Log (Odds)

• The scale in original Odds is not symmetrical
  • The odds of something happening can go from 1 to infinity
  • But the odds of something not happening can go from 1 to 0 which is a small space
  • This asymmetry makes it difficult to compare the odds

[!def] Log Odds Formula
$$
\text{Log-Odds} = log \frac{\text{# of Something Happening}}{\text{# of Something not Happening}}
$$
$$
\text{Log-Odds} = log \frac{probability}{1 - probabiliy}
$$