800% increases aren't always as big as they look

The BBC raised concerns today that Police Crime Commissioners (PCCs) weren't engaging the public enough. Hundreds of meetings with the representatives have gone without a question being asked by a member of the public, says the broadcaster.

The Home Office's response was quite striking:

"the Home Office said its reforms were working and some forces had seen public engagement increase by up to 800%."

The large percentage makes the increase look like a lot, but it's not necessarily all that revealing: if a PCC got one letter one year and nine letters the next, that would be an 800% increase, but the raw numbers don't look very impressive.

A recent National Audit Office report adds some context to this example: the Commissioner for North Wales (population: 679,000) reported receiving over 500 pieces of correspondence in his first year in post compared to 55 received in the last year of the old police authority -  an 800% increase.

The Commissioner for Avon and Somerset recently reported she'd received 20 times the level of correspondence that her old police authority received in its last year (a 1,900% increase using the same logic as before). But without raw numbers in this case, it's not clear how meaningful this increase is.

They're rises which will be welcomed by many, but percentages like these can flatter changes from a low base.