MySQL doesn't support analytic functions, but one way of counting sequential wins/losses is via user variables:
SELECT @seq := IF(@teamid<=>teamid AND @win<=>win,@seq,0)+1 seq,
@teamid := teamid teamid,
@win := win win
FROM RESULTS, (SELECT @teamid:=NULL, @win:=NULL) init
ORDER BY teamid, STR_TO_DATE(eventdate, '%d/%m/%Y')
This query can be used as a basis for performing further analysis. For example, to obtain the longest streaks (both winning and losing) by team:
SELECT teamid, win, MAX(seq) FROM (
SELECT @seq := IF(@teamid<=>teamid AND @win<=>win,@seq,0)+1 seq,
@teamid := teamid teamid,
@win := win win
FROM RESULTS, (SELECT @teamid:=NULL, @win:=NULL) init
ORDER BY teamid, STR_TO_DATE(eventdate, '%d/%m/%Y')
) t GROUP BY teamid, win