• CHESS ANALYTICS 00: Methods: Measuring World-Championship Roads with Stockfish 18 WDL
• CHESS ANALYTICS 00.0: List of Other Chess Analytics Articles

1. 1. CHESS ANALYTICS 02 part 1/2: Karpov 1978 + 1981 vs. Korchnoi
   1. 1.1. Overall verdict
   2. 1.2. The two matches are very different
   3. 1.3. Karpov–Korchnoi 1978: nearly level
   4. 1.4. Karpov–Korchnoi 1981: clear Karpov superiority
   5. 1.5. Game Accuracy and Mutual Accuracy
   6. 1.6. Overall game-by-game edge
   7. 1.7. Which metrics best explain the scores?
   8. 1.8. Metric-family interpretation
   9. 1.9. Chess-style interpretation
   10. 1.10. Final conclusion
2. 2. CHESS ANALYTICS 02 part 2/2: Karpov 1981 vs. Fischer 1971-72
   1. 2.1. Why Karpov 1981 improves the forecast
   2. 2.2. Why Fischer still retains a small statistical edge
   3. 2.3. The key change: Karpov becomes a much better anti-Fischer candidate
   4. 2.4. Revised estimate
   5. 2.5. Final answer

1. CHESS ANALYTICS 02 part 1/2: Karpov vs. Korchnoi, 1978 + 1981

I treated Anatoly Karpov as the main player and Viktor Korchnoi as the opponent throughout. The uploaded report covers the two Karpov–Korchnoi World-Championship matches, 1978 and 1981, under Stockfish 18 WDL expected-score analysis.

1.1. Overall verdict

The combined 1978+1981 Karpov–Korchnoi run is a story of small but real Karpov superiority, with the sharp contrast that 1978 was nearly equal, while 1981 was clearly Karpov’s match.

Overall metric	Karpov	Korchnoi	Edge / ratio
Score	27.5	22.5	Karpov +5.0
Expected Score	26.757	23.243	Karpov +3.514
Conversion	+0.743	−0.743	+1.486 difference
WDL Accuracy	98.193	98.048	Karpov +0.145
PQ	96.573	96.413	Karpov +0.161
Dominance	+0.165	−0.165	+0.329 difference
Mean ES Loss	0.01807	0.01952	Karpov 7.4% lower
RMS ES Loss	0.04575	0.05035	Karpov 9.1% lower
Error Concentration	2.696	2.824	Karpov 4.5% lower
WDL Volatility	0.01942	0.02088	Karpov 7.0% lower
Total WDL Volatility	49.324	52.055	Karpov 5.2% lower
HardRAP	2644.94	2177.18	Karpov 1.215×
SoftRAP	3730.47	3493.06	Karpov 1.068×

The clean mathematical decomposition is:

Actual score margin = Expected-score margin + Conversion swing

So:

+5.000 = +3.514 + +1.486

This means most of Karpov’s overall margin came from objective expected-score superiority, with a smaller but still meaningful addition from conversion.

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1.2. The two matches are very different

Match	Score	Expected Score	Conversion	WDL Acc. edge	PQ edge	Dominance diff.	Mean Loss ratio	RMS Loss ratio	Volatility ratio
1978	16.5–15.5	16.017–15.983	+0.483	+0.043	+0.092	+0.196	0.982	1.004	0.978
1981	11–7	10.740–7.260	+0.260	+0.247	+0.230	+0.463	0.836	0.779	0.855

This is the whole story in miniature:

• 1978: almost dead even by engine-WDL quality; Karpov’s one-point win came mostly from slight conversion and the narrowest possible metric edge.
• 1981: Karpov was clearly better across almost every family: accuracy, PQ, dominance, mean loss, RMS loss, error concentration, volatility, expected score, and RAP.

So the combined run should not be read as one uniform Karpov–Korchnoi relation. It is better read as:

1978 = equality under extreme tension.
1981 = Karpov reasserting technical superiority.

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1.3. Karpov–Korchnoi 1978: nearly level

Metric	Karpov	Korchnoi	Reading
Score	16.5	15.5	Karpov +1
Expected Score	16.017	15.983	almost exactly equal
Conversion	+0.483	−0.483	practical overperformance decides most of the result
WDL Accuracy	97.646 ± 7.442	97.603 ± 7.348	almost equal
PQ	95.669 ± 3.827	95.577 ± 4.021	almost equal
Dominance	+0.098	−0.098	tiny Karpov edge
Mean ES Loss	0.02354	0.02397	Karpov only 1.8% lower
RMS ES Loss	0.05834	0.05813	Korchnoi microscopically better
Error Concentration	2.780	2.644	Korchnoi better
WDL Volatility	0.02498	0.02555	Karpov 2.2% lower
HardRAP	1569.4	1495.9	Karpov 1.049×
SoftRAP	2315.4	2277.2	Karpov 1.017×
Game Accuracy	97.766	—	high but turbulent
Mutual Accuracy	95.622	—	lower than 1981

The 1978 match is one of the clearest examples where the score tells a stronger story than the engine-WDL quality gap.

