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TrueSkill™ Ranking System: Calculators
TrueSkill™ Ranking System

The TrueSkill™ ranking system is a skill based ranking system for Xbox Live developed at Microsoft Research.


TrueSkill™ Ranking System Calculator (form based)
This rank calculator allows you to directly experience the TrueSkill ranking system as it is used in Xbox Live.


TrueSkill™ Ranking System Calculator (AJAX based)
This rank calculator allows you to directly experience the TrueSkill ranking system as it is used in Xbox Live.


TrueSkill™ Ranking Calculator Short Help

We have setup eight hypothetical players (Alice, Bob, Chris, Darren, Eve, Fabian, George and Hillary) that can be arranged in any team configuration with the drop-down list. We use colour names for the teams: red, blue, green, magenta, brown, black, orange, gray. The game outcome will be specified by assigning teams to ranks; rank 1 is the winner and rank 8 is the lowest scoring team. If two teams on consecutive ranks draw, then just check the Draw checkbox. In the form-based version, your changes will not be directly applied; if results (on the right hand side) are invalid they will be stroked and greyed out. You only need to press the Recalculate Skill Level Distribution button (only in the form based version). The match quality of the current team assignment of players and their skills in terms of Mu and Sigma is the quality of the match before it is played so the game outcome (Team Ranking/Game Outcome column) cannot change the match quality.

We have defined a number of pre-defined team scenarios for your in the Select Game Mode drop-down list (at the bottom). If you wish to define your own team configurations you can either add or delete players (Add Player and Delete Player button). Also, if you want to quickly reset every player's skill to the initial skill assigned when the TrueSkill ranking system sees you for the first time, you can press Reset Skills. If you want to try out a series of game outcomes, you can quickly copy all calculated skills into the skill input boxes on the left by pressing the After->Before (or Before <- After) button.

Finally, the TrueSkill ranking system allows to set the chance of drawing for two equally skilled players in the Draw Probability text box. For example, for a Street Race type of game you should set 0% whereas for a Capture-the-Flag type of game, you may want to try 25%. Ok, enough said: Enjoy!

TrueSkill™ Ranking Calculator Long Help

Ok, we claim that it only takes 8 straight wins in an tightly matched 8-player-Free-for-All games for a player to get to Level 50 player. Here is the proof using the interactive rank calculator. We will use Alice to win all the games. Use form or AJAX based calculator.

1: Initially, you should see the following screen. If not, then select '8 Free For All' in the Select Game Mode drop-down list.

2: Since we are assuming a tightly matched game, we set the uncertainty of each other player to 1. Note that all the skill estimates and the match quality have been greyed out to indicate that they are no longer valid. Also, we did not need to change the team ranking; we want to assume that Alice won and the red team, Alice's team, is already assigned to the highest rank, rank 1.

3: Now you have to press the Recalculate Skill Level Distribution button.

4: Now you can already see the updated skill of each player on the right hand side. Also, we see that this match would have had a high quality of roughly 40%. In order to simulate the next match, we press the After -> Before button. This copies all values (for example, Mu=34.927 and Sigma=5.374) into the left hand side. Note, again, that a click on the After->Before button greys out all results as they become invalid.

5: Again, we will assume a tightly matched game and thus, every player will get a Mu of 34.927 and all other player's Sigma except Alice's will be set to 1. This should give the following output.

6: Now we keep on repeating steps 3, 4 and 5 seven more times. We then get the following seven screen.

7: There you have it! After the 8th tightly matched game, Alice has a conservative skill level of 56.995 - 3*1.901 = 51.292. Now try to find out many games it would need for Alice to reach level 50 if she only played Head-to-Head.