- Of the cases he reviewed since 2013, approximately 80% were denied. This would, as you note, be better phrased as "80 percent of the cases he reviewed were denied".
- Each year since 2013, he reviewed an unknown number of cases, and a certain percentage of those cases were denied. The arithmetic mean of those 6 yearly percentages is approximately 80%.
In the second case, the 80% figure is meaningless, but it's a calculation people often perform despite that fact.
- Of the cases he reviewed since 2013, approximately 80% were denied. This would, as you note, be better phrased as "80 percent of the cases he reviewed were denied".
- Each year since 2013, he reviewed an unknown number of cases, and a certain percentage of those cases were denied. The arithmetic mean of those 6 yearly percentages is approximately 80%.
In the second case, the 80% figure is meaningless, but it's a calculation people often perform despite that fact.