Glossary & references

Plain-English definitions of the jargon on this site, and the source papers each method comes from. Everything here is research & education — not financial advice, not a tipping service.

The market

Term	In plain English
Implied probability	A price between 0 and 1, read as a chance. A team priced at 0.16 means the market gives it ~16% to win.
Overround / vig	Add up every team's price in a round and it sums to more than the real number of slots — the excess is the bookmaker's built-in margin.
De-vig	Stripping that margin back out by rescaling a round's prices to sum to its true slot count, so they're comparable to a model.
Favorite–longshot bias	The long-documented tendency for longshots to be over-priced and favorites under-priced versus their true odds.
Liquidity / depth	How much money is resting in a market. A thin market can't be traded at size without moving the price.
Half-spread	Half the gap between the buy and sell price — a rough per-trade cost. We net it off every edge, so a gap that doesn't clear it isn't taken.
Nested ladder	The five linked markets per team: advance → reach QF → SF → final → win.
No-arbitrage	If a team's price to reach a deeper round exceeds its price to reach a shallower one, one of those prices is provably wrong — a riskless inconsistency.

The models

Term	In plain English
Edge	Model probability minus the de-vigged market probability. Positive = the model thinks it's under-priced.
Zero-knowledge model	Knows no football — it only re-shapes the market's own prices with a favorite–longshot correction. The honest baseline.
Informed model	An independent Elo simulation of the bracket, not derived from the market — so it can genuinely disagree.
Elo rating	One number for team strength; the gap between two ratings sets the win probability. From chess, now standard in football.
Expected score	The win probability the Elo gap implies for a single match.
Poisson goals model	Treats each team's goals as a random count whose average is set by the rating gap — the standard way to simulate scorelines.
Dixon–Coles correction	A tweak to the Poisson model that fixes its tendency to under-produce low-score draws (0-0, 1-1).
Shrinkage	Pulling estimates toward the field average to avoid over-confidence — we flatten ratings for the high-variance knockout.
Rating uncertainty	We don't know any team's true strength exactly, so each simulation jitters the ratings — which stops the model printing false 0% / 100%.
Host advantage	The well-documented home-team bump; the three 2026 co-hosts get a disclosed +60 Elo.
Monte Carlo	Simulating the whole tournament tens of thousands of times and counting how often each outcome happens, to read off a probability.

The paper book

Term	In plain English
Paper book	A pretend portfolio — no real money — purely to put a number on the model-vs-market disagreements.
Conviction-weighted	Bigger disagreements get bigger (capped) stakes.
Dollar-neutral	Equal money long and short, so it's a bet on relative mispricing, not on the market rising or falling.
Mark-to-market (MTM)	Re-pricing open positions at the current market to show running profit/loss.
Capital at risk · max ↑ · max ↓	The money deployed, and the loose best/worst-case envelope of that book.
Buy & Hold vs Active Trading	Enter once and hold to the end, versus rebalance each matchday as results land.

Scoring & honesty

Term	In plain English
Out-of-sample	Scored only on data that arrived after the prediction was timestamped. The only honest test.
Brier score	The average squared error of probability forecasts — lower is better.
Skill (vs market)	Our Brier minus the market's Brier. Positive means we beat the crowd — the only comparison that matters.
Breadth / information ratio	More independent bets sharpen a strategy (IR ≈ IC·√breadth). Our Elo edges are highly correlated, so the real breadth is small — and we say so.

References — where the methods come from

The techniques here are standard; these are the sources.

• Elo, A. (1978). The Rating of Chessplayers, Past and Present. Arco Publishing. — the rating system.
• Maher, M. J. (1982). "Modelling association football scores." Statistica Neerlandica 36(3): 109–118. — the Poisson goals model for football.
• Dixon, M. J. & Coles, S. G. (1997). "Modelling Association Football Scores and Inefficiencies in the Football Betting Market." Journal of the Royal Statistical Society: Series C (Applied Statistics) 46(2): 265–280. — the low-score (draw) correction we apply.
• Brier, G. W. (1950). "Verification of forecasts expressed in terms of probability." Monthly Weather Review 78(1): 1–3. — the proper scoring rule we grade ourselves with.
• Snowberg, E. & Wolfers, J. (2010). "Explaining the Favorite–Longshot Bias: Is it Risk-Love or Misperceptions?" Journal of Political Economy 118(4): 723–746. — the bias the zero-knowledge model exploits.
• Ottaviani, M. & Sørensen, P. N. (2008). "The Favorite-Longshot Bias: An Overview of the Main Explanations." In Handbook of Sports and Lottery Markets. — a survey of that bias.
• Grinold, R. C. (1989). "The Fundamental Law of Active Management." Journal of Portfolio Management 15(3): 30–37. — IR ≈ IC·√breadth, the breadth caveat we flag.
• World Football Elo Ratings (eloratings.net) — the live team ratings the informed model runs on.

The full maths, parameters and code pointers are on the methodology page.