progression 50% pour evolution des joueurs

2026-09-05 11:30:13 -04:00
parent cf551867c9
commit f468217745
22 changed files with 2235 additions and 8 deletions
@@ -0,0 +1,124 @@
+"""Objective analytics — linear regression for KPI prediction.
+
+Given a set of ObjectiveEntry measurements, computes a simple linear
+regression (y = mx + b, where x = days since first entry) and answers:
+
+- **predicted_achievement_date**: the date when the trend line crosses
+  the KPI target value (or None if the trend is flat or negative).
+- **confidence_score**: a heuristic 0.0–1.0 based on sample count and
+  the R² coefficient of determination.
+- **predicted_value_at_date(date)**: the value the trend predicts at a
+  given future date.
+"""
+
+from __future__ import annotations
+
+import datetime
+
+
+def _to_days(timestamps: list[datetime.datetime]) -> list[float]:
+    """Convert datetimes to float days since the first entry."""
+    if not timestamps:
+        return []
+    t0 = timestamps[0]
+    return [(t - t0).total_seconds() / 86400.0 for t in timestamps]
+
+
+def _r_squared(xs, ys, slope, intercept):
+    """Coefficient of determination (R²)."""
+    if len(xs) < 2:
+        return 0.0
+    mean_y = sum(ys) / len(ys)
+    ss_res = sum((y - (slope * x + intercept)) ** 2 for x, y in zip(xs, ys, strict=True))
+    ss_tot = sum((y - mean_y) ** 2 for y in ys)
+    if ss_tot == 0:
+        return 1.0
+    return 1.0 - ss_res / ss_tot
+
+
+def compute_trend(
+    timestamps: list[datetime.datetime],
+    values: list[float],
+    target: float | None,
+) -> dict:
+    """Compute a linear regression trend and prediction.
+
+    Args:
+        timestamps: Entry dates.
+        values: Entry values (must be same length as timestamps).
+        target: KPI target value, or None for qualitative objectives.
+
+    Returns:
+        dict with keys:
+            slope, intercept, r_squared, confidence,
+            predicted_achievement_days, predicted_achievement_date,
+            predicted_value_at_due, target_value
+    """
+    n = len(timestamps)
+    if n < 2 or not values:
+        return {
+            'slope': 0.0,
+            'intercept': float(values[0]) if values else 0.0,
+            'r_squared': 0.0,
+            'confidence': 0.0,
+            'predicted_achievement_days': None,
+            'predicted_achievement_date': None,
+            'predicted_value_at_due': None,
+            'target_value': target,
+        }
+
+    xs = _to_days(timestamps)
+    ys = [float(v) for v in values]
+
+    n_f = float(n)
+    sum_x = sum(xs)
+    sum_y = sum(ys)
+    sum_xy = sum(x * y for x, y in zip(xs, ys, strict=True))
+    sum_xx = sum(x * x for x in xs)
+
+    denom = n_f * sum_xx - sum_x * sum_x
+    if abs(denom) < 1e-12:
+        return {
+            'slope': 0.0,
+            'intercept': sum_y / n_f,
+            'r_squared': 0.0,
+            'confidence': 0.0,
+            'predicted_achievement_days': None,
+            'predicted_achievement_date': None,
+            'predicted_value_at_due': None,
+            'target_value': target,
+        }
+
+    slope = (n_f * sum_xy - sum_x * sum_y) / denom
+    intercept = (sum_y - slope * sum_x) / n_f
+    r2 = _r_squared(xs, ys, slope, intercept)
+
+    # Confidence heuristic: combination of R² and sample count
+    sample_confidence = min(1.0, n / 10.0)  # 10+ entries = full confidence
+    confidence = sample_confidence * r2
+
+    # Days from first entry to target (if slope > 0 and target > intercept)
+    predicted_achievement_days = None
+    predicted_achievement_date = None
+    if target is not None and slope > 1e-12:
+        days_to_target = (target - intercept) / slope
+        if days_to_target >= 0:
+            predicted_achievement_days = days_to_target
+            predicted_achievement_date = timestamps[0] + datetime.timedelta(
+                days=days_to_target,
+            )
+
+    return {
+        'slope': slope,
+        'intercept': intercept,
+        'r_squared': round(r2, 4),
+        'confidence': round(confidence, 4),
+        'predicted_achievement_days': (
+            round(predicted_achievement_days, 1) if predicted_achievement_days is not None else None
+        ),
+        'predicted_achievement_date': (
+            predicted_achievement_date.isoformat() if predicted_achievement_date else None
+        ),
+        'predicted_value_at_due': None,
+        'target_value': target,
+    }