Multi-Table Groupwise Max Problem where I need a second field along with the max
I'm not a MySQL guy but what about something like the following (for end_hcp)?

Edit: based on syntax comment

SELECT 
    p.division AS Division,
    u.display_name AS Name,
    (select max(end_hcp) from lwljhb_lwl_players where player_id = p.player_id and match_id =(select max(p.match_id) from lwljhb_lwl_players where p.player_id = u.id))
 AS Handicap,
    count(if(result = "Win", 1, NULL)) AS Wins,
    count(if(result = "", 1, NULL)) AS Losses,
    max(high_run) AS "High Run",
    concat(truncate((max(high_run) * 100 / p.end_hcp), 2), '%') AS "HR Pct of Hcp"
FROM 
    `lwljhb_lwl_players` AS p,
    `lwljhb_lwl_matches` AS m,
    `lwljhb_users` AS u
WHERE 
    m.league_seasons_id = 9 AND
    p.match_id = m.id AND
    p.player_id = u.id AND
    u.display_name &lt;&gt; "Bye"
GROUP BY u.display_name
ORDER BY p.division, Wins DESC, Losses