Not necessarily, look at major trophies won
over last 5 years
Chelsea 5 (6 if they win europa)
United 5
City 2
Liverpool 1
wigan 1
brum 1
swansea 1
over last 10 years
chelsea 10 (11 if they win europa)
united 10
liverpool 3
city 2
arse 2
wigan 1
brum 1
swansea 1
spurs 1
portsmouth 1
over last 5 years
Chelsea 5 (6 if they win europa)
United 5
City 2
Liverpool 1
wigan 1
brum 1
swansea 1
over last 10 years
chelsea 10 (11 if they win europa)
united 10
liverpool 3
city 2
arse 2
wigan 1
brum 1
swansea 1
spurs 1
portsmouth 1