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chess, chess analytics, chess history, engine analysis, Karpov, Kasparov, performance metrics, Stockfish, WDL evaluation, world championship

1. CHESS ANALYTICS 04 part 1/2: the Kasparov-Karpov matches between 1985-90

I treated Garry Kasparov as the main player and Anatoly Karpov as the opponent, because that is how the uploaded run package is structured. The report covers the four Kasparov–Karpov World-Championship matches of 1985, 1986, 1987, and 1990, using Stockfish 18 WDL expected-score analysis.

1.1. Short verdict

Across the four post-1984 title matches, Kasparov is ahead, but by small technical margins, not by overwhelming engine-WDL superiority.

The combined score is:

Kasparov 50 – Karpov 46

The combined expected score is:

Kasparov 50.208 – Karpov 45.792

So the engine-WDL expected-score margin is actually +4.417, slightly larger than the actual score margin of +4.000.

This gives:

Actual score margin = Expected-score margin + Conversion swing
+4.000 = +4.417 − 0.417

So unlike Fischer 1971–72 or Karpov 1974, Kasparov did not owe the overall result to positive conversion. In fact, he slightly under-converted relative to expected score.

The summary thesis is:

Kasparov was the slightly stronger expected-score player across 1985–1990, but Karpov converted better than the engine-WDL expectation.
Kasparov’s superiority appears mostly in expected score, small accuracy/PQ edges, lower ES loss, lower RMS loss, and slightly lower volatility, while Karpov’s resistance appears especially in conversion and error concentration.

1.2. Overall run table

Metric	Kasparov	Karpov	Edge / ratio	Better
Score	50.000	46.000	+4.000 / 1.087×	Kasparov
Expected Score	50.208	45.792	+4.417 / 1.096×	Kasparov
Conversion	−0.208	+0.208	−0.417 difference	Karpov
WDL Accuracy	98.364	98.303	+0.061	Kasparov
PQ	96.843	96.783	+0.060	Kasparov
Dominance	+0.062	−0.062	+0.123 difference	Kasparov
Mean ES Loss	0.0162	0.0168	Kasparov 3.6% lower	Kasparov
RMS ES Loss	0.0464	0.0481	Kasparov 3.4% lower	Kasparov
Error Concentration	2.902	2.854	Kasparov 1.7% higher	Karpov
WDL Volatility	0.0179	0.0182	Kasparov about 1.8% lower	Kasparov
Total WDL Volatility	70.460	71.494	Kasparov lower by 1.034	Kasparov
HardRAP	4853.201	4459.931	Kasparov 1.088×	Kasparov
SoftRAP	7075.066	6875.545	Kasparov 1.029×	Kasparov

The overall edge is extremely narrow in raw move-quality terms:

WDL Accuracy edge: +0.061
PQ edge: +0.060
Mean ES Loss difference: about −0.001
RMS ES Loss difference: about −0.002
Dominance difference: +0.123

This is not a one-sided rivalry by engine-WDL metrics. It is a sustained, very high-level superiority by small margins.

1.3. Match-by-match comparison

Match	Score	Expected Score	Conversion	WDL Acc. edge	PQ edge	Dominance diff.	Mean Loss ratio	RMS Loss ratio	Volatility ratio
1985	13–11	13.046–10.954	−0.046	+0.122	+0.179	+0.364	0.924	0.894	0.934
1986	12.5–11.5	11.974–12.026	+0.526	+0.033	+0.017	+0.030	0.979	1.018	0.992
1987	12–12	12.485–11.515	−0.485	−0.039	−0.050	−0.100	1.029	1.036	1.058
1990	12.5–11.5	12.703–11.297	−0.203	+0.128	+0.095	+0.198	0.944	0.935	0.962

The broad shape:

1985: Kasparov’s clearest technical win.
1986: Almost equal; Kasparov wins the score mainly by conversion.
1987: Karpov slightly better by many quality metrics; match drawn because Kasparov under-converted.
1990: Kasparov again has a clear but modest expected-score edge.

So the rivalry after 1984 is not a simple upward Kasparov curve. It is more like:

1985: Kasparov takes over.
1986: near-equality with Kasparov converting better.
1987: Karpov’s best statistical counterpunch.
1990: Kasparov reasserts a modest but real edge.

