Every time I see an article like this about how the UK government (all large orginzations of people in general though) is obssessed with measuring meaningless things, I am reminded that it is the birthplace of Goodhart's Law [0].
The only thought I've had is to: 1) Rely on a spectrum of metrics, to get a more holistic perspective. Instead of just seeing "crime is down x%" administrators would see how many reports end up classified as a lower-level infractions, how civilians rate the safety of their area, etc. 2) Add common-sense restrictions to make stat-pumping more difficult. For example, bringing in classroom inspections on random days 3) Penalizing institutions and individuals who are clearly attempting to juke the stats. Enforcement would certainly be difficult, but simply having something to this effect on the books would, imho, reduce schools dedicating time to studying for a standardized test
At the very least it should diversify how people try to game the system, and then the "winners" of various bins could be studied to compare usage of different metrics in selection. If the specific formula could be kept mostly secret, perhaps switched up every so often, it would hopefully disincentivize gaming at all.
Along those lines, committees and metrics could both be used. Give committees control over 10% of the spots or something. Corruption is obviously a downside, but I do think committees also have upsides that are difficult if not impossible to replicate with pure metrics. In doing this committee selections could also be tracked against the various metric ones for longer term outcomes.