로또 프리미엄 Phase 1 — 추천 성과 통계 + 회차 공략 리포트 API

- GET /api/lotto/stats/performance: 채점 이력 기반 성과 통계
  (평균 일치 수, 등수 분포, 무작위 대비 개선율)
- GET /api/lotto/report/latest: 다음 회차 공략 리포트 자동 생성
- GET /api/lotto/report/{drw_no}: 특정 회차 공략 리포트
  (과출현/냉각/오버듀 번호, 최근 패턴, 3가지 전략 추천, 신뢰도 점수)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/app/db.py

@@ -596,6 +596,54 @@ def delete_recommendation(rec_id: int) -> bool:
         cur = conn.execute("DELETE FROM recommendations WHERE id = ?", (rec_id,))
         return cur.rowcount > 0
 
+def get_recommendation_performance() -> Dict[str, Any]:
+    """채점된 추천 이력 기반 성과 통계"""
+    with _conn() as conn:
+        rows = conn.execute(
+            "SELECT correct_count, rank FROM recommendations WHERE checked = 1"
+        ).fetchall()
+
+    if not rows:
+        return {
+            "total_checked": 0,
+            "avg_correct": 0.0,
+            "distribution": {str(i): 0 for i in range(7)},
+            "rate_3plus": 0.0,
+            "rate_4plus": 0.0,
+            "by_rank": {"rank_1": 0, "rank_2": 0, "rank_3": 0, "rank_4": 0, "rank_5": 0, "no_prize": 0},
+            "vs_random": {"our_avg": 0.0, "random_avg": 0.8, "improvement_pct": 0.0},
+        }
+
+    total = len(rows)
+    corrects = [r["correct_count"] or 0 for r in rows]
+    ranks = [r["rank"] or 0 for r in rows]
+    avg_correct = sum(corrects) / total
+
+    RANDOM_AVG = 0.8  # 이론 기댓값: 6 * (6/45)
+    improvement = (avg_correct - RANDOM_AVG) / RANDOM_AVG * 100
+
+    return {
+        "total_checked": total,
+        "avg_correct": round(avg_correct, 3),
+        "distribution": {str(i): corrects.count(i) for i in range(7)},
+        "rate_3plus": round(sum(1 for c in corrects if c >= 3) / total, 4),
+        "rate_4plus": round(sum(1 for c in corrects if c >= 4) / total, 4),
+        "by_rank": {
+            "rank_1": ranks.count(1),
+            "rank_2": ranks.count(2),
+            "rank_3": ranks.count(3),
+            "rank_4": ranks.count(4),
+            "rank_5": ranks.count(5),
+            "no_prize": ranks.count(0),
+        },
+        "vs_random": {
+            "our_avg": round(avg_correct, 3),
+            "random_avg": RANDOM_AVG,
+            "improvement_pct": round(improvement, 1),
+        },
+    }
+
+
 def update_recommendation_result(rec_id: int, rank: int, correct_count: int, has_bonus: bool) -> bool:
     with _conn() as conn:
         cur = conn.execute(