Get streak count and streak type from win-loss-tie data
Since you are on SQL Server 2012 you can use a couple of the new windowing functions.

with C1 as
(
  select T.team_id,
         case
           when M.winning_team_id is null then 'T'
           when M.winning_team_id = T.team_id then 'W'
           else 'L'
         end as streak_type,
         M.match_id
  from FantasyMatches as M
    cross apply (values(M.home_fantasy_team_id),
                       (M.away_fantasy_team_id)) as T(team_id)
), C2 as
(
  select C1.team_id,
         C1.streak_type,
         C1.match_id,
         lag(C1.streak_type, 1, C1.streak_type) 
           over(partition by C1.team_id 
                order by C1.match_id desc) as lag_streak_type
  from C1
), C3 as
(
  select C2.team_id,
         C2.streak_type,
         sum(case when C2.lag_streak_type = C2.streak_type then 0 else 1 end) 
           over(partition by C2.team_id 
                order by C2.match_id desc rows unbounded preceding) as streak_sum
  from C2
)
select C3.team_id,
       C3.streak_type,
       count(*) as streak_count
from C3
where C3.streak_sum = 0
group by C3.team_id,
         C3.streak_type
order by C3.team_id;


SQL Fiddle

C1 calculates the streak_type for each team and match.

C2 finds the previous streak_type ordered by match_id desc.

C3 generates a running sum streak_sum ordered by match_id desc keeping a 0 a long as the streak_type is the same as the last value.

Main query sums up the streaks where streak_sum is 0.