# TrueSkill - Through Time

Rust port of [TrueSkillThroughTime.py](https://github.com/glandfried/TrueSkillThroughTime.py).

## Other implementations

- [ttt-scala](https://github.com/ankurdave/ttt-scala)
- [ChessAnalysis #F](https://github.com/lucasmaystre/ChessAnalysis)
- [TrueSkillThroughTime.jl](https://github.com/glandfried/TrueSkillThroughTime.jl)
- [TrueSkillThroughTime.R](https://github.com/glandfried/TrueSkillThroughTime.R)
- [TrueSkill Through Time: Revisiting the History of Chess](https://www.microsoft.com/en-us/research/wp-content/uploads/2008/01/NIPS2007_0931.pdf)
- [TrueSkill Through Time. The full scientific documentation](https://glandfried.github.io/publication/landfried2021-learning/)

## Drift

Skill drift models how a player's true skill can change between appearances. Each time a player reappears after a gap, their skill uncertainty is widened by the drift model before the new evidence is incorporated.

Drift is represented by the `Drift` trait:

```rust
pub trait Drift: Copy + Debug {
    fn variance_delta(&self, elapsed: i64) -> f64;
}
```

`variance_delta` returns the amount to add to `σ²` given the elapsed time since the player last played. Internally, `Gaussian::forget` uses this to compute the new sigma: `σ_new = sqrt(σ² + variance_delta)`.

### ConstantDrift

The built-in `ConstantDrift` implements a linear random walk — skill uncertainty grows proportionally to time:

```
variance_delta = elapsed * γ²
```

This is the standard TrueSkill Through Time model. Use it by passing a `ConstantDrift(gamma)` when constructing a `Player`:

```rust
use trueskill_tt::{Player, Gaussian, drift::ConstantDrift};

// gamma = 0.1 means skill can shift ~0.1 per time unit
let player = Player::new(Gaussian::from_ms(0.0, 6.0), 1.0, ConstantDrift(0.1));
```

### Custom drift

Implement `Drift` to express any other model. For example, a drift that saturates after a long absence (uncertainty grows with the square root of elapsed time instead of linearly):

```rust
use trueskill_tt::drift::Drift;

#[derive(Clone, Copy, Debug)]
struct SqrtDrift {
    gamma: f64,
}

impl Drift for SqrtDrift {
    fn variance_delta(&self, elapsed: i64) -> f64 {
        (elapsed as f64).sqrt() * self.gamma * self.gamma
    }
}

let player = Player::new(Gaussian::from_ms(0.0, 6.0), 1.0, SqrtDrift { gamma: 0.5 });
```

To use a custom drift type with `History`, use the `.drift()` builder method instead of `.gamma()`:

```rust
let h = History::builder()
    .drift(SqrtDrift { gamma: 0.5 })
    .build();
```

## Todo

- [x] Implement approx for Gaussian
- [x] Add more tests from `TrueSkillThroughTime.jl`
- [ ] Add tests for `quality()` (Use [sublee/trueskill](https://github.com/sublee/trueskill/tree/master) as reference)
- [ ] Benchmark Batch::iteration()
- [ ] Time needs to be an enum so we can have multiple states (see `batch::compute_elapsed()`)
- [ ] Add examples (use same TrueSkillThroughTime.(py|jl))
- [ ] Add Observer (see [argmin](https://docs.rs/argmin/latest/argmin/core/trait.Observe.html) for inspiration)