Confidence score

Confidence.java

public class Confidence {
  private static double erf(double x) {
    double a1 = 0.254829592;
    double a2 = -0.284496736;
    double a3 = 1.421413741;
    double a4 = -1.453152027;
    double a5 = 1.061405429;
    double p = 0.3275911;
    x = Math.abs(x);
    double t = 1 / (1 + p * x);
    return 1 - ((((((a5 * t + a4) * t) + a3) * t + a2) * t) + a1) * t * Math.exp(-1 * x * x);
  }

  static double snt(double z) {
    return 0.5 * (1.0 + Math.signum(z) * erf(Math.abs(z) / Math.sqrt(2)));
  }

  private final double z;

  public Confidence(double confidence) {
    z = snt(confidence);
  }

  public double confidence(int ups, int downs) {
    int n = ups + downs;
    if (n == 0) {
      return 0;
    }
    double phat = (double) ups / n;
    return Math.sqrt(phat + z * z / (2 * n) - z * ((phat * (1 - phat) + z * z / (4 * n)) / n)) / (1 + z * z / n);
  }

ConfidenceTest.java

public class ConfidenceTest {

  @Test
  public void testConfidence() {
    Confidence confidence = new Confidence(0.80);
    class Score {
      int ups, downs;
      Score(int ups, int downs) {
        this.ups = ups;
        this.downs = downs;
      }
      double confidence() {
        return confidence.confidence(ups, downs);
      }
    }

    Score s1 = new Score(1, 0);
    Score s2 = new Score(10, 1);
    Score s3 = new Score(40, 20);
    Score s4 = new Score(100, 40);

    List<Score> scores = asList(s1, s2, s3, s4);
    scores.sort(Comparator.comparing(Score::confidence).reversed());
    assertThat(scores, is(equalTo(asList(s2, s4, s3, s1))));
  }
}