How is my PvP tournament rating calculated?

Matchmaking Rating Systems

Matchmaking rating systems are used to calculate your matchmaking rating, or "MMR".

MMR is a single point value that reflects your overall skill in Wreck League. We use this to rank you against other players on our tournament leaderboards.

Matchmaking rating systems generally try to calculate points in a way that feels "fair". For example, beating someone who's more skilled than you should give you more points than beating someone who's less skilled than you. These are known as "expected outcomes".

How is my MMR calculated?

Wreck League uses a modified version of the Elo rating system. Elo has been used for decades by chess and sports organizations to rate their tournament play.

Elo rating changes are calculated based on a pairwise comparison between you and your opponent's scores. If your two scores are identical, then the expected outcome of the match is a coin flip — 50/50. The greater the difference between your two scores, the more the expected outcome of the match will skew towards the higher rated player.

Specifically, the expected outcome for Player 1 looks like this:

$$E_1 = \frac{P_1}{(P_1 + P_2)}$$

Where P1 is equal to:

$$P_1 = 10^{R_1 / skill\_deviation}$$

Parameter	Description
R1	Player 1's MMR
skill_deviation	Tuning parameter used for pairwise comparison of how much rating advantage/disadvantage each player has over the other

As mentioned above, if your MMR is identical to your opponent's MMR then the expected outcomes will look like:

$$E_1 = 0.50\\ E2 = 0.50$$

These expected outcomes are then used to determine how much MMR you should gain or lose after your match ends.

If you won:

$$R'_1 = R_1 + Round(Max(min\_point\_gain, k\_factor * (1 - E_1)) + inflation\_points)$$

If you lost:

$$R'_1 = R_1 + Round(Min(min\_point\_loss, k\_factor * -E_1) + inflation\_points)$$

Parameter	Description
min_point_gain	Minimum MMR a winner will gain from any match
min_point_loss	Minimum MMR a loser will lose from any match
k_factor	Maximum possible MMR adjustment per match
inflation_points	Inflationary MMR gained regardless of win/loss

How is this different from a standard Elo rating implementation?

Wreck League differs from standard Elo implementations in a couple ways:

1. Inflationary points help players climb the leaderboard at lower ranks. Engagement is rewarded since there's upwards MMR pressure regardless of whether you win or lose. This is particularly help for players who join late and need to quickly catch up to the competition. Past a certain MMR threshold this value will be set to 0, meaning that rank inflation ceases to exist and score calculation returns to being purely competitive.

2. Unlike other sports and chess organizations that also use Elo rating, our skill_deviation and k_factor tuning parameters won't always be the same. Because our tournaments are of varying lengths and your MMR doesn't carry over between tournaments, we'll need to continually tweak our tuning to create an optimal competitive experience for everyone.