An archive of Mark's Spring 2018 Numerical Analysis course.

LogLoss

mark

This year’s Hogwart’s Quidditch tournament produced the following results:

My Kaggle file for this tournament looked like so:

Huff_Gryf,0.01
Huff_Rave,0.42
Huff_Slyt,0.18
Gryf_Rave,0.95
Gryf_Slyt,0.7
Rave_Slyt,0.2

Compute the LogLoss of my file.

anonymous_user

In this tournament, we have 3 matchups: Gryffindor vs. Ravenclaw in round 1, Hufflepuff vs. Slytherin in the other game of round 1, and finally the championship match between the winners of the first two rounds.

Gryffindor was predicted to beat Ravenclaw with a probability of 0.95, Slytherin was predicted to beat Hufflepuff with a probability of 0.82, and for the Championship match, Gryffindor is favored over Slytherin with a probability of 0.70.

Since all of the match outcomes were as expected, the log loss function is simply

- \frac{1}{N}\sum_{\rm{Quidditch Games}} \log(p)= -\frac{1}{3}(\log(0.95)+\log(0.82)+\log(0.70))=0.08779.