The expected score was almost equal:

16.017–15.983

That is only a +0.035 expected-score margin for Karpov over 32 games. In other words, Stockfish-WDL does not say Karpov greatly outplayed Korchnoi in the move-quality sense. It says the match was basically level, and Karpov converted slightly better.

1978 stability

The SDs also show near equality:

SD ratio	Value	Meaning
WDL Accuracy SD ratio	1.013	Karpov slightly more variable
PQ SD ratio	0.952	Karpov slightly steadier in PQ
Mean ES Loss SD ratio	1.013	Karpov slightly more variable
RMS ES Loss SD ratio	0.952	Karpov slightly steadier in large-error spread
Error Concentration SD ratio	1.196	Karpov more variable here
Volatility SD ratio	1.012	Karpov slightly more variable

So 1978 was not just close in averages. It was also close in stability. Korchnoi even wins some important technical sub-metrics: RMS ES Loss by a hair and Error Concentration more clearly.

1978 interpretation

Karpov’s 1978 win looks like:

Not a statistical domination, but a survival-and-conversion victory.

Karpov’s edge was not primarily raw accuracy, PQ, or loss suppression. It was that in an almost even match, he scored +0.483 above expected score, enough to turn equality into a one-point match win.

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1.4. Karpov–Korchnoi 1981: clear Karpov superiority

Metric	Karpov	Korchnoi	Reading
Score	11.0	7.0	Karpov +4
Expected Score	10.740	7.260	Karpov +3.480
Conversion	+0.260	−0.260	small additional overperformance
WDL Accuracy	98.740 ± 5.543	98.492 ± 5.671	Karpov +0.247
PQ	97.478 ± 3.106	97.248 ± 2.984	Karpov +0.230
Dominance	+0.231	−0.231	+0.463 difference
Mean ES Loss	0.01260	0.01508	Karpov 16.4% lower
RMS ES Loss	0.03315	0.04256	Karpov 22.1% lower
Error Concentration	2.612	3.004	Karpov 13.1% lower
WDL Volatility	0.01386	0.01621	Karpov 14.5% lower
HardRAP	1075.5	681.3	Karpov 1.579×
SoftRAP	1415.1	1215.9	Karpov 1.164×
Game Accuracy	98.661	—	cleaner than 1978
Mutual Accuracy	97.362	—	much cleaner than 1978

The 1981 match is very different. Here, Karpov’s advantage is visible in almost every relevant metric family.

The expected score was:

10.740–7.260

That is a +3.480 expected-score margin in only 18 games. The actual score margin was +4.0, so the result was mostly explained by objective WDL superiority, not by a huge conversion surplus.

1981 stability

SD ratio	Value	Meaning
WDL Accuracy SD ratio	0.977	Karpov slightly steadier
PQ SD ratio	1.041	Korchnoi slightly steadier in PQ
Mean ES Loss SD ratio	0.977	Karpov slightly steadier
RMS ES Loss SD ratio	1.191	Karpov more variable in RMS loss
Error Concentration SD ratio	0.536	Karpov much steadier
Volatility SD ratio	0.980	Karpov slightly steadier

The biggest stability signal is Error Concentration SD: Karpov’s 0.567 vs Korchnoi’s 1.058, SD ratio 0.536. This suggests Korchnoi’s error structure was much more uneven in 1981, while Karpov’s mistakes were more controlled.

1981 interpretation

Karpov’s 1981 win looks like:

A technical control victory.

Karpov was better in accuracy, PQ, dominance, mean loss, RMS loss, error concentration, and volatility. This is much more “classic Karpov” than 1978: he reduced the opponent’s counterplay, leaked less expected score, and turned that into a stable match win.

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1.5. Game Accuracy and Mutual Accuracy

Match	Game Accuracy	Mutual Accuracy	Meaning
1978	97.766 ± 2.031	95.622 ± 3.915	More turbulent, lower mutual cleanliness
1981	98.661 ± 1.553	97.362 ± 3.027	Cleaner, more controlled, less error-heavy

The 1981 match was substantially cleaner:

• Game Accuracy improved by about +0.895
• Mutual Accuracy improved by about +1.740
• Game Mean ES Loss dropped from 0.02234 to 0.01338
• Game RMS ES Loss dropped from 0.05880 to 0.04026
• Game Volatility dropped from 0.02365 to 0.01445

This suggests that 1981 was not merely “Karpov won by more.” It was a different match texture: fewer severe swings, lower expected-score leakage, and more controlled positions.

