Chira

Prior art, and what this project adds

T12. Four sources were named in the planning documents and none were cited; this is that section. Two were read in full, one blocked automated access and was read by hand on 2026-10-01, one was found on 2026-10-23 after a month marked “not found” and has been read at the abstract only, and one turns out to contradict a claim this project’s own plan made about it. Each entry says which, because a prior-art section whose citations were never opened is worse than none.

1. Le (2026), “Decomposing Crowd Wisdom: Domain-Specific Calibration Dynamics in Prediction Markets”

arXiv:2602.19520, stat.AP. Submitted 23 Feb 2026, revised 4 Aug 2026 (v2). Read 2026-09-25.

This is the closest prior art by a wide margin, and closer than the plan realised. From the abstract: 353 million trades across 429,000 binary contracts on Kalshi and Polymarket, measuring how calibration varies with event domain, time-to-resolution and trade size. It decomposes cell-level logistic recalibration slopes — the same estimand this project calls the Cox slope — and reports:

• persistent underconfidence in political markets, where prices compress toward 50%, as the most robust pattern, replicating on Polymarket;
• large political trades on Kalshi associated with further compression, “a calibration-slope gap of roughly one-half”, surviving market- and event-clustered bootstraps but not robust on Polymarket;
• a Bayesian measurement-error model indicating that, under conservative event-clustered standard errors, roughly half of the raw slope variation reflects estimation noise;
• the conclusion that “calibration is therefore conditional: a price’s meaning depends on what, when and how much is traded.”

What this project adds. A different domain (NBA and NHL game outcomes, not politics), a different size axis (terminal per-market volume, not trade size), a per-game grain with labels taken from the leagues rather than from the venue being measured, and a pre-registered design in which the confound between the size axis and season phase was measured and removed before the test was run (Amendment 3a). Le finds the trade-size compression not robust on Polymarket; this project finds a liquidity slope gap of +0.812 [+0.618, +1.033] on Polymarket NBA moneylines, which is a Polymarket result on an axis Le’s Polymarket arm did not settle.

What this project must take from it, and does. Le’s noise result is a direct warning about our own interval: half of raw slope variation being estimation noise was established under event-clustered standard errors, and our bootstrap resamples games independently. Outcomes cluster by date and team, so an independent-game bootstrap can be optimistic. That is why the writeup reports a date-clustered bootstrap beside the pre-registered one and treats the wider of the two as the honest interval. The comparison exists because this paper was read.

2. Galekwa, Tshimula, Tajeuna and Kyandoghere (2024), “A Systematic Review of Machine Learning in Sports Betting: Techniques, Challenges, and Future Directions”

arXiv:2410.21484, cs.LG. Submitted 28 Oct 2024. Read 2026-09-25.

A review of ML across soccer, basketball, tennis and cricket: support vector machines, random forests and neural networks applied to historical data, in-game statistics and real-time information, aimed at “optimiz[ing] betting strategies and identify[ing] value bets, ultimately improving profitability”, dynamic odds adjustment and risk management for bookmakers, plus anomaly detection for fraud. It names data quality, real-time decision-making and the unpredictability of outcomes as open challenges.

What this project adds, by refusing the review’s objective. This literature optimises profit; Chira scores calibration, and contains no staking system, no odds-setting and no bet placement (PLAN.md, “Out of scope”). The market here is the benchmark, not the thing to beat: the question is how well a price-free model matches a real-money market’s probabilities and where that market is itself miscalibrated. The review’s framing is the reason this project states “the claim is calibration, not profit” in its first paragraph — the adjacent literature is overwhelmingly about returns, and a calibration result read as a betting edge would be a misreading.

3. Wheatcroft (2019), “Evaluating probabilistic forecasts of football matches: The case against the Ranked Probability Score”

arXiv:1908.08980. Submitted 23 Aug 2019. Read 2026-09-25 — and it does not say what this project’s plan said it says.

PLAN.md cites “Wheatcroft 2022” for the proposition that the literature “recommends Brier/log-loss over RPS”. The paper does argue against the RPS: it disputes that sensitivity to distance adds anything, and finds that in two simulation experiments the ignorance score — which is local, i.e. the logarithmic score — outperforms both the RPS and the Brier score, “casting doubt on the value of non-locality and sensitivity to distance as properties of scoring rules in this context”.

So the citation half-holds and half-inverts:

• Holds: RPS is not the right scoring rule here, and this project does not use it.
• Inverts: the paper’s preferred rule is the log score, while PREREGISTRATION.md section 3 makes Brier primary and log loss secondary with no hypothesis test attached.

The pre-registered choice stands, with its reason stated rather than a citation misquoted. Section 3’s argument for Brier primary is boundedness: unclipped log loss is unbounded, so a single mis-joined label at an extreme price could silently decide the headline, which is a real hazard in a pipeline whose labels come from a third party. Both are reported for every result. The honest position is that this paper would rank them the other way round, and a reader who prefers the log score can read it off the same tables. Two smaller corrections: the year is 2019 for the preprint read here, not 2022, and the paper is about three-way football outcomes while this project scores two-way moneylines, where locality and distance-sensitivity arguments are weaker.

