- last post: 01.01.0001 12:00 AM PDT
Posted by: TwoFaced1680
Posted by: Baaaaaaaaaaaaah
Posted by: TwoFaced1680
Posted by: Baaaaaaaaaaaaah
Posted by: TwoFaced1680
Posted by: I3utteRzZ
So...how do I get my sigma higher again, so I can level up faster...again.You can't. Sigma is increased slightly before each calculation to prevent it from ever reaching zero. In general though Sigma always goes down after a game. There is no evidence that shows you can do anything to raise your Sigma.
If Sigma is simply standard deviation, and you go on a streak that consistantly deviates from your expected performance (lots of variance), wouldn't your sigma naturally increase? I would have thought sigma would only approach 0 if you are performing according to the system's expectations.
Been a few years since I have taken a high levels stats course, but that would be my theory.I can't really explain the math behind it, but think of it this way. After each game something is learned about you. Depending on who you played and what the system knows about them will determine just how much can be learned from that one game. Every game you play gives the system a bit more information and allows the system to zero in on your true skill. Thus uncertainty (Sigma) has to go down after each game. In theory once Sigma has dropped very low you should trully be at your skill level and prolonged win streaks shouldn't be possible. However, players skills do change and it's possible you've improved and can suddenly win all your games. In that case the system would increase your skill level over time, but it will take a while to "convince it" to move you.
I absolutely understand that....but I think sigma increases when your "skill" changes, because there is now variation around the expected mean. A larage streak would signify a skill change...so I suspect MU and sigma would go up in that case.Sorry for explaining the obviouse :) I've found no mention in Microsoft's paper that Sigma would begin to rise for any given reason. Here is a quote from the documentation that tells us Sigma goes down after every game:
"The uncertainty of both players (regardless of win/loss/draw) is going to decrease by the factor [equation omitted]"
We know streaks aren't taken into account by TrueSkill. Jay120171 actually wrote microsoft asking this very question and got a response. I'll just post his original post below.
Posted by: Jay120171
OK, so there was a discussion about winning and losing streaks affecting sigma/skill. So, at that time I decided to email MS about it and ask. As it turns out, in the Xbox Live TrueSkill system, it DOES NOT take streaks in to account. Now, we know Bungie uses a modified version of TrueSkill so we can't say with 100% certainty one way or another but still this is useful info.
Here is the email response I received:
TrueSkill as used on Xbox Live stores one mu and one sigma value for each game, game mode; as such, it only takes into account the current game but never considers a streak of wins. BTW, we are currently attending the NIPS conference where we present a paper and an analysis on the game of Chess were we do take whole streaks of wins and losses into account!
Best wishes,
Ralf Herbrich
I think what it comes down to is they lower sigma on a game by game basis rather than take a sample of the most recent games, which I think would be more statistically valid. If you get on a big streak you have volatility around your old expected performance...so sigma should be nowhere close to zero. Older games outside of a reasonable sample set should become less relevant...that way the system recognizes skill changes much quicker.
I can see the current system being frustratingly slow for people that sucked at first, and then improved drastically. Ranking up would take a long, long time.