SQL 2012 :: Deadlocks - Not Showing In Profiler

We have some Deadlock alerts set up in SQL Agent that email us when the performance counter for deadlocks goes above zero. I've used the following script to identify the event file which has deadlock information in there.

select CAST(target_data as xml) as TargetData
from sys.dm_xe_session_targets st
join sys.dm_xe_sessions s on s.address = st.event_session_address
where name = 'system_health'

Now that is fine, and we're looking into that (number of deadlocks appear to be 0.5) but out of interest ran a SQL Profiler session to capture the details as well and nothing is showing, I've received a few alerts and the trace file has information in there - but profiler shows absolutely nothing (all deadlock events are captured)