The Phi Edge Confidence Score

The confidence score tells you how much to trust a given prediction. It’s a monotonic reliability layer for match-outcome predictions. For each forecast the layer emits two quantities:

confidence score $c \in [0,1]$
confidence tier $k \in \{1,\ldots,K\}$ (default $K = 10$ ), where $1$ denotes the lowest and $K$ the highest reliability class

Interpretation

The confidence score quantifies forecast reliability, not economic value.

The score estimates the conditional probability that the model’s directional call is correct:

c \;\approx\; \mathbb{P}\!\left(\hat{y} = y \;\middle|\; \text{forecast context}\right)

where $\hat{y} = \mathbb{1}\{\hat{p} \geq \tfrac{1}{2}\}$ is the predicted side and $y$ is the realised outcome. A value $c = 0.80$ indicates that, among validation forecasts with comparable characteristics, the directional call was correct approximately 80% of the time.

On the platform, it powers the confidence indicator shown alongside win predictions on match pages.

The score is not:

a measure of expected value, edge, or profitability – reliability and profitability are distinct; a highly reliable forecast may still offer no advantage against market prices, and vice versa
a wager recommendation – it does not prescribe stake size, venue, or whether to participate
a recalibrated win probability – the calibrated probability $\hat{p}^*$ answers how likely the favoured side is to win (e.g. 78% for TKR), whereas the confidence score answers how trustworthy that directional call is

Use $c$ and $k$ to rank and filter forecasts by reliability; apply separate, odds-aware logic for profitability decisions.

Methodology

Predictions are produced by a composite forecasting system whose consolidated probability $\hat{p}$ summarises multiple information sources. Beyond the point forecast, the coherence of constituent estimates provides an auxiliary signal: aligned sub-forecasts suggest stable inference, whereas dispersion suggests latent uncertainty.

The reliability layer is estimated on a held-out validation sample and then fixed. At inference it consumes only model outputs (the consolidated probability and, when available, constituent forecasts); it does not access live match state or post-fit labels, which limits overfitting to in-sample artefacts.

Notation

$\hat{p}$	Consolidated win probability
$\hat{p}^*$	Calibrated probability
$\hat{p}_m$	Constituent forecast m = 1, …, M (when available)
$y$	Realised binary outcome
$\phi$	Latent reliability index
$c$	Confidence score
$k$	Confidence tier

Estimation pipeline

1. Probability calibration.

A monotone mapping $f : [0,1] \to [0,1]$ is fit on validation pairs $(\hat{p}, y)$ :

\hat{p}^* = f(\hat{p})

2. Forecast dispersion.

When multiple constituent forecasts are available, dispersion is summarised by

\delta = \sqrt{\frac{1}{M}\sum_{m=1}^{M}\left(\hat{p}_m - \bar{p}\right)^2}, \qquad \bar{p} = \frac{1}{M}\sum_{m=1}^{M}\hat{p}_m

and standardised using validation moments $\mu_\delta, \sigma_\delta$ :

z = \frac{\delta - \mu_\delta}{\sigma_\delta}

When constituent forecasts are unavailable, the dispersion term is omitted ( $z \equiv 0$ ).

3. Latent reliability index.

Decisiveness of the calibrated forecast is measured by its margin from indifference, adjusted for dispersion:

\phi = \left|\hat{p}^* - \tfrac{1}{2}\right| - \lambda z

where $\lambda \geq 0$ is a fixed penalty coefficient estimated on validation.

4. Reliability score.

A second monotone mapping $g$ links the latent index to the empirical frequency of correct directional calls on validation:

c = g(\phi), \qquad g(\phi) \approx \mathbb{P}(\hat{y} = y \mid \phi)

5. Tier assignment.

Validation quantiles $q_1 < \cdots < q_{K-1}$ of $\phi$ define disjoint reliability classes:

k = 1 + \sum_{j=1}^{K-1} \mathbb{1}\{\phi \geq q_j\}

Tiers are monotonic in $\phi$ and therefore in expected reliability.

Single-forecast fallback

When only a consolidated probability is available, the dispersion term is inactive and reliability reduces to a margin-based index derived from $\hat{p}^*$ alone. The layer is therefore applicable to both composite and single-estimator systems.