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1.6. Overall game-by-game edge

Across all 50 games:

Metric family	Karpov better in games
Accuracy	28 / 50
PQ	28 / 50
Dominance	28 / 50
Mean ES Loss	28 / 50
RMS ES Loss	28 / 50
Volatility	31 / 50

By match:

Match	Accuracy better	PQ better	Dominance better	Mean Loss better	RMS better	Volatility better
1978, 32 games	16	16	16	16	16	17
1981, 18 games	12	12	12	12	12	14

This is extremely revealing.

In 1978, the game-level split is basically 16–16 in the major quality metrics. That confirms the match was engine-WDL equal.

In 1981, Karpov wins the game-level metric comparison 12–6 in most families, and 14–4 in volatility. That explains why the second match was so much more convincing.

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1.7. Which metrics best explain the scores?

The game-level correlations with Karpov’s game score were approximately:

Predictor	Correlation with Karpov score
PQ difference	0.958
Mean ES Loss advantage	0.957
Dominance difference	0.957
Accuracy difference	0.957
Volatility advantage	0.923
RMS ES Loss advantage	0.834
Karpov Expected Score	0.827
Karpov Conversion	0.781
Game Volatility	0.153
Game Accuracy	−0.153
Mutual Accuracy	−0.151

The lesson is the same as in the previous run reports:

Relative edge matters much more than absolute game quality.

Game Accuracy and Mutual Accuracy by themselves do not explain who scored. In fact, their correlations with Karpov’s score are slightly negative here, because clean games are often draws or balanced games. What matters is not whether the whole game was clean, but whether Karpov was cleaner than Korchnoi.

The strongest explanatory families are therefore:

1. Relative WDL Accuracy / PQ
2. Dominance
3. Mean ES Loss advantage
4. Volatility advantage
5. RMS ES Loss advantage
6. Expected Score
7. Conversion

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1.8. Metric-family interpretation

A. Accuracy and PQ

Overall WDL Accuracy:

Karpov 98.193 vs Korchnoi 98.048

The gap is only +0.145, so this is not a huge accuracy mismatch. The PQ gap is similarly small:

96.573 vs 96.413, a difference of +0.161.

But this average hides the match split:

Match	WDL Acc. edge	PQ edge
1978	+0.043	+0.092
1981	+0.247	+0.230

So the accuracy/PQ family says:

1978 was nearly equal.
1981 was clearly but not overwhelmingly Karpov-favored.

B. Dominance

Dominance is signed, so differences matter more than ratios.

Match	Karpov dominance	Difference vs Korchnoi
1978	+0.098	+0.196
1981	+0.231	+0.463
Overall	+0.165	+0.329

Dominance is small in 1978 and much clearer in 1981. The 1981 value is more than double the 1978 value.

C. Mean ES Loss and RMS ES Loss

Match	Mean Loss ratio	RMS Loss ratio	Reading
1978	0.982	1.004	effectively equal
1981	0.836	0.779	Karpov clearly better
Overall	0.926	0.909	Karpov modestly better

The RMS story is especially important. In 1978, Korchnoi is microscopically better in RMS loss. In 1981, Karpov’s RMS loss is only 77.9% of Korchnoi’s. That means Karpov’s larger mistakes were much less damaging in 1981.

D. Error Concentration

Match	Karpov	Korchnoi	Better
1978	2.780	2.644	Korchnoi
1981	2.612	3.004	Karpov
Overall	2.696	2.824	Karpov

This is a major reversal.

In 1978, Korchnoi’s error concentration was better. In 1981, Karpov’s was much better. This fits the broader story: 1978 was messy and mutually difficult; 1981 was under Karpov’s control.

E. Volatility

Match	Karpov	Korchnoi	Ratio
1978	0.02498	0.02555	0.978
1981	0.01386	0.01621	0.855
Overall	0.01942	0.02088	0.930

Volatility is the most “Karpovian” family here. Even in 1978, where most metrics are equal, Karpov is slightly less volatile. In 1981, he is much less volatile.

The game-level count reinforces this:

• 1978: Karpov lower volatility in 17/32 games
• 1981: Karpov lower volatility in 14/18 games
• Overall: Karpov lower volatility in 31/50 games

So if one single family captures Karpov’s recurring edge against Korchnoi, it is probably volatility suppression.

