trueskill-tt/tests/predict_margin.rs

//! `predict_margin`: the predictive distribution of a scored matchup.

use smallvec::smallvec;
use trueskill_tt::{
    ConstantDrift, ConvergenceOptions, Event, History, InferenceError, Member, Outcome, Team,
    UnknownKeys,
};

fn builder(policy: UnknownKeys) -> History {
    History::builder()
        .mu(0.0)
        .sigma(6.0)
        .beta(1.0)
        .score_sigma(2.0)
        .drift(ConstantDrift::new(0.0))
        .unknown_keys(policy)
        .convergence(ConvergenceOptions {
            max_iter: 5_000,
            epsilon: 1e-12,
            alpha: 1.0,
        })
        .build()
}

fn round(a: &'static str, b: &'static str, sa: f64, sb: f64) -> Event<i64, &'static str> {
    Event {
        time: 1,
        teams: smallvec![
            Team::with_members([Member::new(a)]),
            Team::with_members([Member::new(b)]),
        ],
        outcome: Outcome::scores([sa, sb]),
    }
}

/// A history where "veteran" and "regular" are well observed and "novice"
/// appears once.
fn fitted(policy: UnknownKeys) -> History {
    let mut h = builder(policy);
    let mut events: Vec<_> = (0..40)
        .map(|t| round("veteran", "regular", 10.0 + f64::from(t % 3), 5.0))
        .collect();
    events.push(round("veteran", "novice", 10.0, 6.0));
    h.add_events(events).unwrap();
    let _ = h.converge().unwrap();
    h
}

/// The property #48 exists for: the interval must widen when the model knows
/// less. Their hand-fitted noise law quoted the same sigma for a competitor
/// with forty rounds and one with none.
#[test]
fn the_interval_widens_as_the_model_knows_less() {
    let h = fitted(UnknownKeys::Prior);

    let well_known = h
        .predict_margin(&[&[&"veteran"], &[&"regular"]])
        .unwrap()
        .sigma();
    let thin = h
        .predict_margin(&[&[&"veteran"], &[&"novice"]])
        .unwrap()
        .sigma();
    let unseen = h
        .predict_margin(&[&[&"veteran"], &[&"stranger"]])
        .unwrap()
        .sigma();

    assert!(
        well_known < thin && thin < unseen,
        "margin width should grow as evidence thins: {well_known} < {thin} < {unseen}"
    );
}

/// #48's second requirement: an unseen competitor is a legitimate question, not
/// an error, and the answer should come from the prior rather than be faked.
#[test]
fn an_unseen_competitor_is_answered_from_the_prior() {
    let h = fitted(UnknownKeys::Prior);
    let g = h.predict_margin(&[&[&"nobody"], &[&"no_one"]]).unwrap();

    // Two unknowns: the gap is centred on zero and carries both priors plus
    // both performance noises plus the observation noise.
    assert!(g.mu().abs() < 1e-9, "mu {}", g.mu());
    let expected = (2.0 * 36.0 + 2.0 * 1.0 + 4.0f64).sqrt();
    assert!(
        (g.sigma() - expected).abs() < 1e-9,
        "sigma {} vs expected {expected}",
        g.sigma()
    );
}

#[test]
fn reject_still_rejects() {
    let h = fitted(UnknownKeys::Reject);
    assert!(matches!(
        h.predict_margin(&[&[&"veteran"], &[&"stranger"]]),
        Err(InferenceError::UnknownKey { .. })
    ));
}

/// The margin is the *difference*, so it must be antisymmetric in the teams.
#[test]
fn swapping_the_teams_negates_the_margin() {
    let h = fitted(UnknownKeys::Prior);
    let forward = h.predict_margin(&[&[&"veteran"], &[&"regular"]]).unwrap();
    let reverse = h.predict_margin(&[&[&"regular"], &[&"veteran"]]).unwrap();

    assert!((forward.mu() + reverse.mu()).abs() < 1e-9);
    assert!((forward.sigma() - reverse.sigma()).abs() < 1e-12);
}

/// The predictive interval must be wider than the skill gap alone: it also
/// carries per-event performance noise and the observation noise.
#[test]
fn the_predictive_interval_exceeds_the_skill_uncertainty() {
    let h = fitted(UnknownKeys::Prior);
    let skill_gap = h
        .joint()
        .unwrap()
        .posterior_of(&[(&"veteran", 1.0), (&"regular", -1.0)])
        .unwrap();
    let predictive = h.predict_margin(&[&[&"veteran"], &[&"regular"]]).unwrap();

    assert!(
        (predictive.mu() - skill_gap.mu()).abs() < 1e-12,
        "means agree"
    );
    // beta^2 twice plus score_sigma^2 = 2 + 4.
    let expected = (skill_gap.sigma().powi(2) + 6.0).sqrt();
    assert!((predictive.sigma() - expected).abs() < 1e-12);
    assert!(predictive.sigma() > skill_gap.sigma());
}

#[test]
fn shape_errors_are_reported() {
    let h = fitted(UnknownKeys::Prior);
    assert!(matches!(
        h.predict_margin(&[&[&"veteran"]]),
        Err(InferenceError::MismatchedShape {
            expected: 2,
            got: 1,
            ..
        })
    ));
    let empty: [&&str; 0] = [];
    assert!(matches!(
        h.predict_margin(&[&[&"veteran"], &empty]),
        Err(InferenceError::EmptyTeam { team: 1, .. })
    ));
}