,000, which is 0.01%.
- After: 2 in 10,000, which is 0.02%.
- Relative change: +100%.
- Absolute change: 1 extra person in 10,000, which is 0.01 percentage points.
In a group of 10,000 people, the number affected goes from 1 to 2. “Doubled” is accurate, and so is “one extra person in ten thousand”. The second is far less alarming, and in many cases it is the more useful one.
When the starting risk is large
The same relative change can matter much more when the baseline is higher. Take a hypothetical risk that affects 20 people in 100 and is halved.
- Before: 20%.
- After: 10%.
- Relative change: −50%.
- Absolute change: 10 percentage points, or 10 fewer people per 100.
Here, a 50% reduction is also a large absolute change. The identical “50%” label hides a difference of 1,000 times in absolute size between this example and the previous one (0.01 percentage points compared with 10). That is why you need both numbers.
Use counts instead of percentages
A helpful habit is to convert percentages into counts of people, because “10 out of 1,000” is usually easier to picture than “1%”. Such counts, sometimes called natural frequencies, make the denominator visible.
A simple method is to picture 1,000 or 10,000 people:
- Take the baseline risk and ask how many of the group would be affected.
- Apply the change and ask how many would be affected now.
- Subtract.
This also guards against percent change versus percentage points confusion, which is a close cousin of this topic.
A comparison with the numbers in games
Suppose a hypothetical game feature appears once in 200 plays (0.5%), and a promotion says a change makes it “50% more likely”. That would take it to 0.75%, or 3 in 400, which is one extra appearance for every 400 plays. The statement “50% more likely” is true, but the extra frequency is small in absolute terms.
The reverse can happen as well. An average return that looks “only 2% lower” can be a considerable relative change in the house edge, as covered under the house edge itself. It is worth checking both framings.
Why this trips people up
- Relative figures sound bigger. They are attractive to anyone who wants a number to sound impressive, whether in a news story or a sales pitch.
- The baseline is often missing. Without it, you cannot compute the absolute figure.
- Comparison groups differ. A relative risk compares two particular groups, which may not match your situation.
- Loss and gain framing. People respond differently to the same facts depending on wording. The framing effect and loss aversion both play a role.
Questions to ask
- What is the risk to begin with, in plain counts?
- What is it afterward?
- How many extra (or fewer) events does that mean per 1,000 or 10,000 people?
- Over what time period, and in which group?
- How certain is the estimate? Small samples or short studies can give unstable results.
Reading it alongside other limits
Even the absolute figure needs context. A risk of 1 in 10,000 per year is different from 1 in 10,000 per lifetime, and a tiny probability can still add up over many repeats. When a figure comes from limited data, treat it cautiously. On the topic of chance in games, the figures quoted are long-run averages, and the actual experience of any one player can differ a lot.
If you gamble, treat it as paid entertainment and decide on a limit before you start. If you notice that gambling is causing stress or you are finding it hard to stop, a national problem-gambling helpline or local health service can help. For personal health questions, a qualified health professional is the right source, not a general article like this one.