F. Conversion

Conversion is signed, so ratios are not useful.

Match	Karpov conversion	Korchnoi conversion	Difference
1978	+0.483	−0.483	+0.965
1981	+0.260	−0.260	+0.520
Overall	+0.743	−0.743	+1.486

Conversion mattered more in 1978 than in 1981.

In 1978, the expected-score margin was almost zero, so Karpov’s +0.483 conversion is basically the difference between a tied match and a won match.

In 1981, the expected-score margin was already +3.480, so conversion was only a small addition.

G. HardRAP and SoftRAP

Match	HardRAP ratio	SoftRAP ratio
1978	1.049×	1.017×
1981	1.579×	1.164×
Overall	1.215×	1.068×

HardRAP strongly magnifies the 1981 match because of the bigger score margin. SoftRAP is more conservative and probably more informative across such close matches. It says:

• 1978: almost equal
• 1981: clear Karpov edge
• Overall: modest Karpov edge

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1.9. Chess-style interpretation

1978: Korchnoi resisted Karpov almost completely

The 1978 numbers show a Korchnoi who was not merely surviving. He was matching Karpov in:

• WDL Accuracy
• PQ
• mean loss
• RMS loss
• dominance structure
• game-level metric wins
• much of the stability profile

Karpov won, but not by a broad engine-quality gap. The match looks like a psychological and practical trial where conversion and endurance mattered more than clear technical superiority.

A compact interpretation:

1978 Karpov–Korchnoi was statistically almost a drawn match. Karpov won by the smallest practical margins: slight volatility control and positive conversion.

1981: Karpov solved the matchup

By 1981, the same pairing looks different. Karpov’s edge becomes visible in nearly every family:

• Higher WDL Accuracy
• Higher PQ
• Higher dominance
• Lower mean ES loss
• Much lower RMS ES loss
• Better error concentration
• Lower volatility
• Higher expected score
• Better RAP

This suggests Karpov was no longer just surviving Korchnoi’s resistance. He was containing it.

A compact interpretation:

1981 was Karpov’s technical correction of 1978: fewer swings, fewer serious losses, lower volatility, and clearer dominance.

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1.10. Final conclusion

The combined 1978+1981 Karpov–Korchnoi run says:

Karpov was better overall, but the superiority is mostly created by 1981.

In 1978, the metrics say “almost equal.” Karpov’s match win came from conversion, resilience, and the tiniest WDL edge. Korchnoi’s resistance was so strong that even the engine-WDL expected-score margin was almost zero.

In 1981, the metrics say “Karpov clearly better.” The score was not merely luck or conversion. Karpov had a large expected-score edge, lower average loss, much lower RMS loss, lower volatility, and better error concentration.

The most explanatory metric families are:

1. Expected Score / Dominance — especially in 1981.
2. Volatility — Karpov’s most consistent stylistic edge.
3. Mean ES Loss and RMS ES Loss — nearly equal in 1978, clearly Karpov in 1981.
4. Error Concentration — Korchnoi better in 1978, Karpov better in 1981.
5. Conversion — decisive in 1978, secondary in 1981.
6. RAP — shows 1978 as almost equal and 1981 as a clear Karpov win.

The article-style thesis could be:

Karpov–Korchnoi 1978 was a near-equal collision decided by conversion. Karpov–Korchnoi 1981 was a controlled technical victory decided by expected-score superiority.
Across both matches, Karpov’s recurring edge was not huge raw accuracy, but lower volatility, smaller serious mistakes, and better conversion of small margins.

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2. CHESS ANALYTICS 02 part 2/2: Karpov 1981 vs. Fischer 1971-72

Yes. Karpov’s 1981 performance does change the estimate, and it changes it in Karpov’s favor — but I would still not make Karpov the clear favorite against a fully active 1971–72 Fischer.

My earlier estimate for Fischer 1971–72 vs Karpov 1974 was roughly:

Fischer 55% – Karpov 45%

After adding Karpov 1981, I would revise the estimate to something closer to:

Fischer 52–54% – Karpov 46–48%

Or, in a 24-game match:

Most likely range: 12–12 to Fischer 12.5–11.5
If forced to pick one result: Fischer 12.5–11.5, but with a very high draw/near-equal probability.

The reason is that 1981 Karpov looks significantly stronger, cleaner, and more controlled than 1974 Karpov, especially compared with his 1978 Korchnoi performance.