1.4. 1985 match: Kasparov’s clearest technical victory

Metric	Kasparov	Karpov	Reading
Score	13.0	11.0	Kasparov +2
Expected Score	13.046	10.954	Kasparov +2.093
Conversion	−0.046	+0.046	Karpov very slightly over-converted
WDL Accuracy	98.522 ± 5.437	98.400 ± 5.657	Kasparov +0.122
PQ	97.129 ± 2.265	96.951 ± 2.341	Kasparov +0.179
Dominance	+0.182	−0.182	+0.364 difference
Mean ES Loss	0.01478	0.01600	Kasparov 7.6% lower
RMS ES Loss	0.04010	0.04485	Kasparov 10.6% lower
Error Concentration	2.721	2.742	Kasparov slightly better
WDL Volatility	0.01556	0.01666	Kasparov 6.6% lower
HardRAP	1262.7	1071.4	Kasparov 1.179×
SoftRAP	1796.9	1699.1	Kasparov 1.058×
Game Accuracy	98.502	—	High quality
Mutual Accuracy	97.038	—	High mutual level

This is the cleanest “Kasparov is better” match in the package. The expected-score margin +2.093 essentially explains the actual +2 score margin. Conversion was basically neutral or very slightly against him.

The SDs also favor Kasparov:

SD ratio	Value
WDL Accuracy SD ratio	0.961
PQ SD ratio	0.968
Mean ES Loss SD ratio	0.961
RMS ES Loss SD ratio	0.941
Error Concentration SD ratio	0.941
Volatility SD ratio	0.961

So in 1985, Kasparov was not only better on average, but also slightly more stable across most families.

Interpretation:
1985 is the most convincing evidence that Kasparov had overtaken Karpov in engine-WDL terms. His advantages appear in accuracy, PQ, dominance, mean loss, RMS loss, volatility, expected score, and RAP.

1.5. 1986 match: a near-equal match decided by conversion

Metric	Kasparov	Karpov	Reading
Score	12.5	11.5	Kasparov +1
Expected Score	11.974	12.026	Karpov tiny expected edge
Conversion	+0.526	−0.526	Kasparov converts above expectation
WDL Accuracy	98.484 ± 6.689	98.451 ± 6.222	Kasparov +0.033
PQ	97.147 ± 2.764	97.130 ± 2.631	Kasparov +0.017
Dominance	+0.015	−0.015	almost zero
Mean ES Loss	0.01516	0.01549	Kasparov 2.1% lower
RMS ES Loss	0.04658	0.04575	Karpov slightly better
Error Concentration	3.087	2.913	Karpov better
WDL Volatility	0.01611	0.01623	equal, tiny Kasparov edge
HardRAP	1220.5	1116.7	Kasparov 1.093×
SoftRAP	1776.0	1723.9	Kasparov 1.030×
Game Accuracy	98.549	—	Very high
Mutual Accuracy	97.137	—	Very high

1986 is not a strong quality-gap win for Kasparov. It is almost equal, and by expected score Karpov actually leads by +0.052.

The result is explained by conversion:

Kasparov conversion: +0.526
Karpov conversion: −0.526
Conversion swing: +1.052

That is almost exactly the final one-point match margin.

The SD picture is mixed:

SD ratio	Value
WDL Accuracy SD ratio	1.075
PQ SD ratio	1.051
Mean ES Loss SD ratio	1.075
RMS ES Loss SD ratio	1.126
Error Concentration SD ratio	0.931
Volatility SD ratio	1.076

Kasparov is more variable in most of the ordinary accuracy/loss/volatility metrics, while Karpov is slightly more variable in error concentration.

Interpretation:
1986 was almost a dead-level match. Kasparov’s title retention/win margin came from conversion, not from a clear expected-score superiority.

