Chapter 21: Key Takeaways - Modeling Combat Sports and Tennis

1. Elo and Glicko-2 systems provide the foundational backbone for individual sports modeling. The Elo system's simplicity makes it a powerful starting point, but sport-specific calibration of the K-factor is critical. MMA requires K-factors of 100-200 due to infrequent competition, while tennis performs best at 20-32. Glicko-2 adds rating deviation and volatility parameters that naturally handle irregular competition schedules, making it particularly well-suited for combat sports.

2. A single rating is insufficient for tennis; surface-specific ratings are essential. A player's ability on clay may differ by 100+ Elo points from their ability on grass. Surface-adjusted Elo systems that blend overall and surface-specific ratings using a sample-size-dependent weight produce significantly better predictions than overall-only ratings, especially during surface transitions at the start of the clay or grass season.

3. Style matchups systematically modify baseline rating predictions in measurable ways. The boxing proverb "styles make fights" can be quantified through a matchup matrix that encodes the log-odds adjustment for each style pairing. Wrestlers consistently overperform their Elo against strikers and counter-strikers. These adjustments are small (typically 2-6 percentage points) but persistent and valuable for identifying mispriced fights.

4. Physical attributes in combat sports provide quantifiable edges beyond what ratings capture. Reach advantages of 3+ inches add approximately 1-2 percentage points per inch to win probability. Age curves follow a predictable decline after age 30 that accelerates nonlinearly. Severe weight cuts and accumulated knockout vulnerability provide additional predictive signals that the market frequently underweights.

5. Live win probability models for tennis can be computed exactly from serve-win probabilities. Tennis's hierarchical scoring structure (points, games, sets, match) allows recursive computation of exact win probabilities at any score state. The key is Bayesian updating of serve-point-win probabilities as the match progresses, incorporating in-match performance while maintaining appropriate prior influence.

6. MMA live modeling requires tracking three simultaneous components: finish probability, scorecard accumulation, and round-by-round evolution. Unlike tennis, where scoring is deterministic, MMA must account for the ever-present possibility of a fight-ending event (KO, submission, stoppage) alongside the 10-point-must scoring system. Knockdowns and submission attempts dramatically increase within-round finish probability.

7. Inactivity handling separates good individual sports models from mediocre ones. Fighters and players returning from layoffs present a unique challenge. Glicko-2's natural rating deviation growth is elegant, but even simpler Elo systems benefit from inactivity decay mechanisms that increase uncertainty rather than simply penalizing the returning competitor.

8. Indoor/outdoor and altitude effects in tennis are significant and often mispriced. Indoor hard courts play faster than outdoor, benefiting serve-dominant players. High-altitude venues reduce air drag by up to 27%, making serves harder to return and topspin less effective. These environmental factors create systematic edges during indoor seasons and at elevation tournaments.

9. Promotion-tier initialization and informed priors dramatically accelerate Elo convergence. A UFC debutant from a top regional promotion should not start at the same rating as a minor regional fighter. Promotion-based initialization and Bayesian prior information reduce the number of fights needed for ratings to stabilize, which is critical in sports where fighters may only compete 2-3 times per year.

10. The chin deterioration phenomenon in combat sports is irreversible, progressive, and modelable. Career KO/TKO losses, total significant strikes absorbed, and age combine to produce a knockout vulnerability index that predicts future finish susceptibility. This is one of the strongest and most underappreciated signals in combat sports modeling.

11. Individual sports markets are structurally less efficient than major team sports markets. The combination of heterogeneous outcome determinants, less sharp action, frequent competition (in tennis), and the complexity of style/surface/physical interactions creates persistent edges for disciplined quantitative bettors. Lower-tier events and Challenger-level tennis offer the widest market inefficiencies.

12. A complete individual sports betting system integrates all components: ratings, matchups, surface/venue, physical attributes, and live modeling. No single component is sufficient on its own. The Elo/Glicko-2 rating provides the backbone, style matchup analysis adds 2-6 percentage points of adjustment, surface effects add another 3-8 points in extreme cases, and physical attributes contribute additional edge. The live model extends the same framework into the match itself.