I feel compelled to apologize for the long absence, I’m in the middle of my college finals so the updates are few and far between lately. Sorry for that, you’ll just have to bear with me I’m afraid. Anyway, I figured that I had to at least leave a something of a post at some point, so in a short break from studying I bring an explanation of the Halo trueskill equation. I have been studying the dynamics of the system for awhile and this all seems pretty accurate.

The Trueskill system is a player skill rating system for Xbox Live. Halo 3 uses a version of the Trueskill system in order to make the matches fairly even.

How Does Trueskill Work?

Trueskill assigns skills on a normal distribution (bell curve, Gaussian). The Trueskill system has two main variables to consider. They are your player skill level (Mu) and your uncertainty factor (Sigma).

Mu is an approximation of your skill level based upon past performance. Win games to raise Mu, and lose games to lower Mu.

Sigma is the numerical representation of the range in which your true skill could lie. Play really consistently, and you have a low Sigma. Play streakily, and you have a higher Sigma.

After a win, the Trueskill system adjusts your skill ranking based upon the Mu and Sigma of all the players in the game. We’ll go deeper into how much it is adjusted later.

Trueskill systems use a conservative ranking Ranking = mu - (K * Sigma) so your skill is likely to be higher than the actual number represented in your Halo 3 highest skill level. K is a constant assigned an arbitrary value by the developers of the game.

Why don’t I level up after winning X games in a row? / Why does my friend go up three levels a game and I don’t?

Mu increases after a win. Always. The increase is proportional to the winner’s Sigma and the Mu difference between the winner and the loser. So, if your Sigma is high, you will proceed faster through the ranking system (in BOTH directions). If your Sigma is low, you will both gain and lose rank more slowly.

So, I want a high Sigma value?

While it sounds as though a high Sigma value is desirable, it CAN be a double edged sword. A high Sigma can mean you increase by one level for every win. It also means you decrease by one level for every loss. In addition, a high Sigma means that your skill ranking will be significantly lower than your actual skill owing to the conservative nature of the Ranking = mu - (K * Sigma) ranking equation.

Also, Sigma value starts out VERY high. So, if this is your friend’s first time in a particular ranked hopper, and he wins consistently, his rank will rise meteorically due to his high Sigma.

Unfortunately this is not a guranteed system, but several experts and myself (not even slightly expert) have looked over this and it seems to be fairly accurate. In short, you only gain points for winning and losing games. Game performance does not count, only the skills of the players involved. Unreliable players rise and fall in skill faster. Hopefully people will find this as helpfull as I did.

Note: All credit of the article goes to Baker06 for his excellently explained article.