1.6. 1987 match: Karpov’s statistical counterpunch

Metric	Kasparov	Karpov	Reading
Score	12.0	12.0	tied match
Expected Score	12.485	11.515	Kasparov +0.970
Conversion	−0.485	+0.485	Karpov converts better
WDL Accuracy	98.618 ± 5.879	98.657 ± 6.204	Karpov +0.039
PQ	97.502 ± 2.030	97.552 ± 2.117	Karpov +0.050
Dominance	−0.050	+0.050	Karpov edge by average dominance
Mean ES Loss	0.01382	0.01343	Karpov 2.9% lower
RMS ES Loss	0.03985	0.03846	Karpov 3.6% lower
Error Concentration	2.881	2.787	Karpov better
WDL Volatility	0.01595	0.01508	Karpov 5.8% lower
HardRAP	1169.9	1175.3	Karpov slightly higher
SoftRAP	1755.0	1758.3	Karpov slightly higher
Game Accuracy	98.750	—	Cleanest match of the four
Mutual Accuracy	97.526	—	Cleanest mutual accuracy

This is a fascinating contradiction: the expected-score table says Kasparov led by +0.970, but the average quality families mostly favor Karpov.

How can that happen? Likely because Kasparov’s favorable expected-score moments were more score-weighted, while Karpov’s average move-quality profile was slightly cleaner. But Kasparov failed to convert that expected-score edge:

Kasparov conversion: −0.485
Karpov conversion: +0.485

So the match ended 12–12.

The SDs mostly favor Kasparov:

SD ratio	Value
WDL Accuracy SD ratio	0.948
PQ SD ratio	0.959
Mean ES Loss SD ratio	0.948
RMS ES Loss SD ratio	0.911
Error Concentration SD ratio	0.985
Volatility SD ratio	0.982

So Kasparov was often slightly less variable, but Karpov’s averages were cleaner. This makes 1987 one of the most nuanced matches: Karpov cleaner on average, Kasparov ahead in expected score, Karpov better in conversion, final score tied.

Interpretation:
1987 is the strongest evidence that Karpov remained Kasparov’s equal in many engine-WDL quality categories. Kasparov survived the match historically, but the metrics do not show simple superiority.

1.7. 1990 match: Kasparov reasserts the edge

Metric	Kasparov	Karpov	Reading
Score	12.5	11.5	Kasparov +1
Expected Score	12.703	11.297	Kasparov +1.406
Conversion	−0.203	+0.203	Karpov slightly over-converts
WDL Accuracy	97.833 ± 6.425	97.705 ± 6.869	Kasparov +0.128
PQ	95.594 ± 3.446	95.499 ± 3.481	Kasparov +0.095
Dominance	+0.099	−0.099	+0.198 difference
Mean ES Loss	0.02167	0.02295	Kasparov 5.6% lower
RMS ES Loss	0.05852	0.06258	Kasparov 6.5% lower
Error Concentration	2.920	2.975	Kasparov slightly better
WDL Volatility	0.02385	0.02480	Kasparov 3.8% lower
HardRAP	1200.0	1096.6	Kasparov 1.094×
SoftRAP	1747.1	1694.3	Kasparov 1.031×
Game Accuracy	97.736	—	lowest of the four matches
Mutual Accuracy	95.545	—	lowest mutual quality of the four

The 1990 match is less clean than 1985–1987 for both players. Game Accuracy and Mutual Accuracy drop, mean loss rises, RMS loss rises, and volatility rises.

But within that rougher environment, Kasparov has the edge. His expected-score margin is +1.406, larger than the final +1 score margin. Karpov again converts slightly better than expectation, reducing the final margin.

The SDs mostly favor Kasparov:

SD ratio	Value
WDL Accuracy SD ratio	0.935
PQ SD ratio	0.977
Mean ES Loss SD ratio	0.935
RMS ES Loss SD ratio	0.940
Error Concentration SD ratio	1.042
Volatility SD ratio	0.947

Kasparov was generally more stable, except in error concentration.

Interpretation:
1990 shows Kasparov again with a real expected-score and loss-profile edge, though Karpov’s conversion prevented the score from becoming wider.

1.8. Game Accuracy and Mutual Accuracy

Match	Game Accuracy	Mutual Accuracy	Reading
1985	98.502	97.038	High quality
1986	98.549	97.137	Similar high quality
1987	98.750	97.526	Cleanest match
1990	97.736	95.545	Roughest / most volatile match
Overall	98.384	96.811	Very high overall

The 1987 match was the cleanest by Game Accuracy and Mutual Accuracy, even though it ended drawn and contained a complicated split of expected-score versus average quality.

