⚽ League Average Goals
Advanced — Select League or Override
Using defaults: Home 1.50 | Away 1.20 (toggle Advanced to change)
Core Model Input
📋 Full Match — Team Statistics
Games Played
iMatches Played (MP)
Number of games in the sample window. Use last 6–15 games for best results. More games = higher model confidence.
Number of games in the sample window. Use last 6–15 games for best results. More games = higher model confidence.
Goals Scored
iGoals For (GF)
Total goals scored by this team across the MP window. Used to estimate the team's attack rating relative to the league average.
Total goals scored by this team across the MP window. Used to estimate the team's attack rating relative to the league average.
Goals Conceded
iGoals Against (GA)
Total goals conceded across the MP window. Used to estimate the team's defence rating. Lower = stronger defence.
Total goals conceded across the MP window. Used to estimate the team's defence rating. Lower = stronger defence.
⚡ Enter last 6–15 games for best accuracy · Yellow border = key shrinkage inputs
Elo Rating Adjustment
Strength-based λ modifier · ±20% cap
Recent Form
PPG-scaled · FormMult 0.85×–1.15× · combined adj capped ±25%
0 / 5 fields filled
Calculating...
💡 How To Use ScoreMatrix
Step 1 — Full Match Stats: Enter both team names, the number of games played (last 6–15 recommended), total goals scored and goals conceded for that period.
Step 2 — 1st Half Stats (Optional): Tap the [+ 1st Half Stats] button to reveal the half-time inputs. Enter goals scored & conceded in the 1st half only. 2nd half values are automatically calculated as Full Time minus 1st Half — no extra entry needed.
Step 3 — League Averages: By default, Home avg = 1.50 and Away avg = 1.20 goals/match. Toggle Advanced if you want to override these for a specific league (e.g. EPL, Serie A).
Step 4 — Calculate: Hit ⚡ Calculate Predictions. Your most likely score, confidence meter, and all market probabilities will be generated across all tabs.
Step 5 — EV Finder: Navigate to the EV Finder tab and enter bookmaker odds to instantly identify positive expected value (+EV) bets.
New Match: Press the subtle ⊕ NEW button above the team statistics table to clear all fields and start fresh.
Enter team data on the Inputs tab and press Calculate.
Enter team data on the Inputs tab and press Calculate.
📋 Match List
0 matches
No matches added yet. Run the model and hit "Add to Match List".
Calculate predictions first, then enter bookmaker odds to find value bets.
📐 Methodology & FAQ
What model does ScoreMatrix use?
ScoreMatrix uses an adaptive combination of two models:
Dixon-Coles (DC) — the foundation. Models each team's goals as an independent Poisson process, then applies a τ (tau) correction to the four low-score cells (0–0, 1–0, 0–1, 1–1) which plain Poisson systematically underestimates.
Bivariate Poisson — an extension that adds a covariance term ρ (rho) to model the positive correlation between both teams' scoring. Open, high-scoring games tend to produce goals for both sides — Bivariate Poisson captures this structural dependency that independent Poisson misses.
Both models are blended adaptively: ρ and τ are calibrated together using league GPG and matches played via getCorrelationParams(leagueGPG, minMP). The top-right badge always shows the live values.
Dixon-Coles (DC) — the foundation. Models each team's goals as an independent Poisson process, then applies a τ (tau) correction to the four low-score cells (0–0, 1–0, 0–1, 1–1) which plain Poisson systematically underestimates.
Bivariate Poisson — an extension that adds a covariance term ρ (rho) to model the positive correlation between both teams' scoring. Open, high-scoring games tend to produce goals for both sides — Bivariate Poisson captures this structural dependency that independent Poisson misses.
Both models are blended adaptively: ρ and τ are calibrated together using league GPG and matches played via getCorrelationParams(leagueGPG, minMP). The top-right badge always shows the live values.
What is Bivariate Poisson and why does it matter?
Standard Poisson assumes the two teams' goal tallies are independent — Arsenal scoring has no bearing on Chelsea's goals. In reality, open games where one team scores often allow the other to score too (high-scoring leagues, attacking teams, tactical contexts).
