The reason two true statistics can contradict each other

Two baseball players. In 1995 the first has the higher batting average. In 1996 the first again has the higher batting average. Combine the two seasons and the second player leads. This is not a rounding artefact and it is not rare; it happened with Derek Jeter and David Justice across those exact years.

What everyone sees

The pair of statements looks like a contradiction, so one of them is assumed to be a mistake or a manipulation. Readers ask which number is the real one. The question has no answer, because both are correctly computed from the same records and they are answering different questions.

What is actually happening

A combined average is a weighted mean, and the weights are the number of attempts in each period. If one player took most of their attempts in the easier season and the other in the harder one, the aggregate can reverse the direction of every component. This is Simpson’s paradox seen from the arithmetic side: the grouping variable, not the performance, determines the sign of the comparison.

Why it stays hidden

The mechanism hides because averages are presented without their weights. A percentage looks self-contained, and the denominators that produced it are usually dropped in the reporting. Nothing in the format signals that two correctly computed figures can point opposite ways, so the reader defaults to assuming one side is being dishonest.