Not sure if someone has asked this before. But according to your equation it should be impossible to level up after a loss. Why then did my friend. Who I know had a very high sigma. Level from 4 to 5. After playing team doubles with me. I think I was around 40 at the time. Game 1: http://www.bungie.net/Stats/GameStatsHalo3.aspx?gameid=176038835&player=Blebbins Win Level 1 - 4 Game 2: http://www.bungie.net/Stats/GameStatsHalo3.aspx?gameid=176044027&player=Blebbins Loss Level 4 -5 Game 3 http://www.bungie.net/Stats/GameStatsHalo3.aspx?gameid=176049375&player=Blebbins Loss Stayed Level 5 Maybe I am missing something. We got creamed in game 2 and he still leveled up. The game before We won and he leveled from 1-4. I just don't see how he could level up after losing according to your method?