skillratings 0.29.0

Calculate a player's skill rating using algorithms like Elo, Glicko-2, TrueSkill and many more.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129

use crate::trueskill::erf::{cdf, pdf};

pub fn v_non_draw(difference: f64, draw_margin: f64, c: f64) -> f64 {
    let diff_c = difference / c;
    let draw_c = draw_margin / c;

    let norm = cdf(diff_c - draw_c, 0.0, 1.0);

    if norm < 2.222_758_749e-162 {
        -diff_c + draw_c
    } else {
        pdf(diff_c - draw_c, 0.0, 1.0) / norm
    }
}

pub fn w_non_draw(difference: f64, draw_margin: f64, c: f64) -> f64 {
    let diff_c = difference / c;
    let draw_c = draw_margin / c;

    let norm = cdf(diff_c - draw_c, 0.0, 1.0);

    if norm < 2.222_758_749e-162 {
        if diff_c < 0.0 {
            return 1.0;
        }
        return 0.0;
    }

    let v = v_non_draw(difference, draw_margin, c);

    v * (v + (diff_c) - (draw_c))
}

pub fn v_draw(difference: f64, draw_margin: f64, c: f64) -> f64 {
    let diff_c = difference / c;
    let draw_c = draw_margin / c;
    let diff_c_abs = diff_c.abs();

    let norm = cdf(draw_c - diff_c_abs, 0.0, 1.0) - cdf(-draw_c - diff_c_abs, 0.0, 1.0);

    if norm < 2.222_758_749e-162 {
        if diff_c < 0.0 {
            return -diff_c - draw_c;
        }
        return -diff_c + draw_c;
    }

    let x = pdf(-draw_c - diff_c_abs, 0.0, 1.0) - pdf(draw_c - diff_c_abs, 0.0, 1.0);

    if diff_c < 0.0 {
        -x / norm
    } else {
        x / norm
    }
}

pub fn w_draw(difference: f64, draw_margin: f64, c: f64) -> f64 {
    let diff_c = difference / c;
    let draw_c = draw_margin / c;
    let diff_c_abs = diff_c.abs();

    let norm = cdf(draw_c - diff_c_abs, 0.0, 1.0) - cdf(-draw_c - diff_c_abs, 0.0, 1.0);

    if norm < 2.222_758_749e-162 {
        return 1.0;
    }

    let v = v_draw(difference, draw_margin, c);

    let p1 = pdf(draw_c - diff_c_abs, 0.0, 1.0);
    let p2 = pdf(-draw_c - diff_c_abs, 0.0, 1.0);

    v.mul_add(
        v,
        (draw_c - diff_c_abs).mul_add(p1, -(-draw_c - diff_c_abs) * p2) / norm,
    )
}

pub fn new_rating(
    rating: f64,
    uncertainty: f64,
    v: f64,
    c: f64,
    dynamics_factor: f64,
    rank_multiplier: f64,
) -> f64 {
    let mean_multiplier = uncertainty.mul_add(uncertainty, dynamics_factor.powi(2)) / c;

    (rank_multiplier * mean_multiplier).mul_add(v, rating)
}

pub fn new_uncertainty(uncertainty: f64, c: f64, w: f64, dynamics_factor: f64) -> f64 {
    let variance = uncertainty.mul_add(uncertainty, dynamics_factor.powi(2));
    let dev_multiplier = variance / c.powi(2);

    (variance * w.mul_add(-dev_multiplier, 1.0)).sqrt()
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_wv_edge_cases() {
        let w = w_non_draw(f64::NEG_INFINITY, 0.0, 1.0);

        assert!((w - 1.0).abs() < f64::EPSILON);

        let v = v_non_draw(f64::NEG_INFINITY, 0.0, 1.0);

        assert!(v == f64::INFINITY);

        let w2 = w_draw(f64::NEG_INFINITY, 0.0, 1.0);

        assert!((w2 - 1.0).abs() < f64::EPSILON);

        let v2 = v_draw(f64::NEG_INFINITY, 0.0, 1.0);

        assert!(v2 == f64::INFINITY);

        let w3 = w_non_draw(1.0, f64::INFINITY, 1.0);

        assert!((w3 - 0.0).abs() < f64::EPSILON);

        let v3 = v_draw(f64::INFINITY, f64::MAX, 1.0);

        assert!(v3 == f64::NEG_INFINITY);
    }
}