Abstract: Judge-specific sensitivity is useful for aggregating pairwise LLM evaluations, but its interpretation depends on which systematic presentation effects the ranking model includes. We introduce OSCAR, an order-aware framework for scoring and calibrating AI rankings, and study position as one such effect. In released judgments from 18 evaluators, the all-response A-minus-B score difference ranges from $-63.11$ to $98.31$ percentage points. Matching question text, response texts, candidate identities, and judge within the released table gives an overall difference of $24.22$ points (95% interval $[22.90,25.54]$), conditional on the released text mapping. A controlled calculation isolates the potential consequence: with true sensitivity fixed at one, omitting a position intercept of four reduces the population-optimal slope to $0.0771$. We extend sensitivity-based ranking with judge-specific position, length, and family terms, characterize local omission-induced displacement and an identification failure, and propagate prompt-cluster uncertainty to adjusted comparisons. Across four released datasets, position provides the largest stand-alone predictive improvement. Refitting bootstrap comparisons show more selective gains from the full model over position-only adjustment. In dependent binary simulations, adjusting both the mean and covariance yields 94.4--95.2% coverage; correcting either alone is insufficient. At $N=10{,}000$, OSCAR reduces mean neutral-target RMSE from $0.1158$ under the sensitivity-only model to $0.0237$.