Science Puzzle
The Lucky Socks
Jamie's football team has played 20 matches this season. Four matches ago, Jamie started wearing a new pair of lucky socks, and the team has won every match since. Jamie is now convinced the socks are bringing the wins.
Do the results show that the socks work?
The Answer
No. The wins came after the socks, but that doesn't mean the socks caused them.
Before the socks, the team won 12 of its 16 matches: three in every four. A team that wins three games in four will win four in a row quite often just by chance. The odds are 0.75 × 0.75 × 0.75 × 0.75, about 1 in 3. So the run of wins is roughly what you'd expect from this team with or without anything on its feet.
Thinking "this happened after that, so that caused it" is such a common mistake that it has a Latin name: post hoc ergo propter hoc, "after this, therefore because of this". It's how lucky charms, rain dances and plenty of shaky health claims stay popular. People also tend to remember the times a charm "worked" and forget the times it didn't.
To test the socks properly, you'd need lots of matches, some with the socks and some without, chosen at random rather than by Jamie's mood, and then compare the win rates. Even then, if Jamie plays, feeling lucky might boost Jamie's confidence a little, which would be an effect of believing in the socks rather than of the socks themselves.
The principle: The post hoc fallacy. One event following another doesn't show the first caused the second; you need a fair comparison against what would have happened anyway.