An LLM router picks which model should answer each query. The appeal is that models fail on different questions. Whatever single model is best overall still gets some wrong, and another model in the pool gets many of those right. Getting that choice right every time is the ceiling, and a router is an attempt to approach it. However, recent work reports that routers do not get close. Across 21 routing methods on five benchmarks, sharply different designs land within a fraction of a point of each other, and all of them stay far below that ceiling. Learned routers often fail to beat simply always calling the strongest model. We ask what those missed questions have in common. We set fourteen models to answer all 294 questions, with 7 task types across 3 languages: Korean, English and Hindi. We ran the whole matrix twice, changing nothing, but 5.37% of the 4,116 model-question pairs came out scored differently anyway. Run-to-run movement like that is normal, and we argue that a small win does not show that routing did anything, ours or anyone else's. Counting an answer correct only when the model got it right in both runs, 29 questions on this matrix can be improved with routing. Every correct-answer count here is on that rule. Task type accounts for most of them: assigning each task type one model in advance, chosen once and never updated, improves 21 of the 29. Splitting each task type by language improves 2 more and leaves 6 of 294 unoptimized. That handful is what a learned router would have been built for, and it is smaller than the run-to-run movement above, which is a share of pairs rather than of questions. The static table we adopted answers 262 of 294 questions at $3.33 per run, against the best single model's 245 at $7.69. All of this is fitted and scored on the same 294 questions with no holdout.
Most document-extraction systems use a single model for all documents. This is simple but can be costly for easy cases and less effective for difficult ones. We examine whether we can predict a document's difficulty before extraction using inexpensive, document-based signals, and use this to choose between a cheaper and a stronger extractor. We find that routing only helps if two conditions hold: the cheaper model fails often enough to make routing worthwhile, and those failures can be predicted from visible features such as image quality and layout. We turn these into a practical test and apply it to five genres. When both conditions are met, the calibrated router reduces cost by 31-33% on receipts and 77% on degraded ad-buy forms while keeping quality within 0.02 F1 of always choosing the large model. Routing does not help if either condition is missing, as with clean digital invoices or nutrition labels that are already easy to read. A small labeled pilot can predict whether routing will work, and in the two cases where we ran it first, the prediction was correct. A simple bag-of-words router works about as well as engineered features, showing that the main limit is the genre, not the router design; we use interpretable features to help explain which genres can be routed. The router must be retrained for each dataset and does not transfer across datasets, even within the same genre. These results hold for two model pairs with cost differences of 5x and 3x.