Sources, Caveats and Folklore 知之為知之

Principle Ⅳ applied to the site itself. Every number here traces to a named source, and where the evidence is weak, contested, or turned out to be invented, this page says so rather than quietly picking a side.

Claims that are folklore, not evidence

The "40-40-20 rule" (40% tactics, 40% endgames, 20% openings) has no identifiable originating source. The studies usually invoked to defend it support prioritising tactics and endgames over openings in principle; they do not validate those percentages. The rule also omits game analysis entirely — the one activity multiple datasets single out as the top predictor of improvement at novice level.
"X% of beginner games are decided by hanging a piece." No credible source has ever measured this. Blunder studies count centipawn loss, which lumps together hanging pieces, missed tactics and endgame errors, and says nothing about which error decided the game. Any specific figure in circulation is invented.
"Longer time controls make you improve faster." Near-universal coach consensus with a plausible mechanism — but no study has ever compared improvement rates across time controls at matched effort. What has been measured is move quality by time control, which is a different claim. One large amateur survey actually suggests some blitz is optimal rather than none.
"I hear and I forget; I see and I remember; I do and I understand" is not Confucius. It appears in no classical Chinese text and surfaces in 1960s English-language education writing. The genuine ancestor is Xunzi, 儒效篇.
"Masters hold 300,000 chunks in memory." Overstated. That figure is a model parameter — the number of nodes in a computational net that reproduces master-level recall — not a measurement. The honest phrasing is "models that reproduce master-level perception require on the order of 300,000 stored patterns."
The "10,000-hour rule" is Gladwell's, not Ericsson's. Ericsson's own data showed the best violinists at 7,410 accumulated hours by age 18. The number was popularised, not published.
"A pattern is yours after N repetitions." Five times, seven, twenty — nobody has measured this for chess and every circulating figure is invented. Simon's (1974) chunk arithmetic is sometimes converted into one; it cannot be. See Tactics for why the numbers do not multiply out.
"Solve puzzles at 85% success." Wilson et al. (2019, Nature Communications) is a real paper and 15.87% is its real optimal error rate — for stochastic gradient-descent algorithms doing binary classification. The authors say the optimum shifts with the noise distribution and that extension beyond binary tasks needs more complex mappings. Useful as a steer away from trivial and impossible puzzles; not a constant, and in unresolved tension with the desirable-difficulties literature this site leans on.
"Seven Circles / 400 points in 400 days." The claim is de la Maza's own and his result is real. In two decades of enthusiastic attempts there is no documented case of anyone reproducing it, and the most-cited outcome among those who completed the full programme is no measurable gain. Heisman's objection is narrower than usually reported — he disputed the drilling scheme, not the man or the whole book.
"Write your move down before you play it, then check." Sound idea, illegal mechanism. Recording a move in advance has been forbidden since 2005 (FIDE Laws, Article 8.1.2). The legal version — record your opponent's move and their clock time while you run the blunder check — is on Calculation.
Capablanca on studying the endgame first. The famous sentence "in order to improve your game, you must study the endgame before everything else" is not traceable to Chess Fundamentals and no quotation site gives a page. What is verifiable is the book's structure, which makes the point anyway. Two more attributions on this site are flagged the same way: "bad bishops protect good pawns" (Suba) and "trade pieces when ahead" (Capablanca) are both sound and both unverified against the text.
The Lucena position is not in Lucena. It does not appear in his 1497 book. The earliest known discussion in print is Salvio's Il Puttino (1634), crediting Scipione Genovino — though an older anonymous sixteenth-century manuscript predates it; the misattribution appears to date from the 1880 Handbuch. The Vancura position's provenance is likewise unresolved — Edward Winter has been unable to exhibit it in any 1920s source.
"Steinitz said you are obliged to attack once you have an advantage." The theory is real; the pithy formulations, including that clause, come from later writers systematising him rather than from a quotable line in the Modern Chess Instructor.
"You play worse because you lost the last game." The most direct test found the population-level effect centred on zero. Streaks beyond chance do exist in a much larger dataset, but nobody has identified the cause, and neither study touches rapid or classical. Mindset carries both. The rules there target the decision to keep playing, not the quality of the next move.
"Adopt a growth mindset and your rating will move." Meta-analytically the effects are small: r = .10 for mindset and achievement, d = 0.08 for interventions, with most effect sizes not distinguishable from zero and the real gains concentrated in low-achieving and low-SES groups. Believing ability is malleable is probably true. It is not a training intervention.

