Statistical Models

Why Not Machine Learning Models

• Better Interpretation: inference and prediction
• Prediction Accuracy: achieve similar performance compared to tree-based ML models
• Time Saving
  • save training time
  • no need for parameter tuning, cross-validation

Model Formulation

$$logit[Pr(i \succ j \ \text{in game} \ k)] = (\lambda_i - \lambda_j)^{\top} \beta + \delta \cdot I(i \in adv)+ \gamma^{\top} z_{ij}$$

where $\lambda_i$ and $\lambda_j$ are the team performance vectors defined based on feature engineering. $I(I \in adv)$ is the indicator for home-court advantage, and $z_{ij}$ are some potential effects not included in the team performance, such as western-eastern effect.

Evaluation Metric

Cross-Entropy Loss

$$\mathcal{L} = - \sum_{i=1}^N y_i log(\hat{p_i})+(1-y_i) log(1-\hat{p_i})$$

Prediction Results

Model Checking

• Overdispersion: quasi-likelihood approach