The 1990 match was the roughest, with the lowest Game Accuracy and Mutual Accuracy and the highest loss/volatility environment.

This reinforces one of your recurring findings:

Absolute game quality does not explain who scores. Relative edge does.

High Game Accuracy often means a clean draw. The stronger predictors are the player-vs-opponent differences.

1.9. Game-by-game metric edge

Across all 96 games:

Metric family	Kasparov better in games
WDL Accuracy	52 / 96
PQ	52 / 96
Dominance	52 / 96
Mean ES Loss	52 / 96
RMS ES Loss	56 / 96
Volatility	50 / 96

By match:

Match	Accuracy	PQ	Dominance	Mean ES Loss	RMS ES Loss	Volatility
1985	14/24	14/24	14/24	14/24	15/24	16/24
1986	13/24	13/24	13/24	13/24	11/24	12/24
1987	12/24	12/24	12/24	12/24	12/24	11/24
1990	13/24	13/24	13/24	13/24	18/24	11/24
Overall	52/96	52/96	52/96	52/96	56/96	50/96

This is not a lopsided game-by-game rivalry. Kasparov’s edge is small but persistent.

The strongest game-count signal is RMS ES Loss, where Kasparov is better in 56/96 games. That suggests he more often avoided the worse severe-error profile.

Volatility is almost equal: 50/96. So the rivalry cannot be reduced to “Kasparov was simply less volatile.” His edge is broader and smaller: slight accuracy, PQ, dominance, mean-loss, RMS-loss, and expected-score advantages.

1.10. Correlations with score

Across the 96 games, the strongest predictors of Kasparov’s game score were:

Predictor	Correlation with Kasparov score
PQ difference	0.915
Mean ES Loss advantage	0.914
Dominance difference	0.914
WDL Accuracy difference	0.914
Kasparov Expected Score	0.911
Volatility advantage	0.883
Kasparov Conversion	0.863
RMS ES Loss advantage	0.844
Game Accuracy	0.023
Mutual Accuracy	0.022
Game Volatility	−0.008

This is very consistent with your earlier packages:

Relative player-vs-opponent edges explain score. Absolute game cleanliness does not.

The score is not well explained by whether the game as a whole was clean. It is explained by whether Kasparov’s accuracy/PQ/loss profile was better than Karpov’s inside that game.

1.11. Which metric families explain the overall 50–46 result?

1.11.1. Expected Score and Dominance

Kasparov’s expected-score edge is:

50.208–45.792 = +4.417

That is the strongest explanation of the overall result. Since the actual score margin is only +4, Kasparov’s expected-score margin was actually larger than his final scoring margin.

Dominance is also positive:

+0.062 vs −0.062, difference +0.123

That is small, but persistent.

1.11.2. Accuracy and PQ

Kasparov’s WDL Accuracy and PQ edges are tiny:

WDL Accuracy: +0.061
PQ: +0.060

But over 96 games, tiny edges matter. These metrics explain the rivalry only as a cumulative accumulation, not as a per-game domination.

1.11.3. Mean ES Loss and RMS ES Loss

Kasparov’s loss profile is slightly better:

Mean ES Loss ratio: 0.964
RMS ES Loss ratio: 0.966

That means he leaked about 3–4% less expected score on average and had a slightly better large-error profile.

This is important because the raw accuracy difference is so small. The loss metrics show the same edge in a more interpretable way.

1.11.4. Volatility

Kasparov’s volatility is only slightly lower:

WDL Volatility ratio: 0.982
Total Volatility difference: −1.034

This helps explain the score but is not the dominant story. Karpov was still extremely good at suppressing volatility.

1.11.5. Conversion

Conversion actually favors Karpov:

Kasparov: −0.208
Karpov: +0.208
Difference: −0.417

So conversion reduced Kasparov’s margin. This is a very important distinction from Fischer’s 1971–72 run or Karpov’s 1974/1981 cases.

The result was not:

Kasparov converted better.

It was:

Kasparov created enough expected-score edge that he won despite slightly worse conversion.

