Post-league game Update:
Sometimes, the game will freeze at the "Reporting Results" screen. Don't panic. Just let it do it's thing and the game will usually report.
Do NOT turn off your xbox at this screen. There is a queue which reports league games and depending on the league server traffic, it may be backed up.
Just don't do anything until the game reports or you're kicked back to the lobby or menu screen (this is rare). Even if you are kicked, the game might still record so just be patient.
If it records but doesn't show on the website, don't worry as it can take up to 20 minutes to show up.