using System;

public class Program

{

    public static void Main()

    {

        var calc = new PointsCalculator();

        for(int ms=0; ms<=8000; ms += 500)

        {

            double test = calc.GetPointsFor(ms);

            Console.WriteLine(ms + " = " + test);

        }

    }

}

​

public class PointsCalculator

{

    private int MIN_RATING;

    private int MAX_RATING;

​

    private int MIN_POINTS;

    private int MAX_POINTS;

​

    private int SIGMOID_RANGE;

​

    public PointsCalculator(int minRating=1, int maxRating=2000, int minPoints=1, int maxPoints=8000, int sigmoidRange = 20)

    {

        MIN_RATING = minRating;

        MAX_RATING = maxRating;

        MIN_POINTS = minPoints;

        MAX_POINTS = maxPoints;

        SIGMOID_RANGE = sigmoidRange;

    }

​

    public double GetPointsFor(double value)

    {

        return MapToRating(value);

    }

​

    /// <summary>

    /// 

    /// </summary>

    /// <param name="x"></param>

    /// <returns></returns>

    public double Sigmoid(double x)

    {

        return 1 / (1 + Math.Exp(-x));

    }

​

    /// <summary>

    /// Map a value from one range to another

    /// </summary>

    /// <param name="value"></param>

    /// <param name="low"></param>

    /// <param name="high"></param>

    /// <param name="new_low"></param>

    /// <param name="new_high"></param>

    /// <returns></returns>

    private double MapToRange(double value, int low, int high, int new_low, int new_high)

    {

        return value * 1.0 / (high - low + 1) * (new_high - new_low + 1);

    }

​

    /// <summary>

    /// Map a value from its rating range to the sigmoid range

    /// </summary>

    /// <param name="value"></param>

    /// <param name="max"></param>

    /// <returns></returns>

    private double MapToSigmoid(double value, int max = 0)

    {

        if(max == 0) max = SIGMOID_RANGE;

        return MapToRange(value, MIN_RATING, MAX_RATING, 1, max) - (max / 2.0);

    }

​

    /// <summary>

    /// Map a points value to a rating value using the sigmoid function

    /// </summary>

    /// <param name="value"></param>

    /// <param name="max"></param>

    /// <returns></returns>

    private double MapToRating(double value, int max = 0)

    {

        if(max == 0) max = SIGMOID_RANGE;

        double rating_range = MapToRange(value, MIN_POINTS, MAX_POINTS, MIN_RATING, MAX_RATING);

        double sigmoid_range = MapToSigmoid(rating_range, max);

        double s = Sigmoid(sigmoid_range);

        double r = 0.0;

        if(s < 0.5)

        {

            r =  Math.Floor(s * MAX_RATING);

        }

        else

        {

            r = Math.Ceiling(s * MAX_RATING);

        }

        return r;

    }

}

​