title: Logloss of binary classifier with constant prediction
body: <p>What is the <code>logloss</code> of a binary classifier if we choose a constant prediction <code>f=0.5</code>?</p>
  
  <p>Is this development of the equation correct?</p>
  
  <pre><code>logloss = (1/N) * sum(-y*log(f)-(1-y)*log(1-f))
  logloss(y=0) = -(1-0)*log(1-f) = -log(f)
  logloss(y=1) = -1*log(f) = -log(f)
  // That is either ground true y is 0 or 1 the cost is -log(f)
  logloss = (1/N) * N * (-log(f)) = -log(f) = -log(5) = 0.69315
  </code></pre>