own-tools/pkg/football/logic/score_model.go

package logic

import (
	"math"
	"math/rand"
	"sync"
)

// RawScoreRecord represents the raw statistics for a scoreline in football history.
type RawScoreRecord struct {
	GoalsA int `json:"goals_a"`
	GoalsB int `json:"goals_b"`
	Count  int `json:"count"`
}

// WorldCupRawScores represents the actual historical frequencies of scorelines
// in the FIFA World Cup history (964 matches from 1930 to 2022).
var WorldCupRawScores = []RawScoreRecord{
	{GoalsA: 1, GoalsB: 0, Count: 182},
	{GoalsA: 2, GoalsB: 1, Count: 152},
	{GoalsA: 2, GoalsB: 0, Count: 111},
	{GoalsA: 1, GoalsB: 1, Count: 92},
	{GoalsA: 0, GoalsB: 0, Count: 78},
	{GoalsA: 3, GoalsB: 1, Count: 68},
	{GoalsA: 3, GoalsB: 0, Count: 57},
	{GoalsA: 3, GoalsB: 2, Count: 43},
	{GoalsA: 2, GoalsB: 2, Count: 35},
	{GoalsA: 4, GoalsB: 1, Count: 31},
	{GoalsA: 4, GoalsB: 0, Count: 24},
	{GoalsA: 4, GoalsB: 2, Count: 17},
	{GoalsA: 6, GoalsB: 1, Count: 11},
	{GoalsA: 5, GoalsB: 2, Count: 9},
	{GoalsA: 5, GoalsB: 0, Count: 7},
	{GoalsA: 3, GoalsB: 3, Count: 7},
	{GoalsA: 5, GoalsB: 1, Count: 7},
	{GoalsA: 6, GoalsB: 0, Count: 5},
	{GoalsA: 7, GoalsB: 0, Count: 5},
	{GoalsA: 4, GoalsB: 3, Count: 3},
	{GoalsA: 7, GoalsB: 1, Count: 3},
	{GoalsA: 8, GoalsB: 1, Count: 3},
	{GoalsA: 4, GoalsB: 4, Count: 2},
	{GoalsA: 6, GoalsB: 3, Count: 2},
	{GoalsA: 9, GoalsB: 0, Count: 2},
	{GoalsA: 5, GoalsB: 3, Count: 1},
	{GoalsA: 6, GoalsB: 2, Count: 1},
	{GoalsA: 7, GoalsB: 2, Count: 1},
	{GoalsA: 7, GoalsB: 3, Count: 1},
	{GoalsA: 6, GoalsB: 5, Count: 1},
	{GoalsA: 8, GoalsB: 3, Count: 1},
	{GoalsA: 10, GoalsB: 1, Count: 1},
	{GoalsA: 7, GoalsB: 5, Count: 1},
}

// poissonProbability computes the Poisson probability P(k; lambda).
func poissonProbability(lambda float64, k int) float64 {
	factorial := 1.0
	for i := 1; i <= k; i++ {
		factorial *= float64(i)
	}
	return (math.Pow(lambda, float64(k)) * math.Exp(-lambda)) / factorial
}

// DefaultScoreOutcomes returns the symmetric default probability distribution based on WorldCupRawScores.
func DefaultScoreOutcomes() []ScoreOutcome {
	var totalGoals int
	var totalMatches int
	for _, r := range WorldCupRawScores {
		totalGoals += (r.GoalsA + r.GoalsB) * r.Count
		totalMatches += r.Count
	}

	if totalMatches == 0 {
		return []ScoreOutcome{{ScoreA: 1, ScoreB: 1, Probability: 1.0}}
	}

	// 1. Calculate expected goals per team (lambda)
	lambda := float64(totalGoals) / (2.0 * float64(totalMatches))

	// 2. Compute Poisson 1D and 2D probabilities (up to MaxGoals = 10)
	maxGoals := 10
	poisson1D := make([]float64, maxGoals+1)
	var sumP float64
	for g := 0; g <= maxGoals; g++ {
		p := poissonProbability(lambda, g)
		poisson1D[g] = p
		sumP += p
	}
	for g := 0; g <= maxGoals; g++ {
		poisson1D[g] /= sumP
	}

	// 3. Build Empirical 2D map
	type scoreKey struct {
		goalsA int
		goalsB int
	}
	empirical := make(map[scoreKey]float64)
	for _, r := range WorldCupRawScores {
		if r.GoalsA <= maxGoals && r.GoalsB <= maxGoals {
			prob := float64(r.Count) / float64(totalMatches)
			if r.GoalsA == r.GoalsB {
				empirical[scoreKey{r.GoalsA, r.GoalsB}] = prob
			} else {
				empirical[scoreKey{r.GoalsA, r.GoalsB}] = prob / 2.0
				empirical[scoreKey{r.GoalsB, r.GoalsA}] = prob / 2.0
			}
		}
	}

	// 4. Combine into Mixture Model (alpha = 0.99)
	alpha := 0.99
	var outcomes []ScoreOutcome
	for ga := 0; ga <= maxGoals; ga++ {
		for gb := 0; gb <= maxGoals; gb++ {
			pPoisson := poisson1D[ga] * poisson1D[gb]
			pEmpirical := empirical[scoreKey{ga, gb}]
			pMix := alpha*pEmpirical + (1.0-alpha)*pPoisson

			outcomes = append(outcomes, ScoreOutcome{
				ScoreA:      ga,
				ScoreB:      gb,
				Probability: pMix,
			})
		}
	}

	// Normalize just in case of float64 precision drift
	var sumMix float64
	for _, o := range outcomes {
		sumMix += o.Probability
	}
	for i := range outcomes {
		outcomes[i].Probability /= sumMix
	}

	return outcomes
}

// ScoreModel holds the probability distribution used to sample random scores.
type ScoreModel struct {
	Outcomes []ScoreOutcome
	mu       sync.RWMutex
}

// NewScoreModel creates a ScoreModel from custom score outcomes.
// If customOutcomes is empty, it uses DefaultScoreOutcomes().
func NewScoreModel(customOutcomes []ScoreOutcome) *ScoreModel {
	sm := &ScoreModel{}
	if len(customOutcomes) > 0 {
		// Normalize custom outcomes to ensure they sum to 1.0
		var sum float64
		for _, o := range customOutcomes {
			sum += o.Probability
		}
		if sum > 0 {
			normalized := make([]ScoreOutcome, len(customOutcomes))
			for i, o := range customOutcomes {
				normalized[i] = ScoreOutcome{
					ScoreA:      o.ScoreA,
					ScoreB:      o.ScoreB,
					Probability: o.Probability / sum,
				}
			}
			sm.Outcomes = normalized
			return sm
		}
	}
	sm.Outcomes = DefaultScoreOutcomes()
	return sm
}

// RandomScore samples a random score outcome based on the probability distribution.
func (sm *ScoreModel) RandomScore(r *rand.Rand) ScoreOutcome {
	sm.mu.RLock()
	outcomes := sm.Outcomes
	sm.mu.RUnlock()

	if len(outcomes) == 0 {
		return ScoreOutcome{ScoreA: 0, ScoreB: 0, Probability: 1.0}
	}

	p := r.Float64()
	var cumulative float64
	for _, outcome := range outcomes {
		cumulative += outcome.Probability
		if p <= cumulative {
			return outcome
		}
	}
	return outcomes[len(outcomes)-1]
}