MySQL Explain: Using index, using temporary, using filesort. Can this query be improved?
Here is your original query

SELECT 
    el.object_id, 
    leo.object_desc, 
    COUNT(el.object_id) as count_rows
FROM 
    event_log el 
    LEFT JOIN lookup_event_objects leo ON leo.object_id = el.object_id
GROUP BY 
    el.object_id
ORDER BY 
    count_rows DESC,
    leo.object_desc ASC
;


It looks as if it is as optimized as it is going to to get

I would change you query

SELECT 
    el.object_id, 
    leo.object_desc, 
    SUM(ISNULL(leo.object_id)=0) as count_rows
FROM 
    event_log el 
    LEFT JOIN lookup_event_objects leo ON leo.object_id = el.object_id
GROUP BY 
    el.object_id
ORDER BY 
    count_rows DESC,
    leo.object_desc ASC
;


This might get you a more accurate count, especially for event logs with no lookup objects.