从以下的体育比赛表格中：

对于选定的比赛id_，我希望返回两位选手在他们各自上一场比赛中的统计数据，无论该选手在上一场比赛中是p1还是p2。请参考下面的预期输出，其中id_ = 11456：

在这个大小的表上，以下的SQL语句完全正常运行：

WITH cte_1 AS (
  (
    SELECT 
      id_, 
      match_date, 
      p1_id AS player_id, 
      p1_stat AS stat 
    FROM 
      test.match_table 
    UNION ALL 
    SELECT 
      id_, 
      match_date, 
      p2_id AS player_id, 
      p2_stat AS stat 
    FROM 
      test.match_table
  )
), 
cte_2 AS (
  SELECT 
    id_, 
    player_id, 
    LAG(stat) OVER (
      PARTITION BY player_id 
      ORDER BY 
        match_date, 
        id_
    ) AS prev_stat 
  FROM 
    cte_1
) 
SELECT 
  m.*, 
  cte_p1.prev_stat AS p1_prev_stat, 
  cte_p2.prev_stat AS p2_prev_stat 
FROM 
  test.match_table AS m 
  JOIN cte_2 AS cte_p1 ON cte_p1.id_ = m.id_ 
  AND cte_p1.player_id = m.p1_id 
  JOIN cte_2 AS cte_p2 ON cte_p2.id_ = m.id_ 
  AND cte_p2.player_id = m.p2_id
WHERE m.id_ = 11456
ORDER BY m.match_date

然而，实际的表格有130万行，大约需要12秒的时间。根据这个回答，问题似乎是CTE加载了所有或大部分的表格行，而不仅仅是需要的行。然而，解决方案并没有涵盖这种情况。

是否有人能提供一些建议，以改善性能？、

以下是创建小表格的SQL语句：

CREATE TABLE `match_table` (
  `id_` int NOT NULL AUTO_INCREMENT, 
  `p1_id` int NOT NULL, 
  `p2_id` int NOT NULL, 
  `match_date` date NOT NULL, 
  `p1_stat` int DEFAULT NULL, 
  `p2_stat` int DEFAULT NULL, 
  PRIMARY KEY (`id_`), 
  KEY `ix__p1_id` (`p1_id`), 
  KEY `ix__p2_id` (`p2_id`), 
  KEY `ix__match_date` (`match_date`), 
  KEY `ix__comp` (`p1_id`, `p2_id`, `match_date`)
);
INSERT INTO `match_table` 
VALUES 
  (
    4760, 2, 1, '1998-05-25', 1190, 1486
  ), 
  (6713, 2, 1, '1999-01-18', 2084, 885), 
  (
    9365, 2, 1, '1999-11-01', 2894, 2040
  ), 
  (
    11456, 1, 2, '2000-05-15', 2358, 1491
  ), 
  (
    13022, 1, 2, '2000-08-14', 2722, 2401
  ), 
  (
    29159, 1, 2, '2002-08-26', 431, 2769
  ), 
  (
    44915, 1, 2, '2002-10-07', 1904, 482
  ), 
  (
    852666, 1, 2, '1997-01-01', 1301, 249
  ), 
  (
    852842, 1, 2, '1997-01-13', 2837, 2441
  ), 
  (
    853471, 2, 1, '1997-05-05', 1474, 952
  );