Precision Analysis: World Championship Matches

The Metric

Precision measures how well a player navigated the positions they faced, normalized for difficulty.

precision = 1 - (avg_actual_loss_ev / avg_expected_loss_ev)

• 1.0 = perfect (zero EV loss)
• 0.0 = average (lost exactly what was expected)
• Negative = below expected (lost more than expected)

Expected loss is the probability-weighted average EV loss across all legal moves — what a typical player would lose given the positions faced. Actual loss is what the player actually lost vs the best move. The ratio normalizes for position complexity: a precision of 0.40 means the player avoided 40% of expected EV loss regardless of whether the positions were simple or chaotic.

Actual and expected loss are accumulated independently. In positions where the played move was highly unexpected (< 1% predicted probability), actual loss still counts but expected loss is not accumulated — the player deviated from the model's expectation and should be judged on the result, not the prediction.

Dataset

WCC matches only, excluding tiebreak games and multi-player World Championship tournaments (1948, 2007). Precision computed over positions after ply 16 with ≥ 1 deeply evaluated candidate move.

Correlation with Game Outcome

Tested against game score (1/0.5/0) across 1,780 player-games:

EV Delta dominates (it's almost tautological — it directly measures position shift). Precision captures real quality-of-play signal with R² = 0.102 and produces better rankings at the match and career level because it removes era/complexity bias.

35% of all player-games have negative precision. This breaks down as: 25% of winners, 26% of drawers, 69% of losers.

Precision Gap Predicts Outcome

The gap between two players' precision is strongly predictive of who wins. Across 890 games (r=+0.520, R²=0.270):

When one player's precision exceeds the other's by > 0.3, they win 64% of games and lose only 2%. At the match level (r=+0.535, R²=0.286), the winner has higher precision in 28/39 decisive matches (72%).

Precision by Match

All WCC matches ranked by average precision. Player precision is averaged across all games regardless of color. P1 is the match winner (or higher scorer). Winner has higher precision in 28/39 decisive matches (72%).

Carlsen's +0.530 in 2021 is the best individual match performance on record. Kramnik's +0.417 vs Kasparov's -0.065 in 2000 is the largest precision gap. Notable cases where the winner was outprecised: Carlsen +0.122 vs Anand +0.281 (2013), Carlsen +0.191 vs Karjakin +0.376 (2016).

Player Performance by Match

Precision per player per match, ranked (min 5 evaluated games, tiebreaks excluded):

Karjakin's +0.376 in 2016 is higher than Carlsen's +0.191 in that same match — Carlsen won in tiebreak despite being outplayed in classical precision. Anand at +0.361 in 2014 is the sixth-best individual WCh performance, yet he lost 3-1. Kramnik vs Kasparov 2000 (+0.417) produced his world-championship upset.

Carlsen Across His Five WCh Matches

Carlsen won all five matches yet was outprecised in three of them (2013, 2014, 2016). In 2013 the gap is substantial (+0.122 vs +0.281) — he won by finding tactically decisive positions, not by playing the most accurate chess. The trajectory from 2013 to 2021 is remarkable: his precision more than quadrupled over eight years.

Best Individual Games

Best Single-Player Performances

Three perfect games (zero EV loss) — Smyslov, Petrosian, and Kramnik. Petrosian's stands out: expected loss was 2.38pp (very complex) and he lost nothing. Gelfand's G12 is similarly remarkable: expected loss 1.92pp, actual 0.05pp. Smyslov appears twice in the top 6, both games from his 1957 title-winning match.

Best Combined Games

Kramnik–Topalov WCh 2006 G1 is the highest-precision decisive game. The highest-quality games are overwhelmingly draws — both players at peak precision produces balanced, theoretically sound play.

Worst Combined Games

Worst Single-Player Performances

Marshall's WCh 1907 G14 as Black is the worst individual performance: expected loss was only 0.46pp but he lost 2.49pp — over five times worse than expected. Kasparov's two appearances from the 2000 match (G10 and G13) reflect his uncharacteristic collapse against Kramnik.