Bivariate Poisson adds a covariance parameter ρ (rho):
P(h,a) = Σk [ Poisson(k,λ₃) × Poisson(h−k,λ₁) × Poisson(a−k,λ₂) ]
where λ₃ = ρ√(λH·λA) captures shared scoring momentum.
Effect on outputs: Bivariate raises BTTS Yes probability slightly, raises scorelines like 2–2 and 3–2, and marginally lowers clean-sheet probabilities — all in the correct direction for open attacking matches.
When it activates: ρ scales in smoothly from game 1 using the league GPG context. High-scoring leagues (Bundesliga, Eredivisie) get a lower ρ base since goals are already baked into the lambdas; low-scoring leagues (Serie A) get a higher ρ base to capture their tighter score correlation patterns.
Bivariate Poisson adds a covariance parameter ρ (rho):
P(h,a) = Σk [ Poisson(k,λ₃) × Poisson(h−k,λ₁) × Poisson(a−k,λ₂) ]
where λ₃ = ρ√(λH·λA) captures shared scoring momentum.
Effect on outputs: Bivariate raises BTTS Yes probability slightly, raises scorelines like 2–2 and 3–2, and marginally lowers clean-sheet probabilities — all in the correct direction for open attacking matches.
When it activates: ρ scales in smoothly from game 1 using the league GPG context. High-scoring leagues (Bundesliga, Eredivisie) get a lower ρ base since goals are already baked into the lambdas; low-scoring leagues (Serie A) get a higher ρ base to capture their tighter score correlation patterns.
How are λ (expected goals) calculated?
Attack Rating = Goals Scored/MP ÷ League Avg. Defence Rating = Goals Conceded/MP ÷ opponent's league avg (cross-division). λH = AttH × DefA × lgH. Home/away asymmetry is captured purely by lgH vs lgA.
What is the Dixon-Coles τ (tau) correction?
The τ correction adjusts the four low-score cells (0–0, 1–0, 0–1, 1–1) which independent Poisson models systematically underestimate. τ=0.13 is the default — a higher value gives more weight to low-scoring outcomes. τ is always active regardless of which model mode is running.
What is the Elo adjustment and where do I get Elo ratings?
Elo ratings measure team strength on a single numerical scale. The formula is:
eloFactor = 10^((HomeElo − AwayElo) / 400)
Capped at ±20% effect on lambdas. A 200-point gap (mid-table vs top-4) gives approximately ×1.12 / ×0.89.
Sources: club-elo.com (European clubs) · eloratings.net (international) · FIFA Ranking · Leave blank to skip.
eloFactor = 10^((HomeElo − AwayElo) / 400)
Capped at ±20% effect on lambdas. A 200-point gap (mid-table vs top-4) gives approximately ×1.12 / ×0.89.
Sources: club-elo.com (European clubs) · eloratings.net (international) · FIFA Ranking · Leave blank to skip.
What is recency weighting, and how does it interact with the form multiplier?
Form Multiplier (L6 Pts + GF-trend) is a two-component signal applied to each team's attack lambda:
PPGScore = tanh(pts/mp − 1.35) — "are results better than a 1.35 PPG average lately?"
GFScore = tanh((recentGFRate − seasonGFRate) / seasonGFRate) — "are they scoring more than their season baseline?"
FormIndex = 65% × PPGScore + 35% × GFScore
FormMult = 1 + FormIndex × 0.12 → range (0.88, 1.12)
Defensive Form (separate channel) compares recent GA rate vs season GA baseline and is applied to the opponent's lambda — not the team's own attack. This keeps attack and defense form signals on completely separate inputs with zero shared data.
Sample-size confidence ramps — both signals scale up gradually: attack form reaches full weight at 6 games, defensive form at 8 games (it's noisier). A 2-game sample contributes ~33% / 25% of face value respectively — consistent with the same pattern used for rho/tau calibration.
Combined cap — the attack FormMult and defensive multiplier are combined, then hard-clamped to ±20% of baseline (ADJ_CAP), so no single match's form can swing a lambda more than 20%.