1.11.6. Error Concentration

Error Concentration favors Karpov slightly:

Kasparov: 2.902
Karpov: 2.854

Lower is better, so Karpov was better by about 1.7%. This is one of the clearest statistical signs of Karpov’s continued resilience: his errors were slightly less concentrated, even while Kasparov had the better expected-score result.

1.12. Overall chess interpretation

The four-match package shows a rivalry of near-equals, with Kasparov gradually holding the measurable edge.

Kasparov’s advantage was not that Karpov collapsed. Karpov remained extraordinarily close in:

WDL Accuracy
PQ
Mean ES Loss
RMS ES Loss
Volatility
Error Concentration
RAP

Instead, Kasparov’s edge was that he was slightly better in more decisive relative categories often enough:

+4.417 expected-score margin
+0.123 dominance difference
52/96 game advantage in accuracy/PQ/dominance/mean loss
56/96 game advantage in RMS loss
+393 HardRAP
+200 SoftRAP

But Karpov’s resistance was visible in:

positive conversion overall
slightly better error concentration
almost equal volatility
the 1987 match, where he was arguably cleaner by many average quality metrics

So the compressed verdict is:

Kasparov was better across 1985–1990, but Karpov remained close enough that the superiority appears as cumulative pressure rather than domination.

1.13. Article-style thesis

A good final thesis for this article part would be:

The post-1984 Kasparov–Karpov matches show Kasparov’s narrow but persistent takeover.
Across 96 games, Kasparov led 50–46 and also led the engine-WDL expected score 50.208–45.792. His advantage came from small cumulative edges in WDL Accuracy, PQ, Dominance, Mean ES Loss, RMS ES Loss, Volatility, and RAP.
But Karpov’s resistance remained extraordinary: he converted slightly better than expectation, had slightly better Error Concentration, drew the 1987 match, and kept almost every metric close.
Thus, the rivalry is not measured as Kasparov crushing Karpov, but as Kasparov repeatedly finding just enough expected-score superiority to overcome Karpov’s technical resilience.

2. CHESS ANALYTICS 04 part 2/2: comparisons between 1970s to 1990s player metrics

Yes: across the matches you have analysed so far, there is a clear broad increase in “clean technical quality” from Fischer 1971–72 into the Karpov/Kasparov era, but it is not linear, and it depends heavily on match texture.

The strongest trend is not simply “newer = better.” It is more like:

Fischer’s run is more dominant; later Karpov/Kasparov matches are generally cleaner, lower-loss, and lower-volatility.

The comparison below uses the uploaded run reports for Fischer 1971–72, Karpov 1974, Karpov–Korchnoi 1978/1981, Karpov–Kasparov 1984, and Kasparov–Karpov 1985–1990.

2.1. Compact chronological table

Here I use both-player match averages where possible. Higher is better for WDL Accuracy, Game Accuracy, Mutual Accuracy, PQ. Lower is generally better for Mean ES Loss, RMS ES Loss, Error Concentration, Volatility.

Match	Score	WDL Acc.	Game Acc.	Mutual Acc.	PQ	Mean Loss	RMS Loss	Error Conc.	Volatility
Fischer–Taimanov 1971	6–0	97.772	97.641	95.347	95.350	0.0223	0.0760	3.399	0.0230
Fischer–Larsen 1971	6–0	97.315	97.246	94.573	94.576	0.0269	0.0789	2.977	0.0275
Fischer–Petrosian 1971	6.5–2.5	96.836	96.881	93.878	93.882	0.0316	0.0799	2.612	0.0333
Fischer–Spassky 1972	12.5–7.5	97.893	97.910	95.885	95.888	0.0211	0.0610	3.152	0.0226
Karpov–Polugaevsky 1974	5.5–2.5	98.591	98.670	97.365	97.366	0.0141	0.0395	2.640	0.0148
Karpov–Spassky 1974	7–4	98.426	98.471	96.971	96.972	0.0157	0.0494	3.037	0.0168
Karpov–Korchnoi 1974	12.5–11.5	98.341	98.285	96.627	96.629	0.0166	0.0499	2.983	0.0175
Karpov–Korchnoi 1978	16.5–15.5	97.625	97.766	95.622	95.623	0.0238	0.0582	2.712	0.0253
Karpov–Korchnoi 1981	11–7	98.616	98.661	97.362	97.363	0.0138	0.0379	2.808	0.0150
Karpov–Kasparov 1984	25–23	98.598	98.780	97.589	97.590	0.0140	0.0358	2.586	0.0148
Kasparov–Karpov 1985	13–11	98.461	98.502	97.038	97.040	0.0154	0.0425	2.732	0.0161
Kasparov–Karpov 1986	12.5–11.5	98.468	98.549	97.137	97.138	0.0153	0.0462	3.000	0.0162
Kasparov–Karpov 1987	12–12	98.638	98.750	97.526	97.527	0.0136	0.0392	2.834	0.0155
Kasparov–Karpov 1990	12.5–11.5	97.769	97.736	95.545	95.546	0.0223	0.0606	2.947	0.0243

