Underdog Advisor for Soccer Betting — (Unified Betting Portfolios)

Goal: Learn from opening and closing odds/lines to spot value (esp. underdogs & mispricings), then build unified portfolios (mix of singles and 2‑leg parlays) at two risk levels: Low and High.

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Data

Data Source: https://football-data.co.uk/

We used opening and closing odds of Bet365.

Notation (symbols used in formulas)

• Moneyline open: $O_H$ (B365H), $O_D$ (B365D), $O_A$ (B365A)
• Moneyline close: $C_H$ (B365CH), $C_D$ (B365CD), $C_A$ (B365CA)
• Totals open: $O_{&gt;2.5}$ (B365>2.5), $O_{&lt;2.5}$ (B365<2.5)
• Totals close: $C_{&gt;2.5}$ (B365C>2.5), $C_{&lt;2.5}$ (B365C<2.5)
• AH: open line $h_{\text{open}}$ (AHh), close line $h_{\text{close}}$ (AHCh); home odds $O_{\text{AH,H}}$ (B365AHH), away odds $O_{\text{AH,A}}$ (B365AHA); closing $C_{\text{AH,H}}$ (B365CAHH), $C_{\text{AH,A}}$ (B365CAHA)

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Engineered features

To avoid ambiguous subscripts, we introduce simple aliases used only in the formulas below:

$$ \begin{aligned} & \text{Let } O_H,O_D,O_A \text{ be OPEN 1X2 odds; } C_H,C_D,C_A \text{ be CLOSING 1X2 odds}.\\ & \text{Let } O_O,O_U \text{ be OPEN odds for Over/Under 2.5; } C_O,C_U \text{ be CLOSING odds for Over/Under 2.5}.\\ & \text{Let } h_o,h_c \text{ be AH open/close lines; } O_H^{AH},O_A^{AH},C_H^{AH},C_A^{AH} \text{ be AH odds}. \end{aligned} $$

1) 1X2 gaps & changes

$$ \mathrm{ml_{open_gap}} = O_A - O_H $$

$$ \mathrm{ml_{close_gap}} = C_A - C_H $$

$$ \mathrm{ml_{gap_change}} = \mathrm{ml_{close_gap}} - \mathrm{ml_{open_gap}} $$

$$ \mathrm{ml_{open_min}} = \min{O_H,O_D,O_A}, \quad \mathrm{ml_{open_max}} = \max{O_H,O_D,O_A} $$

$$ \mathrm{ml_{close_min}} = \min{C_H,C_D,C_A}, \quad \mathrm{ml_{close_max}} = \max{C_H,C_D,C_A} $$

$$ \mathrm{ml_{delta_H}}=C_H-O_H, \quad \mathrm{ml_{reld_H}}= \frac{C_H}{O_H}-1 $$

$$ \mathrm{ml_{delta_D}}=C_D-O_D, \quad \mathrm{ml_{reld_D}}= \frac{C_D}{O_D}-1 $$

$$ \mathrm{ml_{delta_A}}=C_A-O_A, \quad \mathrm{ml_{reld_A}}= \frac{C_A}{O_A}-1 $$

2) Totals movement (Over/Under 2.5)

$$ \mathrm{tot_{delta_{over}}} = C_O - O_O, \qquad \mathrm{tot_{delta_{under}}} = C_U - O_U $$

$$ \mathrm{tot_{reld_{over}}} = \frac{C_O}{O_O} - 1, \qquad \mathrm{tot_{reld_{under}}} = \frac{C_U}{O_U} - 1 $$

3) Asian Handicap movement

$$ \mathrm{ah_{line_change}} = h_c - h_o $$

$$ \mathrm{ah_{delta_{home_odds}}}=C_H^{AH}-O_H^{AH}, \qquad \mathrm{ah_{reld_{home_odds}}}= \frac{C_H^{AH}}{O_H^{AH}}-1 $$

$$ \mathrm{ah_{delta_{away_odds}}}=C_A^{AH}-O_A^{AH}, \qquad \mathrm{ah_{reld_{away_odds}}}= \frac{C_A^{AH}}{O_A^{AH}}-1 $$

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Models

• Moneyline (1X2) — Multinomial Logistic Regression (softmax).
• Totals (Over 2.5) — Gradient Boosting Classifier.
• AH EV (Home/Away) — Gradient Boosting Regressors (predict per‑unit EV).

All numeric features are imputed and scaled.

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Some Math

Implied probability (naïve)

Given decimal odds $o$,

$$ \hat{p}=\frac{1}{o}. $$

Moneyline (multinomial logistic)

For features $x$ and classes $k\in{H,D,A}$,

$$ P(y=k\mid x)=\frac{e^{w_k^\top x}}{\sum_{j\in{H,D,A}} e^{w_j^\top x}}. $$

Totals (binary)

$$ P(\text{Over}\mid x)=\sigma(f(x))=\frac{1}{1+e^{-f(x)}}. $$

Expected value (single bet)

With model probability $p$ and odds $o$,

$$ \mathrm{EV}=p,(o-1)-(1-p). $$

Variance proxy (per $1)

Let $\mu=\mathrm{EV}$, win payoff $o-1$, loss payoff $-1$:

$$ \sigma^2 = p,(o-1-\mu)^2 + (1-p),(-1-\mu)^2. $$

Scoring & selection

Sharpe‑like score (keep $\mu&gt;0$):

$$ \mathrm{score}=\frac{\mu}{\sigma+\varepsilon}. $$

Kelly stake (capped)

Let $b=o-1$, $q=1-p$,

$$ f^*=\frac{b,p-q}{b}. $$

Parlays (2‑leg, independence)

$$ p_{\text{par}}=p_1p_2,\quad o_{\text{par}}=o_1o_2,\quad \mathrm{EV}_{\text{par}}=p_{\text{par}}(o_{\text{par}}-1)-(1-p_{\text{par}}). $$

AH per‑unit profit (label)

Let $g=\mathrm{FTHG}-\mathrm{FTAG}$, line $h$, odds $o$.
Quarter‑lines split the unit in half; profit:

$$ \mathrm{profit}(g,h,o)= \begin{cases} o-1, & \text{win},\\ 0, & \text{push},\\ -1, & \text{loss}, \end{cases} $$

with half‑wins / half‑losses for $h=\pm0.25,\pm0.75$.

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Usage

python train_model.py --data_dir ./data --models_dir models
python recommend.py --fixture_file tonight.csv --models_dir models --bankroll 1000 --max_games 5 --max_picks 8 --debug

Artifacts: portfolio_low.csv, portfolio_high.csv, *_summary.csv, (--debug) recommend_debug.json.

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Reading the portfolios

Columns: Type, Market, Description, Odds, p, EV_per_unit, Stake, StakePct.
Low‑risk uses tighter caps; High‑risk allows larger stakes and more parlay exposure.

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Worked examples

Here is an example how we find an underdog game EPL: Bournemouth vs Manchester City

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Troubleshooting

• Empty portfolios → all $\mathrm{EV}\le0$ or risk caps filtered them. Check recommend_debug.json.
• Missing columns → the recommender lists them explicitly.
• No models → run training; verify models/ has pickles and meta.json.

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