PPGScore = tanh(pts/mp − 1.35) — "are results better than a 1.35 PPG average lately?"
GFScore = tanh((recentGFRate − seasonGFRate) / seasonGFRate) — "are they scoring more than their season baseline?"
FormIndex = 65% × PPGScore + 35% × GFScore
FormMult = 1 + FormIndex × 0.12 → range (0.88, 1.12)
Defensive Form (separate channel) compares recent GA rate vs season GA baseline and is applied to the opponent's lambda — not the team's own attack. This keeps attack and defense form signals on completely separate inputs with zero shared data.
Sample-size confidence ramps — both signals scale up gradually: attack form reaches full weight at 6 games, defensive form at 8 games (it's noisier). A 2-game sample contributes ~33% / 25% of face value respectively — consistent with the same pattern used for rho/tau calibration.
Combined cap — the attack FormMult and defensive multiplier are combined, then hard-clamped to ±20% of baseline (ADJ_CAP), so no single match's form can swing a lambda more than 20%.
What is the Neutral Ground toggle?
When checked, the model removes the structural home advantage encoded in lgH vs lgA. It does this by scaling λH's baseline toward the midpoint of both league averages:
lgNeutral = (lgH + lgA) / 2
homeAdv = lgNeutral / lgH
For symmetric leagues (lgH = lgA = 1.65, as in the WC preset), homeAdv = 1.0 — no change. For asymmetric leagues (lgH=1.50, lgA=1.20), homeAdv ≈ 0.90 — the home team's lambda is reduced by ~10%.
Use for: cup finals, playoff legs at neutral venues, international tournaments. The WC 2026 section enables this automatically.
lgNeutral = (lgH + lgA) / 2
homeAdv = lgNeutral / lgH
For symmetric leagues (lgH = lgA = 1.65, as in the WC preset), homeAdv = 1.0 — no change. For asymmetric leagues (lgH=1.50, lgA=1.20), homeAdv ≈ 0.90 — the home team's lambda is reduced by ~10%.
Use for: cup finals, playoff legs at neutral venues, international tournaments. The WC 2026 section enables this automatically.
How does the WC Group Stage Stats row work?
After selecting both WC teams, a second row appears labelled Current WC Group Stage Stats. Enter each team's MP, GF, GA from their actual group stage matches so far.
The model blends these into the qualification baseline at 2× weight — each WC game counts as two qualification games. The rationale: tournament matches are higher-stakes, current-form, and same-competition data; they should carry more weight than a friendly from 8 months ago.
effectiveGF = qualificationGF + (wcGF × 2)
effectiveMP = qualificationMP + (wcMP × 2)
Leave blank to use qualification data only. The fields are saved across sessions so you don't need to re-enter them.
The model blends these into the qualification baseline at 2× weight — each WC game counts as two qualification games. The rationale: tournament matches are higher-stakes, current-form, and same-competition data; they should carry more weight than a friendly from 8 months ago.
effectiveGF = qualificationGF + (wcGF × 2)
effectiveMP = qualificationMP + (wcMP × 2)
Leave blank to use qualification data only. The fields are saved across sessions so you don't need to re-enter them.
What statistical refinements does ScoreMatrix v3 use?
ScoreMatrix applies five statistical refinements beyond the base Dixon-Coles model:
1. Bayesian Shrinkage — Attack and defence ratings are shrunk toward the league average using an 8-game prior. A team with 4 games and 12 goals is rated closer to 2.0 goals/game (not 3.0) — preventing extreme early-season overreaction.
2. League-average fallback — If inputs produce an invalid lambda, the model falls back to lgH/lgA (league average) rather than 0.5, giving a sensible neutral estimate.
3. Decoupled form multiplier (v3) — FormMult is driven by L5 points only (range ×0.85–×1.15), keeping it structurally independent from the L5 GF/GA used in recency weighting. This eliminates double-counting of recent scoring. GD context is shown in the form index label but does not affect the multiplier.
