Openskill

Elixir implementation of Weng-Lin Rating, as described at https://www.csie.ntu.edu.tw/~cjlin/papers/online_ranking/online_journal.pdf

Installation

Add openskill to your list of dependencies in mix.exs:

def deps do
  [
    {:openskill, "~> 1.0"}
  ]
end

Usage

Ratings are kept as a tuple {mu, sigma} which represent a gaussian curve, where mu represents the mean, and sigma represents the spread or standard deviation. Create these with:

> a1 = Openskill.rating
{25, 8.333333333333334}
> a2 = Openskill.rating(32.444, 5.123)
{32.444, 5.123}
> b1 = Openskill.rating(43.381, 2.421)
{43.381, 2.421}
> b2 = Openskill.rating(25.188, 6.211)
{25.188, 6.211}

If a1 and a2 are on a team, and wins against a team of b1 and b2, send this into rank

> [[a1, a2], [b1, b2]] = Openskill.rate([[a1, a2], [b1, b2]])
[
  [
    {28.669648436582808, 8.071520788025197},
    {33.83086971107981, 5.062772998705765}
  ],
  [
    {43.071274808241974, 2.4166900452721256},
    {23.149503312339064, 6.1378606973362135}
  ]
]

In more simplified matches with one team against another, the losing team's players' mu components should always go down, and up for the winning team's players. sigma components should always go down.

Extended usage

You can use Openskill.rate_with_ids to place an identifier next to each rating and preserve that identifier in the result.

> [[a1, a2], [b1, b2]] = Openskill.rate_with_ids([[{"a1", a1}, {"a2", a2}], [{"b1", b1}, {"b2", b2}]])
[
  [
    {"a1", {28.669648436582808, 8.071520788025197}},
    {"a2", {33.83086971107981, 5.062772998705765}}
  ],
  [
    {"b1", {43.071274808241974, 2.4166900452721256}},
    {"b2", {23.149503312339064, 6.1378606973362135}}
  ]
]

This function also has the option `:as_map` which can be used to produce a flat map of the results.
> [[a1, a2], [b1, b2]] = Openskill.rate_with_ids([[{"a1", a1}, {"a2", a2}], [{"b1", b1}, {"b2", b2}]], as_map: true)
%{
  "a1" => {28.669648436582808, 8.071520788025197},
  "a2" => {33.83086971107981, 5.062772998705765},
  "b1" => {43.071274808241974, 2.4166900452721256},
  "b2" => {23.149503312339064, 6.1378606973362135}
}

Showing ratings

When displaying a rating, or sorting a list of ratings, you can use ordinal

> Openskill.ordinal({43.071274808241974, 2.4166900452721256})
35.821204672425594

By default, this returns mu - 3*sigma, showing a rating for which there's a 99.5% likelihood the player's true rating is higher, so with early games, a player's ordinal rating will usually go up and could go up even if that player loses.

TODO

• Support shuffled rankings, e.g. Openskill.rank([[p1],[p2],[p3],[p4]], ranks: [1, 4, 2, 3]).
• Support tied rankings, e.g. Openskill.rank([[p1],[p2],[p3],[p4]], ranks: [1, 2, 2, 4])
• Configurable alternate gamma to avoid ill-conditioning problems from large numbers of teams, as discussed in the paper.