2.2. Is there a quality trend?

Yes, especially from Fischer 1971–72 to Karpov 1974 and the 1980s

The clearest improvement is visible in these families:

Metric family	Fischer 1971–72 range	Karpov/Kasparov best-era range	Trend
WDL Accuracy	~96.84–97.89	often ~98.34–98.64	Later matches usually higher
Game Accuracy	~96.88–97.91	often ~98.47–98.78	Clear increase
Mutual Accuracy	~93.88–95.89	often ~96.97–97.59	Very clear increase
PQ	~93.88–95.89	often ~96.97–97.59	Very clear increase
Mean ES Loss	~0.021–0.032	often ~0.014–0.016	Large decrease
RMS ES Loss	~0.061–0.080	often ~0.036–0.049	Large decrease
Volatility	~0.023–0.033	often ~0.015–0.017	Large decrease

The strongest “quality increase” signal is probably Mutual Accuracy / PQ / Mean ES Loss / RMS ES Loss / Volatility.

WDL Accuracy rises, but because WDL Accuracy compresses elite play into a narrow high-90s range, it hides some of the difference. The loss metrics show the trend more clearly.

2.3. The strongest trend: Mutual Accuracy and PQ rise

Mutual Accuracy is especially useful because it asks: how clean was the game when both players’ play is combined?

Fischer-run mutual accuracy:

Match	Mutual Accuracy
Fischer–Taimanov	95.347
Fischer–Larsen	94.573
Fischer–Petrosian	93.878
Fischer–Spassky	95.885

Later Karpov/Kasparov-era peaks:

Match	Mutual Accuracy
Karpov–Polugaevsky 1974	97.365
Karpov–Korchnoi 1981	97.362
Karpov–Kasparov 1984	97.589
Kasparov–Karpov 1987	97.526

This is a very large shift. The Fischer matches are often in the 94–96 mutual-accuracy zone; the best Karpov/Kasparov matches are in the 97.3–97.6 zone.

So, by Mutual Accuracy, the broad trend is:

The later matches are cleaner from both sides.

The same is true of PQ, because the PQ values are nearly identical to the mutual-accuracy pattern in these tables.

2.4. Mean ES Loss and RMS ES Loss show the trend even better

Lower is better.

Fischer-run Mean ES Loss:

Match	Mean ES Loss
Fischer–Taimanov	0.0223
Fischer–Larsen	0.0269
Fischer–Petrosian	0.0316
Fischer–Spassky	0.0211

Typical Karpov/Kasparov-era values:

Match	Mean ES Loss
Karpov–Polugaevsky 1974	0.0141
Karpov–Spassky 1974	0.0157
Karpov–Korchnoi 1981	0.0138
Karpov–Kasparov 1984	0.0140
Kasparov–Karpov 1987	0.0136

That is a major difference. The later elite matches often have only about half to two-thirds of the mean expected-score loss of Fischer’s 1971 Candidates matches.

RMS ES Loss tells the same story:

Match	RMS ES Loss
Fischer–Taimanov	0.0760
Fischer–Larsen	0.0789
Fischer–Petrosian	0.0799
Fischer–Spassky	0.0610
Karpov–Korchnoi 1981	0.0379
Karpov–Kasparov 1984	0.0358
Kasparov–Karpov 1987	0.0392

This suggests that the later matches have fewer or smaller large expected-score losses.

Article-style sentence:

The Fischer run is more dominant, but the Karpov/Kasparov era is cleaner: the later matches leak less expected score per move and show much smaller RMS loss profiles.