4. Confidence bands — Model confidence is classified as LOW (<50%), MEDIUM (50–80%), or HIGH (>80%) based on matches played, so users know when to trust the output.
5. Dynamic matrix size — The score matrix expands automatically for high-scoring teams: maxGoals = max(10, ceil(λH + λA + 5)), capturing more tail probability instead of clipping at a fixed ceiling.
1. Bayesian Shrinkage — Attack and defence ratings are shrunk toward the league average using an 8-game prior. A team with 4 games and 12 goals is rated closer to 2.0 goals/game (not 3.0) — preventing extreme early-season overreaction.
2. League-average fallback — If inputs produce an invalid lambda, the model falls back to lgH/lgA (league average) rather than 0.5, giving a sensible neutral estimate.
3. Decoupled form multiplier (v3) — FormMult is driven by L5 points only (range ×0.85–×1.15), keeping it structurally independent from the L5 GF/GA used in recency weighting. This eliminates double-counting of recent scoring. GD context is shown in the form index label but does not affect the multiplier.
4. Confidence bands — Model confidence is classified as LOW (<50%), MEDIUM (50–80%), or HIGH (>80%) based on matches played, so users know when to trust the output.
5. Dynamic matrix size — The score matrix expands automatically for high-scoring teams: maxGoals = max(10, ceil(λH + λA + 5)), capturing more tail probability instead of clipping at a fixed ceiling.
How does the Adaptive Model work?
ScoreMatrix v3 uses a fully league-aware, sample-size-scaled calibration for both ρ (rho) and τ (tau) simultaneously — no hard thresholds or cliffs.
leagueGPG = lgH + lgA — the total goals per game context of the league. Higher GPG (Bundesliga, Eredivisie) → lower rho and tau base values, because open high-scoring leagues have less low-score clustering. Lower GPG (Serie A, Ligue 1) → higher base values.
Confidence curve — both parameters scale together from game 1 using: confidence = (min(homeMP, awayMP) / calibMax) ^ 0.85. For standard league matches, full calibration is reached at 18 games. For cup matches (toggle the Cup match checkbox in League Avg Inputs), full calibration is reached at 10 games, reflecting the smaller typical cup sample. At 5 games confidence≈34%, at 10 games≈61%, at 16 games≈91%, at 18 games=100%.
Why both parameters together? — A high-scoring league not only needs less bivariate covariance (ρ) but also less DC low-score correction (τ), because 0-0 and 1-0 results are genuinely rarer. Calibrating them independently would be inconsistent.
The live ρ, τ, and confidence % are always shown in the top-right badge and Results context bar after you calculate.
leagueGPG = lgH + lgA — the total goals per game context of the league. Higher GPG (Bundesliga, Eredivisie) → lower rho and tau base values, because open high-scoring leagues have less low-score clustering. Lower GPG (Serie A, Ligue 1) → higher base values.
Confidence curve — both parameters scale together from game 1 using: confidence = (min(homeMP, awayMP) / calibMax) ^ 0.85. For standard league matches, full calibration is reached at 18 games. For cup matches (toggle the Cup match checkbox in League Avg Inputs), full calibration is reached at 10 games, reflecting the smaller typical cup sample. At 5 games confidence≈34%, at 10 games≈61%, at 16 games≈91%, at 18 games=100%.
Why both parameters together? — A high-scoring league not only needs less bivariate covariance (ρ) but also less DC low-score correction (τ), because 0-0 and 1-0 results are genuinely rarer. Calibrating them independently would be inconsistent.
The live ρ, τ, and confidence % are always shown in the top-right badge and Results context bar after you calculate.
What are the default league averages?
Home = 1.50, Away = 1.20 goals/match. Toggle Advanced on the Inputs tab to enter custom league averages for your specific league.
Ideal Dixon-Coles τ (Tau)?
τ = 0.13 is recommended for multi-league use. Provides balanced correction for low-scoring scorelines without over-weighting them.
What about Half Time & 2nd Half?
