A Fairness Audit of the Duckworth-Lewis-Stern Method: Format-Specific and Gender-Differential Bias, with an Interpretable Calibration Layer for Cricket Target Revision

We study how algorithmic review changes the initial decisions that a system is designed to correct. Using Hawk-Eye data from professional tennis, we compare umpire decisions with and without review against a common accuracy benchmark. Under review, initial errors were 8.6 percentage points higher just outside the line and lower for comparably close balls inside. We find no evidence that average initial accuracy deteriorated. Within matches, reversals were followed by larger adjustments than upheld calls, consistent with adaptation to correction. Overall, correction offsets worse initial decisions for incorrect in calls and reinforces better initial decisions for incorrect out calls. Whether review lowers organizational costs depends jointly on these changes and the costs of remedying corrected errors. A conditional illustration shows how utilization spreads fixed review costs across calls.

Typed decision models (TDMs) return a probability for each allowed answer instead of generating text, which makes them candidates for cheaply replacing LLM judges that compare two answers. Whether they share the biases of LLM judges is untested. We run the CALM benchmark's bias tests on eight TDMs and seven LLM judges of 2024 and 2026. Every TDM is biased, in three to eight of twelve tests. Emotional tone affects them most, and rewriting the better answer in such a tone lowers the accuracy of a typical TDM from 99% to 42%. TDMs are more biased than 2026 LLM judges. All eight change verdicts when the answers swap places, which the 2026 LLM judges hardly do, and several side with an answer that most people allegedly prefer or that a famous model allegedly wrote. Yet both kinds of judge are tripped up by the same prompts. The TDMs' probabilities show that most tests mainly flip verdicts the TDM was unsure of, and that good calibration does not protect against bias. As TDMs are more consistent and 37 times cheaper than 2026 LLM judges, our results suggest they can be attractive judges if their biases are tested for the task.

Football score forecasting combines a strong statistical core with a difficult contextual edge. Dynamic Poisson-family models estimate team strength, expected goals, and coherent score probabilities, but do not directly understand roles, tactical matchups, motivation, or how a first goal changes behaviour. Large language models (LLMs) can reason about such concepts, yet are not calibrated probability engines. We combine both components through an auditable information harness. This paper documents four iterations: V1, a dynamic score-driven Dixon-Coles baseline; V2, which maps LLM contextual ratings back into expected-goal parameters; V3, which replaces scalar correction with goal-by-goal simulations over a frozen score-candidate set; and V4, which adds shared first-breakthrough and post-goal cascade judgments, time-aware stopping, and deterministic tail candidates. The harness defines input semantics, supplies pre-match evidence, and constrains the LLM to an inspectable reasoning route. On a chronological replay of the first 150 matches of the 2025-26 English Premier League, V1 achieved 10.0% Top-1 and 26.7% Top-3 exact-score accuracy. V3 reached 12.0% and 30.0%, while V4 reached 14.7% and 30.7%. V4 increased candidate coverage from 77.3% to 84.7%, although no added tail candidate became a Top-3 exact hit. V1's native 1X2 distribution achieved 53.3% argmax accuracy, 0.9878 log loss, 0.5870 Brier score, and 0.2095 ranked probability score. These results are exploratory: the development slice is not an untouched benchmark, and temporal input isolation cannot exclude outcome memory in a closed LLM. The contribution is an auditable hybrid architecture, a clear design evolution, and negative findings showing where football-aware simulation does and does not improve score selection.