I don’t know if this helps… but I’ve been updating a dot point type explanation of how I think ranking works for my Halo group. I’ve added a few bits and posted below. It’s still a work in progress!
THE MMR:
Your skill in TrueSkill2 is represented by your MMR - which is a normal curve describing the probability range of your likely rank.
It is not a “simple” number.
The curve has a mean (mu) and a width (described it’s standard deviation, sigma).
The mean of the curve is your most likely skill rank, but there is a 50% chance your actual rank is lower than this.
The important part of the curve is plus or minus three standard deviations from the mean (covering 99.7% of your possible rank range).
The curve starts off wide and free to move (the system has low confidence in your rank) and then, with consistent play, gradually narrows and tends to resist change (higher confidence).
The key to ranking up is to beat teams ranked above you and not to lose to teams ranked below you.
The system uses curves because it allows it to do the fancy maths;
- The player’s curves can be averaged to get a team MMR curve.
- Subtracting team curves gives a probability curve of the expected result.
- And finally the difference and overlap of the player and opponent curves can be used to work out how much the MMR needs to change based on the result.
The MMR is also influenced by personal performance. Specifically by kill and (to a lesser extent) death rates; KPM (kills per minute) and DPM (deaths per minute). These are fundamentally different to conventional metrics such as K/D, KDA, and K-D. Your KPM is a better reflection of you ability to win a “1v1”.
TrueSkill2 can “ball-park” your rank in a handful of games.
And it can very accurately rank you in less than 50 games (for a single player from a 4v4 play list).
The Global MMR;
To minimise the data footprint all the data for your recent games are contained in a “global” MMR. This is the part that holds information on recent form etc.
But each different game mode has it’s own functional MMR curve offset from this. Each has it’s own mu and independent sigma values.
An immature game mode MMR can certainly be influenced by the global MMR, but this effect weakens with game time.
And if you are playing in a brand new game mode then the system “borrows” a current MMR from a similar game mode. In rare cases this may not work very well (eg. if the only mode you have to borrow from is Bots).
YOUR CSR
343 use a CSR to give a single (non-curve) value that has a more stable trajectory than your MMR (which can be very volatile, especially early in the Season).
It goes up with a win, and down with a loss - to a maximum of 15 points.
The bigger the “upset” the bigger the change.
And finally, the CSR is always chasing the left hand edge of your MMR curve. It will tend to resist moving away from this value.
The CSR change at the end of each game does not take into account personal performance for that game. It doesn’t matter how many kills you get. How many flags your return. Or what your K/D was. Your recent personal performance can influence your MMR though, and this will indirectly affect your CSR in the next game.
And finally, it’s not easy to compare CSR changes between players. You don’t know the shape of their MMR curve compared to yours, or the influence of their recent peronal performance.
An Example;
As an example; let’s consider someone with a relatively stable MMR; with a mean of 1500 and a standard deviation of 5.
This would give you a 98% probability curve of having a rank somewhere between 1485 and 1515 (plus or minus three standard deviations from the mean).
Mathematically your MMR will behave closer to the mean of 1500.
Matchmaking will tend to treat you more across the whole range of 1485 to 1515.
As for your CSR, in this case it will be trying to settle at 1485 (three standard deviations below the mean). It will still go up with a win and down with a loss - but it will resist moving too far away from that specific value.
If your CSR is above 1485 it will tend to not go up much with a win and down in bigger jumps with a loss. If your CSR is lower than 1485 it will jump with a win and only small amounts with a loss.
What tends to happen, is that your CSR will oscillate around 1485. It drifts up a bit with each win against sides ranked equal or below you (people often describe grinding up 10 to 15 points) and then falls back down to 1485 with a loss - up to 15 points at a time.
And this is why it’s a bit silly to get hung up over every single CSR point. Your actual MMR is a range. That range is a moving target. And your CSR tries to balance rewarding every win but also not straying too far away from that target. Combine that with the fact that natural form can fluctuate plus or minus 150 points on any given night and it’s just not worth it.