FH and SH now follow the same full pipeline as the full-match model:
1. FH/SH League Baselines — When FH GF data is entered for both teams, the model derives the actual goal-timing split from the data (e.g. 41% FH / 59% SH) rather than assuming a fixed 43/57 split. Falls back to 43/57 if FH data is absent. This makes FH predictions more accurate for leagues or teams that deviate from the average (high-press sides score earlier; low-block sides concede later).
2. Recency Blending — L5 full-match recent rates are scaled proportionally (×0.43 for FH, ×0.57 for SH) and blended 70/30 with the season FH/SH rate. A team that has been pressing aggressively in recent games will show in FH lambda too.
3. Bayesian Shrinkage — FH/SH samples are smaller than FT, so shrinkage toward the league baseline is even more important here. Same 8-game prior as FT.
4. Attack/Defence Ratings — Same cross-division formula as FT (hFHAtt = fhGFRate / lgFHH; hFHDef = fhGARate / lgFHA).
5. Elo Adjustment — Applied to FH and SH lambdas. Stronger teams tend to dominate first halves too.
6. Decoupled Form Multiplier — The same pts-only FormMult from the FT pipeline is applied. No separate FH form system needed.
7. Standard Dixon-Coles (no Bivariate) — FH/SH use DC with tau correction only (rho=0). FH/SH score distributions are much tighter, so the Bivariate covariance term is not needed.
2nd half goals are auto-derived as Full Time minus 1st Half.
1. FH/SH League Baselines — When FH GF data is entered for both teams, the model derives the actual goal-timing split from the data (e.g. 41% FH / 59% SH) rather than assuming a fixed 43/57 split. Falls back to 43/57 if FH data is absent. This makes FH predictions more accurate for leagues or teams that deviate from the average (high-press sides score earlier; low-block sides concede later).
2. Recency Blending — L5 full-match recent rates are scaled proportionally (×0.43 for FH, ×0.57 for SH) and blended 70/30 with the season FH/SH rate. A team that has been pressing aggressively in recent games will show in FH lambda too.
3. Bayesian Shrinkage — FH/SH samples are smaller than FT, so shrinkage toward the league baseline is even more important here. Same 8-game prior as FT.
4. Attack/Defence Ratings — Same cross-division formula as FT (hFHAtt = fhGFRate / lgFHH; hFHDef = fhGARate / lgFHA).
5. Elo Adjustment — Applied to FH and SH lambdas. Stronger teams tend to dominate first halves too.
6. Decoupled Form Multiplier — The same pts-only FormMult from the FT pipeline is applied. No separate FH form system needed.
7. Standard Dixon-Coles (no Bivariate) — FH/SH use DC with tau correction only (rho=0). FH/SH score distributions are much tighter, so the Bivariate covariance term is not needed.
2nd half goals are auto-derived as Full Time minus 1st Half.
What is the EV Finder?
EV% = (Model Prob × Bookie Odds − 1) × 100. Positive EV = bookmaker offering above fair value. Margin-adjusted EV corrects for bookmaker overround — a more realistic measure of true edge.
The EV Finder covers 11 markets: 1X2 (Home/Draw/Away), Over/Under 1.5, Over/Under 2.5, Over/Under 3.5, BTTS Yes/No. Enter the bookmaker's decimal odds for any market to see EV instantly. Rows highlighted in blue indicate >3% edge; 🔥 badge indicates >7% edge.
The Combo Market in the probability bars shows BTTS Yes × Over 2.5 as a joint probability — a popular accumulator leg that isn't directly priced by most bookmakers but can be derived by multiplying the individual prices.
The EV Finder covers 11 markets: 1X2 (Home/Draw/Away), Over/Under 1.5, Over/Under 2.5, Over/Under 3.5, BTTS Yes/No. Enter the bookmaker's decimal odds for any market to see EV instantly. Rows highlighted in blue indicate >3% edge; 🔥 badge indicates >7% edge.
The Combo Market in the probability bars shows BTTS Yes × Over 2.5 as a joint probability — a popular accumulator leg that isn't directly priced by most bookmakers but can be derived by multiplying the individual prices.
