multi_skill/systems/
bar.rs

1//! The so-called Bayesian Approximation Ranking, or Algorithm 1 (BT-Full)
2//! from https://jmlr.csail.mit.edu/papers/volume12/weng11a/weng11a.pdf
3
4use super::util::{standard_logistic_cdf, Player, Rating, RatingSystem, TANH_MULTIPLIER};
5use rayon::prelude::*;
6
7#[derive(Debug)]
8pub struct BAR {
9    pub beta: f64,
10    pub sig_drift: f64,
11    pub kappa: f64,
12}
13
14impl Default for BAR {
15    fn default() -> Self {
16        Self {
17            beta: 400. * TANH_MULTIPLIER / std::f64::consts::LN_10,
18            sig_drift: 35.,
19            kappa: 1e-4,
20        }
21    }
22}
23
24impl BAR {
25    fn win_probability(&self, sig_perf: f64, player: &Rating, foe: &Rating) -> f64 {
26        let c_sq = player.sig.powi(2) + foe.sig.powi(2) + 2. * sig_perf.powi(2);
27        let z = (player.mu - foe.mu) / c_sq.sqrt();
28        standard_logistic_cdf(z)
29    }
30}
31
32impl RatingSystem for BAR {
33    fn round_update(&self, contest_weight: f64, mut standings: Vec<(&mut Player, usize, usize)>) {
34        let all_ratings: Vec<(Rating, usize)> = standings
35            .par_iter_mut()
36            .map(|(player, lo, _)| {
37                player.add_noise_and_collapse(self.sig_drift);
38                (player.approx_posterior, *lo)
39            })
40            .collect();
41
42        let sig_perf_sq = self.beta.powi(2) / contest_weight;
43        standings.into_par_iter().for_each(|(player, my_lo, _)| {
44            let my_rating = &player.approx_posterior;
45            let old_sig_sq = my_rating.sig.powi(2);
46            let mut info = 0.;
47            let mut update = 0.;
48            for (rating, lo) in &all_ratings {
49                let outcome = match my_lo.cmp(lo) {
50                    std::cmp::Ordering::Less => 1.,
51                    std::cmp::Ordering::Equal => 0.5,
52                    std::cmp::Ordering::Greater => 0.,
53                };
54                let probability = self.win_probability(sig_perf_sq.sqrt(), my_rating, rating);
55
56                let c_sq = old_sig_sq + rating.sig.powi(2) + 2. * sig_perf_sq;
57                info += probability * (1. - probability) / c_sq;
58                update += (outcome - probability) / c_sq.sqrt();
59            }
60            // Treat the round as one highly informative match
61            info = 0.25 / (old_sig_sq + 2. * sig_perf_sq);
62            update /= all_ratings.len() as f64;
63
64            // Compute new rating deviation
65            info *= old_sig_sq;
66            let sig = my_rating.sig * self.kappa.max(1. - info).sqrt();
67
68            // Compute new rating
69            update *= old_sig_sq;
70            let mu = my_rating.mu + update;
71
72            player.update_rating(Rating { mu, sig }, 0.);
73        });
74    }
75}
multi_skill/systems/bar.rs

multi_skill/systems/
bar.rs
