Better per match yet worse overall accuracy

Teams A and B played two separate matches. In each match, A's shooting accuracy (goals divided by shots) was higher than B's. Does it follow that A's accuracy over both matches combined was higher than B's? Justify your answer or give a counterexample.

No — this is Simpson's paradox. For example, A scores 1 of 100 shots in match 1 while B scores 0 of 1; in match 2 A scores 1 of 1 while B scores 99 of 100. A wins each match on accuracy, but combined A has $2/101\approx2\%$ and B has $99/101\approx98\%$, because the shot counts weight the matches very differently.