1. The Theoretical Boundary of Pre-Match Features
The XGBoost model powering Tennis Glicko is trained on historical pre-match feature matrices I_pre, comprising surface-adjusted Glicko-2 ratings, Elo ratings, head-to-head history, rest days, and tournament tier dynamics.
Mathematically, the output is a prior probability distribution P(Y=1 | I_pre). It answers a specific question: Given historical performance up to time t_0, what is the probability that Player A wins the match?
This formulation explicitly excludes intra-match state variables $S_t$ (e.g., service hold rates in current set, physical distress, weather/wind shifts during play, break point conversions).
2. Point-by-Point State Transitions: Markov Chains vs Static Gradient Boosting
Live, in-play tennis modeling requires dynamic state-space tracking. A tennis match can be modeled as a discrete-time Markov Chain where the state S_t = (g_A, g_B, s_A, s_B, server) tracks games, sets, and points.
In a live environment, the win probability updates conditional on point outcomes:
Because static pre-match XGBoost architectures cannot dynamically update state transitions during a match, attempting to apply pre-match model outputs or VOPO deltas to live markets constitutes an out-of-domain statistical error.
3. Summary of Model Application Boundaries
| USE CASE | STATUS | RATIONALE |
|---|---|---|
| Pre-Match Line Evaluation | VALID | Features strictly match pre-game information state I_pre. |
| Historical Backtesting | VALID | Evaluates out-of-sample Brier Score against closing lines. |
| Live In-Play Execution | INVALIDATED | Lacks Markov point-by-point dynamic state updating. |
| Micro-Betting / Next Point | INVALIDATED | Model does not estimate intra-game serve/return probabilities. |
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