2.5. Volatility also drops strongly

Volatility is one of the clearest stylistic differences.

Fischer-run volatility:

Match	Volatility
Fischer–Taimanov	0.0230
Fischer–Larsen	0.0275
Fischer–Petrosian	0.0333
Fischer–Spassky	0.0226

Karpov/Kasparov-era low-volatility matches:

Match	Volatility
Karpov–Polugaevsky 1974	0.0148
Karpov–Korchnoi 1981	0.0150
Karpov–Kasparov 1984	0.0148
Kasparov–Karpov 1987	0.0155

That is a strong difference. Karpov’s mature matches, and the Karpov–Kasparov matches at their cleanest, have much lower volatility than Fischer’s 1971 Candidates run.

This does not necessarily mean Fischer was weaker. It means the games were less controlled, sharper, or more destabilizing. Fischer’s run created more separation; Karpov/Kasparov often created cleaner near-equilibrium.

So:

Fischer’s era in this sample shows higher dominance and score violence.
Karpov/Kasparov shows lower volatility and higher mutual precision.

2.6. Standard deviations: later play is usually more stable, but not always

The SD trend mostly supports the same conclusion.

WDL Accuracy SD

Match group	Typical WDL Accuracy SD
Fischer 1971–72 matches	~7.2–8.2
Karpov 1974 matches	~5.1–6.2
Karpov–Korchnoi 1978	7.4
Karpov–Korchnoi 1981	5.6
Karpov–Kasparov 1984	6.0
Kasparov–Karpov 1985–87	~5.5–6.5
Kasparov–Karpov 1990	6.65

So the broad trend is toward lower SDs, meaning more stable quality. But the 1978 and 1990 matches are exceptions.

Game Accuracy SD

Match	Game Accuracy SD
Fischer–Petrosian	1.497
Fischer–Spassky	1.562
Karpov–Polugaevsky	0.877
Karpov–Spassky 1974	0.861
Karpov–Kasparov 1984	1.272
Kasparov–Karpov 1987	1.040
Kasparov–Karpov 1990	1.520

Game Accuracy SD drops sharply in some Karpov-era matches, especially 1974, but rises again in more turbulent matches.

Mutual Accuracy SD

Match	Mutual Accuracy SD
Fischer–Spassky	3.036
Karpov–Polugaevsky	1.725
Karpov–Spassky 1974	1.695
Karpov–Korchnoi 1978	3.915
Karpov–Kasparov 1984	2.486
Kasparov–Karpov 1987	2.046
Kasparov–Karpov 1990	2.951

Again, the trend is not strictly chronological. The stable Karpov technical matches have low SDs; the stressful Korchnoi 1978 and Kasparov–Karpov 1990 matches are rougher and more variable.

The best interpretation:

Stability generally improves from Fischer’s run into Karpov’s mature period, but match tension and style can override chronology.

2.7. Error Concentration does not show a simple historical trend

Error Concentration is the least linear of the requested metrics.

Match	Error Concentration
Fischer–Petrosian	2.612
Karpov–Polugaevsky	2.640
Karpov–Kasparov 1984	2.586
Kasparov–Karpov 1986	3.000
Kasparov–Karpov 1990	2.947

The lowest values are not simply the latest. Fischer–Petrosian already has a low error-concentration value. Karpov–Kasparov 1984 has the best value in the whole group, but 1986 and 1990 are higher.

So Error Concentration should not be used as the main historical “quality increase” metric. It seems more sensitive to how errors are distributed inside the match than to general playing strength.

Better summary:

Error Concentration does not show a clean chronological improvement. It is more match-texture-dependent than WDL Accuracy, Mutual Accuracy, Mean Loss, RMS Loss, or Volatility.

2.8. The major exceptions to the trend

The trend is real, but three major exceptions matter.

Exception 1: Fischer–Spassky 1972 was cleaner than Fischer’s Candidates matches

Fischer–Spassky has:

WDL Accuracy: 97.893
Game Accuracy: 97.910
Mutual Accuracy: 95.885
RMS Loss: 0.0610
Volatility: 0.0226

This is still not as clean as Karpov–Kasparov 1984 or Kasparov–Karpov 1987, but it is clearly cleaner than Fischer–Petrosian and Fischer–Larsen.

