Statistics Literacy

Correlation Is Not Causation

Illustrative sport and gaming examples show how two numbers can move together because of a hidden shared cause, and how to question a claimed link.

On this page
  1. What a correlation is
  2. The hidden common cause
  3. Reverse direction
  4. Coincidence
  5. Selection in the sample
  6. Overall versus grouped
  7. Questions to ask of a claimed cause
  8. Using the idea without overcorrecting

What a correlation is

Two quantities are correlated when they tend to move together: when one is higher, the other tends to be higher too (a positive correlation), or lower (a negative correlation). Correlation is a statement about patterns in data. Causation is a stronger claim: that changing one thing would change the other.

The gap between the two is where a great deal of sports and gaming commentary goes wrong. A link in the numbers is a reason to ask questions, not an answer.

The hidden common cause

The most common reason for a non-causal link is a third factor that influences both. Statisticians call it a confounder.

An illustrative example. Suppose a survey of competitive players finds that those who own more expensive peripherals tend to have higher ranks. It is tempting to read this as “better equipment raises your rank”. But a more likely explanation is that players who spend more hours playing, and who care more about the game, both improve more and spend more on equipment. Hours of practice is the hidden cause behind both numbers. Buying the equipment without the practice would not be expected to produce the same rank.

Another illustration: in a football league, teams with more expensive stadium facilities might win more. But clubs with large budgets tend to spend on both facilities and players. Budget drives both.

Notice that in neither case is the correlation false. The data really does show the link. What is false is the interpretation.

Reverse direction

Sometimes the arrow runs the other way. If teams that are leading late in a game tend to take fewer risks, a statistic might show “teams that play conservatively win more”. But winning may have caused the conservative play, not the reverse. Time-of-game context matters here, because the situation determines the behaviour.

Coincidence

With enough numbers, some will line up by chance. A player’s results may seem to follow the day of the week, the colour of a jersey or a pre-match routine. If many such factors are examined, a few will appear linked just by luck. This is the same reason people see patterns in random events, and the idea of coincidence myths and lucky rituals covers how easily the mind builds causal stories from them. When only the striking match is reported, it also overlaps with cherry-picked statistics.

Selection in the sample

A link can also appear because of who is in the data. If only professional players are studied, a trait that seems unrelated to skill in the wider population may look important or unimportant simply because everyone in the group already passed a threshold. This is related to survivorship bias, where only the visible successes are counted.

Overall versus grouped

Sometimes a relationship in the combined data is the opposite of the relationship within each subgroup. Simpsons paradox is the best-known example, and it is a reminder that grouping decisions can change the apparent direction of a link.

Questions to ask of a claimed cause

  • Could something else drive both? Think about practice time, budget, skill level, opponent strength, or difficulty.
  • Could the direction be reversed? Does the outcome influence the supposed cause?
  • Is it just chance? How many comparisons were tried, and how big is the sample?
  • Is the pattern consistent? Does it appear across seasons, teams, or patches, or only in one stretch?
  • Is there a plausible mechanism? A believable explanation does not prove a cause, but the absence of any makes the claim weaker.
  • Was anything actually changed? The best evidence for causation comes from comparing similar groups where one thing was deliberately different, such as an experiment or a well-designed trial. Observational data, which is most sports data, rarely offers this.

Using the idea without overcorrecting

The phrase “correlation is not causation” is sometimes used to dismiss any statistical link, which is also a mistake. Correlation can be a useful clue, and some correlations do reflect causes. It is better read as “correlation alone does not settle causation”. Treat it as a prompt to look for more evidence, not as a verdict in either direction.

In practice, this means holding conclusions loosely. When you see a headline like “players who do X win more”, picture the alternative explanations before accepting the cause. If a player’s improvement began just after a change in routine, remember that unusual runs of form also tend to fade on their own, a pattern explained by regression to the mean. A change that seems to have worked may only have coincided with a return to the player’s normal level.

Careful readers do not need to reject statistics. They simply separate what the numbers show, which is a pattern, from what the commentator says they mean, which is a story.

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