Where sources genuinely disagree

Question	The disagreement
Play-heavy or study-heavy?	Amateur survey data says 65–97% playing. Academic data (Charness et al. 2005) says serious solitary study is worth roughly six times tournament play per log unit — 200 rating points versus 33. Different populations, different strength levels, both correlational. Neither is settled.
Do endgames matter below 1200?	The phase-by-phase blunder data puts the endgame highest at every level (45.9% at 400–600 against 43.2% middlegame and 19.6% opening) and shows it improving least with strength, which favours studying them early. Against that, only 14% of amateur classical games in a 12.6M-game sample reached a technical endgame at all, and Solon reports never having lost half a point to a missing theoretical ending. Both numbers have real problems — centipawn loss is not comparable across phases, and the 14% definition is strict — and nobody has tested whether studying endgames raises anyone's rating against a control. Endgames reports the argument in exactly these terms and resolves it by keeping the early curriculum small.
Is blitz useful?	Prominent coaches say avoid it entirely. One large amateur survey's regression recommends 25–30% of total chess time in blitz. Sample sizes and confidence intervals for that sub-analysis were never published.
Does who you are playing change how you play?	Backus et al. (2023, Quantitative Economics) find women's engine-measured error about 11% larger against male opponents. Stafford (2018, Psychological Science), 5.5 million games, finds women outperform their expected score against men and reports no stereotype-threat effect. Move quality versus results — reconcilable, but not settled. The Mindset page treats "playing the person" as coach observation, not demonstrated effect.
Rating conversion between platforms	Two widely used conversion tables are irreconcilable — one maps chess.com rapid 1100–1200 to USCF 970–1060, another maps chess.com rapid 1420 to USCF 1415. This site uses the larger, more recent, methodologically documented sample.

Quality of the underlying data

The improvement-rate dataset (n≈384) is the best available on amateur improvement, but respondents are self-selected motivated improvers who volunteered to track themselves for years. Its medians are closer to a ceiling for a typical hobbyist than to an average.
The blunder-curve and puzzle-correlation studies (~162,000 games; 5.88M puzzle records) have stated methodology, sample sizes and engine versions — but come from a small commercial site, are not peer-reviewed, and have not been independently replicated. Cite with that caveat.
Rating percentiles have an ambiguous denominator: sources disagree on whether they cover all rated accounts or only players active in the last 90 days. This materially changes what a percentile means.
Percentiles have also drifted enormously. A 1000 rapid rating was around the 39th percentile in 2016 and the 81st by 2024 — driven by a mass influx of true beginners, not by rating deflation. Analysis comparing engine accuracy across those years found only ~2% difference.

Improvement and expertise research

Bryant, "Can Adults Improve At Chess" (chess.com, updated Jan 2025) — ~8,000 rated players from 1991, manually screened. Source of the 1,000+ cases of 200+ point adult gains, the 200 cases of 500+, the median peak age of 41 among the 500+ point gainers specifically, and the national-master-per-year figures.
Gobet & Campitelli (2007), n=104 — hours to master level ranged 3,016 to 23,608. On starting age, two findings that are often welded together and should not be: the probability of reaching international level (grandmaster or international master) was .24 for those starting by age 12 against .018 for later starters — but these are raw proportions (χ²(1) = 12, p < .002), not adjusted for practice hours. The controlling-for-practice result is separate: partial correlations of −.23 to −.40 between rating and starting age. Quoting the .24/.018 figures as if they survived a practice control overstates them.
Charness et al. (2005), N=375 — serious study alone correlates r = .54 and .48 with rating in its two samples (N=375 is the pooled figure used for the regression, not the sample yielding .54); each log unit of solitary study ≈ 200 rating points versus 33 for tournament play; combined chess activities explain ~40% of skill variance.
Macnamara, Hambrick & Oswald (2014) — meta-analysis, 157 effect sizes, 11,135 participants. Deliberate practice explains 26% of variance in games, 12% across all domains, and only 5% when practice is measured by logs rather than recall.
Chase & Simon (1973) — five-second recall: master ~16 pieces, Class A ~8, beginner ~4 on real positions; advantage largely collapses on random positions.
de Groot (1946) — masters do not search deeper or wider; they see the right candidate almost immediately. Skill is perceptual before it is calculational.
ChessGoals descriptive data and SmarterChess models — annual gain distributions and expected gains by band; the basis of this site's projection model.
Lichess, "How long does it take to get good?" — 5.5 years of database trajectories; players at 1600–2000 take four years or more to gain 100 points; no clean relationship between games played and improvement rate.