What do the EV row highlight colours mean?
After entering bookmaker odds in the EV Finder tab, rows are highlighted by edge strength:
No highlight — edge between 0–3%. Marginal value, within typical model variance.
Blue highlight — edge >3%. Meaningful value worth considering.
🔥 Strong badge — edge >7%. Strong value signal — the model sees a significant mispricing.
These thresholds are guides, not guarantees. Always consider sample size and context.
No highlight — edge between 0–3%. Marginal value, within typical model variance.
Blue highlight — edge >3%. Meaningful value worth considering.
🔥 Strong badge — edge >7%. Strong value signal — the model sees a significant mispricing.
These thresholds are guides, not guarantees. Always consider sample size and context.
What is the Results context bar?
The thin bar at the top of the Results tab shows exactly which settings produced the current output — model mode (Pure DC or DC+Bivariate), τ and ρ values, and both teams' form adjustments. If you changed form or model inputs, it updates on the next Calculate press so you always know what generated the numbers you're looking at.
⚽ World Cup 2026 — Edition Notes
This edition of ScoreMatrix is configured specifically for the 2026 FIFA World Cup (USA · Canada · Mexico, June–July 2026) — the first edition with 48 teams across 104 matches.
Team Database — All 48 qualified teams are pre-loaded with stats compiled from their respective qualification campaigns (CONMEBOL 18-game qualifying, UEFA qualifying + Nations League, CAF, AFC R3, CONCACAF R3, and intercontinental playoffs). Select any team from the World Cup 2026 dropdown to auto-fill.
Neutral Venue Settings — WC matches are played at neutral venues. The model sets lgH = lgA = 1.65 goals/game (based on WC 2026 group stage pace) and homeAdv = 1.0, eliminating home advantage asymmetry. This is the correct setting for tournament football.
Group Stage vs Knockouts — Group stage matches tend to be more open (teams chasing qualification); knockout matches are tighter (elimination pressure, more conservative tactics). Consider adjusting league averages slightly downward (e.g. 1.10/1.10) for semi-finals and finals where both teams play cautiously.
Intercontinental teams — DR Congo, Bahrain, and Curaçao are making rare or debut World Cup appearances. Their stats are based on qualification data but treat model confidence accordingly — smaller competitive sample sizes mean higher uncertainty.
Tournament starts: June 11, 2026 · Final: July 19, 2026 · MetLife Stadium, New Jersey.
Team Database — All 48 qualified teams are pre-loaded with stats compiled from their respective qualification campaigns (CONMEBOL 18-game qualifying, UEFA qualifying + Nations League, CAF, AFC R3, CONCACAF R3, and intercontinental playoffs). Select any team from the World Cup 2026 dropdown to auto-fill.
Neutral Venue Settings — WC matches are played at neutral venues. The model sets lgH = lgA = 1.65 goals/game (based on WC 2026 group stage pace) and homeAdv = 1.0, eliminating home advantage asymmetry. This is the correct setting for tournament football.
Group Stage vs Knockouts — Group stage matches tend to be more open (teams chasing qualification); knockout matches are tighter (elimination pressure, more conservative tactics). Consider adjusting league averages slightly downward (e.g. 1.10/1.10) for semi-finals and finals where both teams play cautiously.
Intercontinental teams — DR Congo, Bahrain, and Curaçao are making rare or debut World Cup appearances. Their stats are based on qualification data but treat model confidence accordingly — smaller competitive sample sizes mean higher uncertainty.
Tournament starts: June 11, 2026 · Final: July 19, 2026 · MetLife Stadium, New Jersey.
Disclaimer
ScoreMatrix is a research and statistical tool. Predictions are probabilistic — not guarantees. Please bet responsibly. — by Victor Korir
📬 Contact the Developer
Questions about the model, licensing, or custom builds? Reach out directly:
✉️ kipvic@yahoo.com WhatsApp: (+254) 794 755 670 📞 (+254) 794 755 670
✉️ kipvic@yahoo.com WhatsApp: (+254) 794 755 670 📞 (+254) 794 755 670