MySQL: Optimize Join - mysql

Question

I currently try to optimize a MySQL statement. It takes about 10 sec and outputs an average difference of two integer. The event table contains 6 cols and is indexed by it's id and also by run_id + every other key.
The Table holds 3308000 rows for run_id 37, 4162050 in total.
Most time seems to be needed for the join, so maybe there is a way to speed it up.
send.element_id and recv.element_id are unique, is there a way to express it in sql which might lead in a better performance?
|-------------------
|Spalte Typ
|-------------------
|run_id int(11)
|element_id int(11)
|event_id int(11) PRIMARY
|event_time int(11)
|event_type varchar(20)
|event_data varchar(20)
The Query:
select avg(recv.event_time-send.event_time)
from
(
select element_id, event_time
from event
where run_id = 37 and event_type='SEND_FLIT'
) send,
(
select element_id, event_time
from event
where run_id = 37 and event_type='RECV_FLIT'
) recv
where recv.element_id = send.element_id
The Explain of the Query:
+----+-------------+------------+------+-----------------------------------------------------+-------------+---------+-------------+--------+-----------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | extra |
+----+-------------+------------+------+-----------------------------------------------------+-------------+---------+-------------+--------+-----------------------+
| 1 | PRIMARY | <derived3> | ALL | NULL | NULL | NULL | NULL | 499458 | NULL |
| 1 | PRIMARY | <derived2> | ref | <auto_key0> | <auto_key0> | 4 | element_id | 10 | NULL |
| 3 | DERIVED | event | ref | run_id,run_id_2,run_id_3,run_id_4,run_id_5,run_id_6 | run_id_5 | 26 | const,const | 499458 | Using index condition |
| 2 | DERIVED | event | ref | run_id,run_id_2,run_id_3,run_id_4,run_id_5,run_id_6 | run_id_5 | 26 | const,const | 562556 | Using index condition |
+----+-------------+------------+------+-----------------------------------------------------+-------------+---------+-------------+--------+-----------------------+

Answer 1

One way is to group by element_id and to use sum to determine the difference, which you can then pass to avg.
select avg(diff) from (
select
sum(case when event_type = 'SEND_FLIT' then -1 * event_time else event_time end)
as diff
from event
where run_id = 37
and event_type in ('SEND_FLIT','RECV_FLIT')
group by element_id
) t