A combined success rate can reverse the comparison seen within separate groups. The following invented training example shows why the mix of cases deserves attention before a headline declares a winner.
In an easier task, team A succeeds in 9 of 10 attempts, while B succeeds in 80 of 100. A has the higher rate: 90% versus 80%. In a harder task, A succeeds in 30 of 100 and B in 2 of 10. Again A has the higher rate: 30% versus 20%.
Combine the attempts, however, and A has 39 successes from 110, about 35.5%. B has 82 from 110, about 74.5%. B handled many more of the easier cases; the combined rates weight the task types differently.
Keep the counts in view
Recalculate both subgroup rates and the overall rates from their numerators and denominators. Do not average the two percentages without accounting for how many attempts each represents.
The arithmetic alone does not establish why assignments differed or which comparison answers a real policy question. That requires knowledge of the process and the question being investigated.
For a chart or report, retain the subgroup counts alongside the aggregate. The apparent contradiction is an invitation to inspect composition, not permission to select whichever headline favours your preferred team.
Editorial illustration from this site’s image library; not documentary evidence of the example or object discussed.