Sounds to me like you need to rethink your table layouts. Initially I see 6 tables:
Players, Teams, Seasons, Games, Game Stats, Awards. Now, here's how I'd do it:
Players
[indent]player_id
team_id
first_name
last_name
jersey_number
height
weight
dominance
*NOTE: The "dominance" field is for whether they're right or left handed (or ambidextrous).[/indent]
Teams
[indent]team_id
team_name
year_founded
head_coach
owner
city
country
team_color1
team_color2
team_color3
mascot
arena_name
mascot_nickname
team_nickname[/indent]
Seasons
[indent]season_id
season_title
start_date
end_date[/indent]
Games
[indent]game_id
season_id
game_date
game_time
home_team_id
away_team_id[/indent]
Game Statistics
[indent]stat_id
game_id
team_id
player_id
season_id
statistic
amount[/indent]
Awards
[indent]award_id
season_id
player_id
award
description[/indent]
Now, the "Awards" table is completely useless in this instance, but it's there as an example of what you could do with setting it up like this. From here, you can query for individual games based upon the "Games" table, or seasons based upon the "Seasons" and "Games" table to find out total number of scores, total number of fights, etc.
So using the above as a guide, you could do something like this:
<?php
// Given that $sid is the season ID
$query = "SELECT CONCAT(p.`last_name`, ', ', p.`first_name`) AS `name`, gs.`amount`
FROM (SELECT MAX(SUM(`amount`)) AS `amount`, `player_id`
FROM `game_stats`
WHERE `season_id` = '" . intval($sid) . "'
GROUP BY `player_id`) AS gs
LEFT JOIN `players` AS p
ON gs.`player_id` = p.`player_id`
ORDER BY gs.`amount` DESC";
$result = mysql_query($query) or die('MySQL Error: ' . mysql_error());
if(!$result || mysql_num_rows($result) < 1)
die('MySQL returned no results. There might have been an error:<br />' . mysql_error());
$row = mysql_fetch_row($result);
echo 'The leading scorer for the requested season was ' . $row['name'] . ' with ' . $row['amount'] . ' total scores throughout the season.';
Now the SQL might need some tweaking, but that's how i'd go about doing it. You can get a lot more information from the tables if you set it up like this. You could combine some tables if you really wanted to; however, you then need to think about trades, a misspelling in a name (or names) and maintenance.
Hope I helped somehow...