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2.1. Why Karpov 1981 improves the forecast

Karpov’s 1974 run was already clean, but the Korchnoi final was very narrow: 12.5–11.5, with only a +0.563 expected-score margin and a very small +0.219 conversion.

By contrast, Karpov’s 1981 match against Korchnoi was much clearer:

Metric	Karpov 1981	Korchnoi 1981	Meaning
Score	11.0	7.0	+4 actual margin
Expected Score	10.740	7.260	+3.480 expected-score margin
Conversion	+0.260	−0.260	small extra overperformance
WDL Accuracy	98.740	98.492	Karpov +0.247
PQ	97.478	97.248	Karpov +0.230
Dominance	+0.231	−0.231	+0.463 difference
Mean ES Loss	0.0126	0.0151	Karpov 16.4% lower
RMS ES Loss	0.0332	0.0426	Karpov 22.1% lower
Error Concentration	2.612	3.004	Karpov 13.1% lower
Volatility	0.0139	0.0162	Karpov 14.5% lower

That is no longer “Karpov barely outlasts Korchnoi.” It is Karpov containing Korchnoi. The 1981 version of Karpov shows a stronger version of the exact profile that would be dangerous to Fischer: low loss, low volatility, low error concentration, and high technical control.

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2.2. Why Fischer still retains a small statistical edge

Fischer’s 1971–72 run remains more dominant in relative separation. His whole run produced:

Metric	Fischer 1971–72	Karpov 1981 vs Korchnoi
Score %	75.6%	61.1%
Expected Score %	62.9%	59.7%
Conversion	+5.194 over run	+0.260 in match
WDL Accuracy edge	+0.788 overall	+0.247
PQ edge	+0.779 overall	+0.230
Dominance difference	+1.606 overall	+0.463
HardRAP ratio	3.069×	1.579×
SoftRAP ratio	1.416×	1.164×

Fischer’s run was still much more explosive in result production and opponent separation. His expected-score margin, dominance, conversion, and RAP separation were all larger than Karpov’s 1981 match figures.

So 1981 Karpov narrows the gap, but does not fully erase Fischer’s edge if we assume Fischer retains his 1971–72 form.

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2.3. The key change: Karpov becomes a much better anti-Fischer candidate

Against Karpov 1974, Fischer’s likely route to victory was:

create volatility → generate pressure → force expected-score losses → convert.

Against Karpov 1981, that route becomes harder.

Karpov 1981’s statistical profile says:

Anti-Fischer quality	Karpov 1981 signal
Reduces volatility	0.0139 vs Korchnoi’s 0.0162
Avoids large errors	RMS loss 0.0332 vs 0.0426
Keeps errors less concentrated	2.612 vs 3.004
Maintains very high accuracy	98.740
Wins expected-score battle	+3.480 over 18 games
Converts without needing chaos	+0.260

This matters because Fischer’s greatest statistical weapon was not simply raw accuracy. It was separation power: dominance, conversion, and making opponents’ play more costly. Karpov 1981 looks much better equipped than Karpov 1974 to suppress that separation.

So the matchup becomes:

Fischer’s separation power vs Karpov’s suppression power.

That is much closer than Fischer 1971–72 vs Karpov 1974.

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2.4. Revised estimate

Against Karpov 1974

I would keep the old estimate:

Fischer 55% – Karpov 45%

Because Karpov 1974 still had a narrow escape against Korchnoi, and Fischer’s full run dominance was much larger.

Against Karpov 1981

I would revise to:

Fischer 52–54% – Karpov 46–48%

The 1981 Karpov is probably strong enough that the match is almost equal if Fischer’s edge is not fully intact.

In result terms:

Assumption	Likely result
Fischer fully retains 1971–72 form	Fischer 12.5–11.5 or 13–11
Karpov successfully suppresses volatility	12–12 or Karpov 12.5–11.5
Fischer has any inactivity/rust penalty	Karpov becomes slight favorite
Fischer raises tactical/psychological volatility	Fischer remains slight favorite

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2.5. Final answer

Yes, Karpov’s 1981 performance significantly improves his hypothetical chances. It turns the earlier “Fischer narrow-to-moderate favorite” estimate into a near coin-flip with Fischer only slightly favored.

My revised thesis:

Against Karpov 1974, Fischer’s 1971–72 dominance probably makes him the favorite.
Against Karpov 1981, Fischer is still slightly favored by domination metrics, but Karpov’s low-volatility technical control nearly neutralizes that edge.

Final estimate:

1971–72 Fischer vs 1981 Karpov: Fischer 52–54%, Karpov 46–48%.

Most likely match score:

Fischer 12.5–11.5, with 12–12 nearly as plausible.