Formula 1 has evolved into a data-centric sport where strategic decisions, particularly tire compound selection (Soft, Medium, Hard), are critical for success. The ability to accurately identify a competitor's compound from observable telemetry data offers a significant strategic advantage, yet the predictive signals are subtle and difficult to distinguish. This study implements and compares two distinct machine learning methodologies to classify F1 tyre compounds using telemetry data from the 2022 Dutch Grand Prix. First, a baseline model was established using standard dynamic features (e.g., avg_speed, avg_rpm). While this approach confirmed the superiority of XGBoost over SVC, it yielded a modest accuracy of 67.99% and revealed a critical deficiency: a failure to reliably identify the HARD compound, registering a poor F1-score of 0.57. To address these limitations, an advanced methodology was developed, integrating hybrid feature engineering (e.g., LapTime, SectorTime, TyreLife) with deep hyperparameter optimization via Optuna. This enhanced approach resulted in a significantly more robust XGBoost model, achieving a final, stable accuracy of 77.34%. More importantly, it solved the baseline's primary flaw, increasing the F1-score for the critical HARD compound by 36.8% to 0.78. A feature importance analysis confirmed this methodological shift, as the most dominant predictors changed from the baseline's generalized avg_speed to the advanced model's outcome-based features (LapTime, Sector3Time). The findings definitively conclude that while algorithm selection is important, the most critical factor for this task is the quality of feature engineering. Integrating outcome-based and strategic-context features is essential to successfully extracting the subtle performance signatures that differentiate F1 tyre compounds.