### Install OpenSkillSharp via NuGet

Source: https://github.com/myssto/openskillsharp/blob/master/README.md

Install the OpenSkillSharp package using the .NET CLI or Package Manager Console.

```shell
# via the dotnet CLI
dotnet add package OpenSkillSharp
```

```shell
# via the Package Manager CLI
Install-Package OpenSkillSharp
```

--------------------------------

### Get Ordinal Rating for Sorting

Source: https://github.com/myssto/openskillsharp/blob/master/README.md

Retrieve the ordinal rating, calculated as mu - 3 * sigma, for displaying or sorting ratings. This provides a conservative estimate of a player's true rating.

```csharp
PlackettLuce model = new();
IRating player = model.Rating(mu: 43.07, sigma: 2.42);

player.Ordinal
>> 35.81
```

--------------------------------

### Create and Customize OpenSkillSharp Models

Source: https://github.com/myssto/openskillsharp/blob/master/README.md

Instantiate a rating model with default parameters or customize its properties like Mu and Sigma.

```csharp
// Create a model with default parameters
PlackettLuce model = new();
```

```csharp
// Or customize to your needs
ThurstoneMostellerPart model = new() {
  Mu = 28.67,
  Sigma = 8.07,
  ...
}
```

--------------------------------

### Create Player Ratings

Source: https://github.com/myssto/openskillsharp/blob/master/README.md

Generate player ratings using a model, either with default values or specified Mu and Sigma.

```csharp
PlackettLuce model = new();

IRating a1 = model.Rating();
>> {Rating} {Mu: 25, Sigma: 8.33148112355601}
```

```csharp
IRating a2 = model.Rating(mu: 32.444, sigma: 5.123);
>> {Rating} {Mu: 32.444, Sigma: 5.123}
```

```csharp
IRating b1 = model.Rating(mu: 43.381, sigma: 2.421);
>> {Rating} {Mu: 43.381, Sigma: 2.421}
```

```csharp
IRating b2 = model.Rating(mu: 25.188, sigma: 6.211);
>> {Rating} {Mu: 25.188, Sigma: 6.211}
```

--------------------------------

### Predict Match Winner Probabilities

Source: https://github.com/myssto/openskillsharp/blob/master/README.md

Calculate the relative probabilities of each team winning a match using the PredictWin method. The sum of probabilities for all teams in a match equals 1.

```csharp
PlackettLuce model = new();

Team t1 = new() { Players = [model.Rating()] };
Team t2 = new() { Players = [model.Rating(mu: 33.564, sigma: 1.123)] };

List<double> probabilities = model.PredictWin([t1, t2]).ToList();
>> { 0.45110899943132493, 0.5488910005686751 }

probabilities.Sum();
>> 1
```

--------------------------------

### Update Player Ratings After a Game

Source: https://github.com/myssto/openskillsharp/blob/master/README.md

Update player ratings based on game outcomes using the Rate method. This method takes teams and returns updated teams with new ratings.

```csharp
List<ITeam> result = model.Rate(
  [
    new Team() { Players = [a1, a2] },
    new Team() { Players = [b1, b2] }
  ]
).ToList();

result[0].Players
>> {Rating} {Mu: 28.669648436582808, Sigma: 8.071520788025197}
>> {Rating} {Mu: 33.83086971107981, Sigma: 5.062772998705765}

result[1].Players
>> {Rating} {Mu: 43.071274808241974, Sigma: 2.4166900452721256}
>> {Rating} {Mu: 23.149503312339064, Sigma: 6.1378606973362135}
```

--------------------------------

### Predict Match Draw Probability

Source: https://github.com/myssto/openskillsharp/blob/master/README.md

Estimate the relative chance of a draw occurring in a match using the PredictDraw method. This value is relative to other matches and may need meta-function adjustment for game-specific rules.

```csharp
double prediction = model.PredictDraw([t1, t2]);
>> 0.09025530533015186
```

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