4. Reichenbach and Walther, “Accuracy, Skill, and Bias on Polymarket” (SSRN 5910522)

Read by a human, 2026-10-01. papers.ssrn.com refuses automated access (HTTP 403, a Cloudflare notice, 2026-09-25), so the project owner read it in a browser. What follows is that reading. No number from the paper is quoted here, because none was transcribed.

What it does:

• It compares Polymarket’s accuracy with bookmakers’ and finds Polymarket the more accurate.
• It tests for a favorite-longshot bias and finds none at the scale of the market. The bias it does find sits with individual traders, and much of the paper reports how the top and bottom percentiles of traders perform.
• Its markets are tennis and politics. It covers no NBA or NHL markets.

What it does not do:

• It does not score calibration with Brier, a calibration slope or an intercept. Its question is whether the market is biased, answered on market-wide averages.
• It does not split anything by liquidity, volume or market size.

What that means for this project: the contribution stands as written below. The paper answers a different question, bias or no bias, pooled across the market. This project asks whether calibration differs between thin and liquid markets. Its finding is also consistent with headline 2’s picture: on NBA moneylines the pooled market looks well calibrated, because thin markets that are too timid and liquid markets that are too extreme pull in opposite directions. That consistency is not a confirmation, since the domains differ (tennis and politics against NBA and NHL). It is a reason to expect a pooled test to miss the effect.

5. Wilkens (2026), “Can simple models predict football — and beat the odds? Lessons from the German Bundesliga”

Sascha Wilkens (independent researcher), Journal of Sports Analytics 12, SAGE, published online 2026-02-06. DOI 10.1177/22150218261416681. Open access under CC BY-NC 4.0.

Found 2026-10-23; read at the abstract only. It was marked “not found” from 2026-09-25 because the search covered arXiv and the paper is a journal article. The title, author, venue, date, DOI and licence above come from the publisher’s own Crossref record, and so does the abstract. The full text has not been read, so nothing below goes beyond what the abstract states.

What it does, per the abstract:

• A simple model built on recent expected goals (xG), turned into win–draw–loss probabilities through a Skellam distribution and calibrated with isotonic regression.
• Eleven Bundesliga seasons, 2014/15 through 2024/25, against bookmaker odds.
• The bookmakers are better calibrated than the model.
• The model nonetheless “captures certain signals not fully reflected in market prices”: simulated betting returns about 10% on average odds and nearly 15% at the best available prices.
• Profits come mostly from home-win bets. Backing away wins loses money consistently, and profitability varies considerably by season and bet type.

What that means for this project. It is the closest published result to headline 1: a simple, transparent model scored against the market’s prices.

• It agrees on calibration. Headline 1 finds the same ordering, the market ahead of the model in both sports (NBA +0.01152 Brier, NHL +0.00499 on matched priced games).
• It disagrees on the part a bettor would care about. On the 2025-26 NBA holdout, every one of section 9’s edge tiers has its model-side hit rate’s 95% interval entirely below 0.5. Where this project’s model disagreed with the closing price, the market was right more often than the model, and most often where the disagreement was largest. The nested test adds nothing over the NBA close either. Nothing here reproduces “signals not fully reflected in market prices”.

The two results differ on enough that neither contradicts the other:

• The sport. Football’s three-way market against NBA and NHL moneylines.
• The input. xG measures chance quality inside a match. This project’s model is a results-based Elo plus schedule terms, which carries less information about how a team actually plays.
• The venue. Bookmaker odds carry a margin, and “best available prices” means choosing the best of several books. This project scores one market’s close.
• The test. Wilkens’s returns are simulated across eleven seasons. Whether the isotonic calibration and the betting rules were fixed out of sample is not stated in the abstract, and it matters, because this project’s own dev-period edge did not survive its holdout.

Not load-bearing for artifact v1. Cited in v2 as the nearest comparison for headline 1, and as a contrast rather than as support.

Data sources this project did not reuse

Two bulk Polymarket datasets were identified during planning and not evaluated: manja316/polymarket-historical-data (13,964 markets, 10.8M price records) and SII-WANGZJ/Polymarket_data (107GB, 1.1B records, 268K markets). They are third-party and unvetted, so provenance, per-game NBA/NHL coverage and fidelity are all unknown, which is why the census was collected first-hand. They remain a cheap cross-validation of it rather than a replacement, and that check (T16) is still open.

Where this leaves the contribution

Stated narrowly, because the honest version is narrow:

1. A liquidity-conditioned calibration result on Polymarket sports moneylines, on the same estimand as Le (2026) but a different domain and size axis, on the platform where Le’s trade-size result did not hold.
2. A pre-registered design whose confounds were measured, not asserted — the volume/season-phase correlation removed before testing (Amendment 3a), the price-range artifact tested by caliper matching, the event-volume proxy withdrawn on measurement (Amendment 4).
3. Per-cell noise floors simulated from the census’s own price pool, which is what makes “this cell is miscalibrated” a falsifiable statement at n≈225 rather than a plotted wiggle.
4. A census whose collection is reproducible from public endpoints, with every miss classified and the reconciliation identity enforced, rather than a dataset of unknown provenance.

Not claimed: novelty of the estimand, novelty of the question, or that any of this beats a market.

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