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    openskill
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    3.0.1 • Public • Published

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

    Speed

    Up to 20x faster than TrueSkill!

    Model Speed (higher is better) Variance Samples
    Openskill/bradleyTerryFull 62,643 ops/sec ±1.09% 91 runs sampled
    Openskill/bradleyTerryPart 40,152 ops/sec ±0.73% 91 runs sampled
    Openskill/thurstoneMostellerFull 59,336 ops/sec ±0.74% 93 runs sampled
    Openskill/thurstoneMostellerPart 38,666 ops/sec ±1.21% 92 runs sampled
    Openskill/plackettLuce 23,492 ops/sec ±0.26% 91 runs sampled
    TrueSkill 2,962 ops/sec ±3.23% 82 runs sampled

    See this post for more.

    Installation

    Add openskill to your list of dependencies in package.json:

    npm install --save openskill

    Usage

    If you're writing ES6, you can import, otherwise use CommonJS's require

    import { rating, rate, ordinal } from 'openskill'

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

    > const { rating } = require('openskill')
    > const a1 = rating()
    { mu: 25, sigma: 8.333333333333334 }
    > const a2 = rating({ mu: 32.444, sigma: 5.123 })
    { mu: 32.444, sigma: 5.123 }
    > const b1 = rating({ mu: 43.381, sigma: 2.421 })
    { mu: 43.381, sigma: 2.421 }
    > const b2 = rating({ mu: 25.188, sigma: 6.211 })
    { mu: 25.188, sigma: 6.211 }

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

    > const { rate } = require('openskill')
    > const [[x1, x2], [y1, y2]] = rate([[a1, a2], [b1, b2]])
    [
      [
        { mu: 28.67..., sigma: 8.07...},
        { mu: 33.83..., sigma: 5.06...}
      ],
      [
        { mu: 43.07..., sigma: 2.42...},
        { mu: 23.15..., sigma: 6.14...}
      ]
    ]

    Teams can be asymmetric, too! For example, a game like Axis and Allies can be 3 vs 2, and this can be modeled here.

    Ranking

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

    > const { ordinal } = require('openskill')
    > ordinal({ mu: 43.07, sigma: 2.42})
    35.81

    By default, this returns mu - 3*sigma, showing a rating for which there's a 99.7% 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.

    Artificial Ranking

    If your teams are listed in one order but your ranking is in a different order, for convenience you can specify a ranks option, such as

    > const a1 = b1 = c1 = d1 = rating()
    > const [[a2], [b2], [c2], [d2]] = rate([[a1], [b1], [c1], [d1]], {
        rank: [4, 1, 3, 2] // 🐌 🥇 🥉 🥈
      })
    [
      [{ mu: 20.963, sigma: 8.084 }], // 🐌
      [{ mu: 27.795, sigma: 8.263 }], // 🥇
      [{ mu: 24.689, sigma: 8.084 }], // 🥉
      [{ mu: 26.553, sigma: 8.179 }], // 🥈
    ]

    It's assumed that the lower ranks are better (wins), while higher ranks are worse (losses). You can provide a score instead, where lower is worse and higher is better. These can just be raw scores from the game, if you want.

    Ties should have either equivalent rank or score.

    > const a1 = b1 = c1 = d1 = rating()
    > const [[a2], [b2], [c2], [d2]] = rate([[a1], [b1], [c1], [d1]], {
        score: [37, 19, 37, 42] // 🥈 🐌 🥈 🥇
      })
    [
      [{ mu: 24.689, sigma: 8.179 }], // 🥈
      [{ mu: 22.826, sigma: 8.179 }], // 🐌
      [{ mu: 24.689, sigma: 8.179 }], // 🥈
      [{ mu: 27.795, sigma: 8.263 }], // 🥇
    ]

    Predicting Winners

    For a given match of any number of teams, using predictWin you can find a relative odds that each of those teams will win.

    > const { predictWin } = require('openskill')
    > const a1 = rating()
    > const a2 = rating({mu:33.564, sigma:1.123})
    > const predictions = predictWin([[a1], [a2]])
    [ 0.45110899943132493, 0.5488910005686751 ]
    > predictions[0] + predictions[1]
    1

    Predicting Draws

    Also for a given match, using predictDraw you can get the relative chance that these teams will draw. The number returned here should be treated as relative to other matches, but in reality the odds of an actual legal draw will be impacted by some meta-function based on the rules of the game.

    > const { predictDraw } = require('openskill')
    > const prediction = predictDraw([[a1], [a2]])
    0.09025530533015186

    This can be used in a similar way that you might use quality in TrueSkill if you were optimizing a matchmaking system, or optimizing an tournament tree structure for exciting finals and semi-finals such as in the NCAA.

    Alternative Models

    By default, we use a Plackett-Luce model, which is probably good enough for most cases. When speed is an issue, the library runs faster with other models

    import { bradleyTerryFull } from './models'
    const [[a2], [b2]] = rate([[a1], [b1]], {
      model: bradleyTerryFull,
    })
    • Bradley-Terry rating models follow a logistic distribution over a player's skill, similar to Glicko.
    • Thurstone-Mosteller rating models follow a gaussian distribution, similar to TrueSkill. Gaussian CDF/PDF functions differ in implementation from system to system (they're all just chebyshev approximations anyway). The accuracy of this model isn't usually as great either, but tuning this with an alternative gamma function can improve the accuracy if you really want to get into it.
    • Full pairing should have more accurate ratings over partial pairing, however in high k games (like a 100+ person marathon race), Bradley-Terry and Thurstone-Mosteller models need to do a calculation of joint probability which involves is a k-1 dimensional integration, which is computationally expensive. Use partial pairing in this case, where players only change based on their neighbors.
    • Plackett-Luce (default) is a generalized Bradley-Terry model for k ≥ 3 teams. It scales best.

    Implementations in other languages

    Install

    npm i openskill

    DownloadsWeekly Downloads

    258

    Version

    3.0.1

    License

    MIT

    Unpacked Size

    111 kB

    Total Files

    37

    Last publish

    Collaborators

    • philihp