Which Bridges Get Replaced? Following 45,274 Ohio and New York Bridges from the 2005 to the 2025 National Bridge Inventory with Isotonic Estimates and an Exact Likelihood Equivalence

Condition ratings are meant to drive bridge replacement. I test how closely they do, by following every Ohio and New York highway bridge in the 2005 National Bridge Inventory to the 2025 inventory. Of 45,274 bridges with a valid rating and year built, 21.3% had been replaced in place (a new year built under the same structure number) or had left the inventory twenty years later. The share falls steeply with the lowest of the deck, superstructure, substructure and culvert ratings in 2005: 71% at rating 3 (serious), 57% at 4 (poor), 33% at 5, 19% at 6, 10% at 7 and 7% at 9. The pool-adjacent-violators estimate of a non-increasing replacement probability pools only ratings 1 and 2. I prove that, for grouped binary data, this isotonic least-squares fit is also the exact maximum-likelihood estimate under the monotonicity constraint. Replacement also rises with age, from 6% for bridges under 10 years old to 47% for those over 100. As a ranking device the 2005 rating has an area under the ROC curve of 0.751, age 0.714, and a logit using both 0.799. Of the 5,073 bridges rated poor or worse in 2005, 61% had been replaced or removed by 2025, but 530 (10.4%) were still in service under their original year built and still rated poor or worse: 5.1% in Ohio and 17.8% in New York. Ohio mostly removes and renumbers structures, while New York mostly rebuilds under the same number, so the two outcomes must be combined.