Behind every band average there are hundreds of individual sites, and the average alone cannot show how they are spread.

What the plot shows

Each site has a log protection ratio: more protective designations than hazard layers scores above zero, equal numbers score zero, and more hazard layers than designations scores below zero. Because designations and hazard layers are small whole numbers, the ratio takes only a handful of values, so the figure shows the share of each band’s sites in the three groups. One square is 1% of the band.

The median ratio is 0.00 in every band, so the median alone would hide the finding. The gap between bands comes from the share of sites with more designations than hazard layers, which rises from 30% in the most deprived band to 50% in the most affluent. Percentages are rounded, so rows can sum to 99–101%. The mean ratio rises from 0.20 to 0.31 to 0.37 (five working protections; the only hazard layer is coal). With flood zone also counted as a hazard layer the means are 0.10, 0.24 and 0.34, the share of deprived-band sites where hazard layers outnumber designations rises from 3% to 15%, and the gap widens.

What the ratio can’t see

A site with no designations at all and a site wedged between ten designations and ten hazard layers both score exactly zero, because ln(1) − ln(1) = ln(11) − ln(11). One has no recorded designations (which may be a gap in the data, not an absence of protection); the other is a dense thicket of competing designations. The ratio can’t tell them apart. A baseline spatial-intensity index is needed to separate them.

Revised 12 November 2026: Added the flood-as-hazard result, noted that percentages are rounded, and changed the wording from “shields and hazards” to “designations and hazard layers”.