Exception 2: Karpov–Korchnoi 1978 was unusually rough

Karpov–Korchnoi 1978 has:

WDL Accuracy: 97.625
Mutual Accuracy: 95.622
Mean Loss: 0.0238
RMS Loss: 0.0582
Volatility: 0.0253

This looks much closer to Fischer–Spassky 1972 than to Karpov–Korchnoi 1981 or Karpov–Kasparov 1984. It was a long, tense, psychologically rough match, not a clean technical laboratory.

Exception 3: Kasparov–Karpov 1990 was rougher than 1984–1987

The 1990 match drops to:

WDL Accuracy: 97.769
Mutual Accuracy: 95.545
Mean Loss: 0.0223
RMS Loss: 0.0606
Volatility: 0.0243

That is a major decline from the very clean 1984–1987 zone. It does not mean the players were weaker in any simple sense. It likely means the match produced more complex, risky, or error-inducing positions.

2.9. Peak-quality matches by metric

Best WDL Accuracy

Rank	Match	WDL Accuracy
1	Kasparov–Karpov 1987	98.638
2	Karpov–Korchnoi 1981	98.616
3	Karpov–Kasparov 1984	98.598
4	Karpov–Polugaevsky 1974	98.591

Best Game Accuracy

Rank	Match	Game Accuracy
1	Karpov–Kasparov 1984	98.780
2	Kasparov–Karpov 1987	98.750
3	Karpov–Polugaevsky 1974	98.670
4	Karpov–Korchnoi 1981	98.661

Best Mutual Accuracy / PQ

Rank	Match	Mutual Accuracy / PQ
1	Karpov–Kasparov 1984	97.589 / 97.590
2	Kasparov–Karpov 1987	97.526 / 97.527
3	Karpov–Polugaevsky 1974	97.365 / 97.366
4	Karpov–Korchnoi 1981	97.362 / 97.363

Lowest Mean ES Loss

Rank	Match	Mean ES Loss
1	Kasparov–Karpov 1987	0.0136
2	Karpov–Korchnoi 1981	0.0138
3	Karpov–Kasparov 1984	0.0140
4	Karpov–Polugaevsky 1974	0.0141

Lowest RMS ES Loss

Rank	Match	RMS ES Loss
1	Karpov–Kasparov 1984	0.0358
2	Karpov–Korchnoi 1981	0.0379
3	Kasparov–Karpov 1987	0.0392
4	Karpov–Polugaevsky 1974	0.0395

Lowest Volatility

Rank	Match	Volatility
1	Karpov–Polugaevsky 1974	0.0148
2	Karpov–Kasparov 1984	0.0148
3	Karpov–Korchnoi 1981	0.0150
4	Kasparov–Karpov 1987	0.0155

This ranking is revealing: the top quality matches cluster around Karpov 1974, Karpov 1981, Karpov–Kasparov 1984, and Kasparov–Karpov 1987.

Fischer’s run ranks much higher in dominance and score separation than in absolute mutual cleanliness.

2.10. Final conclusion

There is a real trend in increasing quality, but it should be stated carefully.

Best formulation

From Fischer’s 1971–72 run to the Karpov/Kasparov era, the matches generally become cleaner by WDL Accuracy, Game Accuracy, Mutual Accuracy, PQ, Mean ES Loss, RMS ES Loss, and Volatility. The later matches usually show higher mutual precision, smaller expected-score losses, and lower volatility.

But:

The trend is not linear. Match style matters. Karpov–Korchnoi 1978 and Kasparov–Karpov 1990 are rougher and more volatile than several earlier matches, while Fischer–Spassky 1972 is cleaner than Fischer’s earlier Candidates matches.

The most defensible article thesis would be:

Fischer 1971–72 remains the greatest domination run in this dataset, but not the cleanest technical run.
The cleanest technical chess appears later, especially in Karpov’s 1974/1981 performances and the Karpov–Kasparov matches of 1984 and 1987.
The historical trend is therefore not simply “players got stronger,” but more precisely: elite World-Championship play became lower-loss, lower-volatility, and more mutually accurate, while domination margins became smaller because both sides were increasingly accurate.