Chapter 29 Key Takeaways: Neural Networks for Sports Prediction

Key Concepts

1. Feedforward Networks for Tabular Data: Feedforward neural networks apply layers of linear transformations followed by nonlinear activations to learn complex feature interactions. For sports prediction, they serve as flexible function approximators. Architecture design should be conservative: 2-3 hidden layers with 64-256 neurons each, combined with dropout, batch normalization, and weight decay to prevent overfitting on typically small sports datasets.

2. When Neural Networks Beat Tree Models: Neural networks outperform tree-based models (XGBoost, LightGBM) primarily when entity embeddings add value, when sequential patterns matter beyond hand-crafted rolling features, when multi-task learning is beneficial, or when datasets exceed 100,000 observations. For small tabular datasets with well-engineered features, tree models remain competitive and should serve as the baseline.

3. LSTM and Sequence Models: LSTM cells solve the vanishing gradient problem through gated cell states, enabling the network to learn long-range dependencies in game-by-game sequences. The forget, input, and output gates learn when to discard, update, and expose information. For sports prediction, LSTMs can discover temporal patterns --- regime changes, momentum, fatigue effects --- that hand-crafted rolling features may miss.

4. Entity Embeddings: Learned dense vector representations of categorical variables (teams, players, venues) capture similarity structures that one-hot encoding cannot. Similar teams cluster in embedding space. Embeddings require sufficient data per entity (20+ appearances) and can be transferred across seasons to provide warm-start initialization for new models.

5. Training Pipeline Essentials: A production-quality PyTorch pipeline includes: proper data loading with batching and shuffling, forward pass with loss computation, backpropagation with gradient clipping, Adam optimizer with weight decay, ReduceLROnPlateau scheduler, validation-based early stopping, and model checkpointing. Every component serves a specific purpose in producing reliable predictions.

6. Hyperparameter Tuning with Optuna: Bayesian optimization (TPE algorithm) explores the hyperparameter space more efficiently than grid or random search. Optuna's MedianPruner terminates unpromising trials early. For sports networks, tune: number of layers, layer widths, dropout rate, learning rate, weight decay, and batch size.

7. Regularization is Non-Negotiable: Sports datasets are small by deep learning standards (5,000-20,000 observations vs. millions in vision and NLP). Multiple regularization techniques must be combined: early stopping (most important), dropout (0.2-0.5), weight decay (1e-4 to 1e-2), and batch normalization. Omitting regularization virtually guarantees overfitting.

Key Formulas

Neural Network Decision Framework

When building neural networks for sports prediction, follow this process:

Step 1 -- Establish a tree-model baseline. Train XGBoost or LightGBM on your engineered features. This baseline is often hard to beat and provides a performance floor.

Step 2 -- Start with a simple feedforward network. Use 2 hidden layers, 128/64 neurons, dropout 0.3, Adam optimizer with lr=1e-3 and weight_decay=1e-4. Early stopping with patience 15. Compare to the tree baseline.

Step 3 -- Add entity embeddings if you have high-cardinality categoricals. Teams, players, venues. Use the dimension heuristic as a starting point. This is the most common source of neural network advantage over trees.

Step 4 -- Add LSTM components only if temporal sequences add value. Build a game-sequence dataset, train an LSTM, and compare to the feedforward model. The LSTM should demonstrate improvement on validation data before you commit to the added complexity.

Step 5 -- Tune hyperparameters with Optuna. Run 50-200 trials with MedianPruner. Focus on architecture parameters first, training parameters second.

Step 6 -- Ensemble multiple models. Train 5-10 models with different seeds; average predictions. The ensemble typically outperforms any single model.

Step 7 -- Evaluate rigorously. Use Brier score on walk-forward validation. Compare to the tree baseline with the Diebold-Mariano test. Only deploy the neural network if it significantly outperforms the baseline.

The core principle: Complexity must earn its place. Every architectural addition --- more layers, LSTM cells, embedding layers, attention mechanisms --- must demonstrate measurable improvement on held-out validation data. A simple 2-layer feedforward network with well-engineered features and proper regularization is a surprisingly strong baseline that many complex architectures fail to beat.

Ready for Chapter 30? Self-Assessment Checklist

Before moving on to Chapter 30 ("Model Evaluation and Selection"), confirm that you can do the following:

• [ ] Build a feedforward neural network in PyTorch with configurable layers, batch normalization, and dropout
• [ ] Implement a complete training loop with early stopping, learning rate scheduling, and gradient clipping
• [ ] Explain the LSTM cell equations and why the cell state update uses addition
• [ ] Create a Dataset and DataLoader for both tabular and sequential sports data
• [ ] Implement entity embeddings for teams and players and combine them with continuous features
• [ ] Transfer learned embeddings from one season to the next
• [ ] Set up and run an Optuna hyperparameter search with trial pruning
• [ ] Explain when neural networks outperform tree models and when they do not
• [ ] Train an LSTM on game sequences and compare to a feedforward baseline
• [ ] Save and load model checkpoints with metadata

If you can check every box with confidence, you are well prepared for Chapter 30. If any items feel uncertain, revisit the relevant sections of Chapter 29 or work through the corresponding exercises before proceeding.