The optimization process and recommendations:

1. Avoid Calling Functions With Indexed Columns (query line: 23): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `GAME_DATE` is indexed, the index won’t be used as it’s wrapped with the function `ABS`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

CREATE INDEX team_1_idx_home_team_opp_team ON TEAM_SUMMARY_1 (HOME_TEAM,OPP_TEAM);

The optimized query:

SELECT
        A.GAME_DATE,
        A.GAME_NUMBER,
        A.INDEXING,
        A.HOME_TEAM,
        A.OPP_TEAM,
        B.OPP_TEAM AS SHARED_OPP,
        B.SCORE_DIFF AS OPP_SCORE_DIFF,
        C.SCORE_DIFF AS HOME_SCORE_DIFF,
        MIN((A.GAME_DATE - B.GAME_DATE) + (A.GAME_DATE - C.GAME_DATE) + ABS(B.GAME_DATE - C.GAME_DATE)) AS TOTAL_DATE_DIFF 
    FROM
        TEAM_SUMMARY_1 A 
    LEFT JOIN
        TEAM_SUMMARY_1 B 
            ON A.OPP_TEAM = B.HOME_TEAM 
    LEFT JOIN
        TEAM_SUMMARY_1 C 
            ON A.HOME_TEAM = C.HOME_TEAM 
    WHERE
        B.OPP_TEAM <> A.HOME_TEAM 
        AND A.OPP_TEAM <> C.OPP_TEAM 
        AND B.OPP_TEAM = C.OPP_TEAM 
        AND ABS(B.GAME_DATE - C.GAME_DATE) < 5 
        AND A.GAME_DATE - B.GAME_DATE < 20 
        AND A.GAME_DATE - B.GAME_DATE > 0 
        AND A.GAME_DATE - C.GAME_DATE < 20 
        AND A.GAME_DATE - C.GAME_DATE > 0 
    GROUP BY
        A.GAME_DATE,
        A.GAME_NUMBER,
        A.INDEXING,
        A.HOME_TEAM,
        A.OPP_TEAM,
        B.OPP_TEAM,
        B.SCORE_DIFF,
        C.SCORE_DIFF 
    ORDER BY
        A.GAME_DATE,
        A.HOME_TEAM,
        A.OPP_TEAM