Guide

• Elo ratings: like a chess points system — beat a strong team and you gain more, lose to a weak one and you drop more. The data is from eloratings.net, tracking each national team's results over time. The gap between two teams' Elo is our measure of relative strength.
• Dixon–Coles model: goals in football behave like rare random events, modelled with the statistical Poisson distribution — each team's expected goals comes from the Elo gap. Dixon–Coles then adds one correction so the probabilities of low scores (0:0, 1:1) stay closer to reality.
• Where do these numbers come from? They aren't guessed. How an Elo gap turns into goals, how big home advantage is, how strong the low-score correction should be — all of it is fitted (backtested) on about 1,900 real international matches since 2010, with more recent matches weighted more heavily. We then tested this fitted version on matches it had never seen; it predicted better than the older hand-set one, so it's the version we run (internally, dc-v1.1).
• Home advantage: all else equal, a team playing at home tends to do a little better. For this World Cup the three hosts (USA, Canada, Mexico) get a boost of about 85 Elo points when they play in their own stadiums; every other match is treated as neutral ground.
• The model builds a full scoreline-probability grid for each match (how likely 1:0, 2:1, and so on), then sums those into 1X2 (home/draw/away), over/under, and more.
• Advancement odds: the same model drives a Monte Carlo simulation — the whole group stage is replayed tens of thousands of times, ranked by FIFA rules each run, counting how often each team advances across 10,000 runs.
• ⚠️ Experimental: the model is experimental, and closing market odds are usually more accurate. We show the model alongside the market for comparison only — not as betting advice.

• Decimal: what the Taiwan Sports Lottery uses. Payout = stake × odds (your stake included). E.g. odds 2.50, stake 100 → you get 250 back (150 profit). Implied probability = 1 ÷ odds (2.50 → 40%).
• American (Moneyline): common in Canada and the US. A positive number (e.g. +200) is how much you net on a 100 stake; a negative number (e.g. −150) is how much you must stake to net 100.
• Hong Kong: = decimal − 1 (the net-profit multiple only).
• The widget below converts any one format into the others plus the implied probability. The EV calculator accepts all five formats.

• A bookmaker's odds aren't the true probability — they shade every outcome a little to guarantee a profit. That shading is the vig (also called juice or the margin).
• Add up the implied probability of every outcome and it exceeds 100%; the excess is the bookmaker's margin. The Taiwan Sports Lottery's vig is far higher than Pinnacle's (a book known for a thin margin).
• De-vig means scaling those over-100% implied probabilities back to 100%, giving the fair probability after removing the margin.
• How the EV calculator uses this: it de-vigs Pinnacle to get a near-true fair probability as the benchmark, then compares your book's odds (e.g. the Taiwan Sports Lottery) against that fair probability to judge whether your price is good.

• EV (expected value) in plain words: "if you placed this same bet many times, how much would you win or lose per bet on average?" Any single match is uncertain; EV is about the long-run average, not this one result.
• Formula: EV = (fair probability × your odds) − 1. The fair probability comes from chapter 3 — market mode uses Pinnacle with the vig removed; model mode uses the model probability (experimental).
• The calculator grades the result in three tiers: 🟢 good price (EV > 0, better than fair), 🟡 close to fair (EV between −2.5% and 0 — note this is still negative EV, just a low vig), 🔴 expensive (EV below −2.5%).
• "Per 100 staked you win/lose X on average" is simply EV × 100 — the abstract percentage turned into money you can feel.
• "Breakeven win rate" = 1 ÷ odds. Read it next to the fair probability: if the breakeven bar is higher than the fair probability, this price loses money in the long run.

Bankroll and Kelly staking

• Bankroll = the total budget you are willing to bet and could lose without it affecting your life — not your savings. All stake suggestions are a percentage of it.
• The Kelly formula sizes the bet by the size of your edge: bigger edge → bigger stake; no edge → no bet. This site uses ¼ Kelly (a quarter of the full Kelly suggestion) — more conservative, smaller swings.
• Example: bankroll 1,000 and the calculator suggests 3.2% → stake 32 on this bet (negative EV always suggests 0).
• Model-mode stake suggestions sit behind a calibration unlock gate: the model must accumulate at least 30 settled matches this tournament with prediction accuracy (Brier) no more than 10% behind the market before stakes unlock; until then only the calibration progress (e.g. 0/30) is shown. Market mode is unaffected. This is deliberate — a model without real-tournament validation should not size your bets.

1. (Lower on the page) The "model vs market: biggest divergences" list is a research entry point: clicking a row prefills the calculator. It is NOT a value list — a big divergence usually means the model is wrong.
2. Pick the "probability source": the default is "market (de-vig)" (recommended for most users); "model probability (experimental)" is for advanced comparison — the result card switches to experimental colours and always shows the market reference alongside.
3. Search and select your match in the "select match" picker.
4. Pick the "bet type" (Match result (1X2) = home/draw/away; over/under = total goals) and the "outcome".
5. For over/under an extra "goal line" field appears, prefilled with the current market line: in market mode, changing it shows "line mismatch" and no EV is computed; in model mode any line within 1.5–4.5 (0.25 steps) works.
6. Pick your "odds format" (Taiwan Sports Lottery = Decimal; Canadian friends can pick American/Moneyline — see chapter 2) → enter the odds your app shows → (optional) enter your bankroll.
7. Read the result card: EV% with the traffic-light verdict (chapter 4), "per 100 staked…", "breakeven win rate vs fair probability", the suggested stake (¼ Kelly; model mode must pass the calibration gate first), and same-line price comparison (which book has the best price).
8. If an "approximate" tag appears: this line can push (refund) or settle as split half-stakes, and two-way market odds carry neither — treat the numbers as a guide, not exact values.