SQL Calculate winning and losing streaks

If I have a SQL table that looks like this below how can I calculate the current winning or losing streak (and having the winning or losing streak grouped/reset by season). I want to update the table and fill in the streak for every record.

So for #1 the streak would be "-1", #2 would be "1", #3 would be "2" but once we got down to #7 it would be reset to "1" again. (+1 means "Won 1 game" and -1 means "Lost 1 game", etc.)

ID    team    date         Result    season     streak
1     76ers   2000-01-01   Loss      2000       Null
2     76ers   2000-01-05   Win       2000       Null
3     76ers   2000-01-08   Win       2000       Null
4     Lakers  2000-01-03   Loss      2000       Null
5     Lakers  2000-01-07   Loss      2000       Null
6     Lakers  2000-01-01   Win       2000       Null

7     76ers   2002-03-01   Win       2001       Null
8     76ers   2002-03-05   Win       2001       Null
9     76ers   2002-03-08   Loss      2001       Null
10    Lakers  2002-03-03   Loss      2001       Null
11    Lakers  2002-03-07   Loss      2001       Null
12    Lakers  2002-03-01   Win       2001       Null

For each game, count games with the same result that came before it, such that there is no game with the opposite result in between. Store the results in a temporary table:

CREATE TEMPORARY TABLE STREAK_TABLE
SELECT
    ID,
    (
        SELECT 1 + COUNT(*)                 -- Earlier games with the same result, team and season.
        FROM YOUR_TABLE T2
        WHERE
            T1.Result = T2.Result
            AND T1.team = T2.team
            AND T1.season = T2.season
            AND T1.date > T2.date
            AND NOT EXISTS (
                SELECT *                    -- The games in between, with the same team and season but opposite result.
                FROM YOUR_TABLE T3
                WHERE
                    T2.Result <> T3.Result
                    AND T1.team = T3.team
                    AND T1.season = T3.season
                    AND T3.date BETWEEN T2.date AND T1.date
            )
    ) S
FROM YOUR_TABLE T1

Then, update the original table (and negate the losing streaks in the process):

UPDATE YOUR_TABLE
SET streak = (
    SELECT CASE Result WHEN 'Win' THEN S ELSE -S END
    FROM STREAK_TABLE
    WHERE STREAK_TABLE.ID = YOUR_TABLE.ID
)

Finally, clean-up the temporary table: