Regularization is important for end-to-end speech models, since the models are highly flexible and easy to overfit. Data augmentation and dropout has been important for improving end-to-end models in other domains. However, they are relatively under explored for end-to-end speech models. Therefore, we investigate the effectiveness of both methods for end-to-end trainable, deep speech recognition models. We augment audio data through random perturbations of tempo, pitch, volume, temporal alignment, and adding random noise.We further investigate the effect of dropout when applied to the inputs of all layers of the network. We show that the combination of data augmentation and dropout give a relative performance improvement on both Wall Street Journal (WSJ) and LibriSpeech dataset of over 20%. Our model performance is also competitive with other end-to-end speech models on both datasets.