So in each of these statements:
$v->ExistsInTable('League Id', $_GET['league'], 'teams', 'League_Id');
$v->ExistsInTable('Player Id', $_GET['player'], 'players', 'Player_Id');
$v->IsNumeric('League Id', $_GET['league'], 1, NULL);
// ...
$league = new League($_GET['league']);
$player = new Player($_GET['player']);
// ...
$stats = $player->PlayerStatsTable($_GET['player'], $_GET['league']);
// ...
if (file_exists('/home/sois/public_html/leaguestatbook/engine/images/headshots/' . $_GET['player'] . '.png'))
you're referencing external variables without first checking that they actually exist (e.g. via [man]isset/man, [man]empty/man, [man]array_key_exists/man, etc.). If they don't, you'll see the error messages you posted above.