The main issue is that the inner query cannot be related to your where
clause on the outer update
statement, because the where filter applies first to the table being updated before the inner subquery even executes. The typical way to handle a situation like this is a multi-table update.
Update
Competition as C
inner join (
select CompetitionId, count(*) as NumberOfTeams
from PicksPoints as p
where UserCompetitionID is not NULL
group by CompetitionID
) as A on C.CompetitionID = A.CompetitionID
set C.NumberOfTeams = A.NumberOfTeams