Learning science

Cepeda et al. (2006) — meta-analysis, 839 assessments across 317 experiments. Spaced beat massed by ~10.6 percentage points.
Cepeda et al. (2008) — the parametric spacing study, n≈1,350. Optimal gap ≈ 20% of the test delay for delays of a few weeks, falling to about 5–7% at a one-year delay. The absolute gap grows with the retention interval; the proportion shrinks steeply. +111% recall at a 70-day horizon for an optimal versus zero-day gap.
Roediger & Karpicke (2006) — testing effect. One week later: restudy 42%, retrieval 56%. Crucially, massed restudy wins at five minutes and loses badly at one week.
Karpicke & Blunt (2011, Science) — retrieval 0.67 vs concept mapping 0.45, d = 1.50; 75% predicted concept mapping would be just as effective or more effective — which is weaker than "predicted the opposite," and is how the Method chapter states it.
Rohrer & Taylor (2007) — interleaving. Blocked practice 89% during practice and 20% a week later; interleaved 60% then 63%.
Bjork — desirable difficulties, the New Theory of Disuse, and illusions of competence.
Walker et al. (2002, Neuron) — sleep consolidation: no significant gain after 12 waking hours, then ~+20% by the next morning. The +17.0% after one night and +26.2% after three are from a different paper — Walker, Brakefield, Seidman, Morgan, Hobson & Stickgold (2003, Learning & Memory 10(4):275–284). An earlier version of this chapter merged the two. Both used a motor-sequence finger-tapping task; extension to chess pattern consolidation is inference, not a demonstrated result.
Ericsson (2007) — states explicitly that flow states are "incompatible with deliberate practice."
Bisra et al. (2018) — meta-analysis of self-explanation prompts, 69 effect sizes across 64 reports, g = 0.55. The nearest indirect support for engine-off-first analysis, and none of the studies is a chess player reviewing their own game.
Sala & Gobet (2017) — training effects collapse once an active control group is used (music 0.25 SD passive vs 0.03 SD active; chess 0.34 SD overall but 0.10 SD in the one study with an active control). Borrowed on Calculation as a methodological warning; the meta-analysis itself is about far transfer out of chess.
Wilson et al. (2019, Nature Communications) — "The Eighty Five Percent Rule," optimal error rate 15.87% for binary classification by gradient descent. See the folklore list for why it is not a puzzle-difficulty setting.
Simon (1974, Science) — a master's vocabulary estimated at 25,000–100,000 chunks, 5–10 seconds to fixate one. Multiplied out that is 35–280 hours, far below the observed 3,016–23,608 to reach master, which is why the chunk model describes storage rather than acquisition.
Lally et al. (2010) — 96 volunteers, 84 days: median 66 days to automaticity, range 18–254, and "missing one opportunity to perform the behaviour did not materially affect the habit formation process." Only 39 of 82 usable participants fitted the curve the 66 days comes from, and the behaviours were eating, drinking and exercise. Cochran & Tesser (1996) for the what-the-hell effect, studied in dieting.
Sisk et al. (2018) and Yeager et al. (2019, Nature) — the growth-mindset meta-analysis and the pre-registered 12,490-student trial behind the folklore entry above.
Palomäki, Laakasuo & Salmela (2014) — the working definition of tilt, from poker (n = 417). Note it is the definition the researchers supplied to participants, not one they measured.

Single-source chess analyses — real numbers, thin foundations

These carry a great deal of weight on the six Train pages and none of them is peer-reviewed or replicated. Each is cited at the point of use with this caveat attached; it is collected here so the pattern is visible.

The puzzle/game rating study — 2,763 players, ~950,000 games with Stockfish 17, 5.88M puzzle records. R = 0.815 between puzzle and game rating; the gap positive at every band (+363 below 600 to +64 at 2000+); volume of puzzles solved correlates −0.02 with closing it. An objection the study does not make itself: the two ratings are on different scales, so the absolute gap is partly an artefact. The shape and the −0.02 survive it. Single platform, no control group, no replication.
The phase-by-phase blunder study — ~162,000 Lichess rapid games, Stockfish 17, blunder = 300+ centipawns. Source of the endgame-first argument and its own best objection: centipawn loss is not comparable across phases.
The 10.7M-game blunder and clock analysis (movelibrary.com, April 2024, by "Matt") — 3.33M blunders at 400+ centipawns; 72% punished by a check or capture against ~11% of legal replies; the effect weakest (63%) exactly where a serious improver plays; centipawn loss by seconds remaining (25.2 / 29.7 / 39.6); the fitted ~100 points per second. Establishes that refutations are forcing moves, which is not the claim that scanning prevents blunders.
The endgame-frequency study — Lichess September 2017, 12.6M games, 2.74M classical; only 14% reached a technical endgame under a strict definition; 67% of those contained rooks. Internally inconsistent on the rook figure, and nobody has published the sensitivity analysis for the definition.
The puzzle-repetition study — 120,513 attempts by 1,017 users over seven weeks. Cycle 1→2 accuracy 85.8%→95.8% on 55 and 54 users; cycles 3 and 4 rest on 10 and 4. Its own conclusion is the important one: "We do not have data on whether improvements on the platform transfer to over-the-board play."
Solon's space analysis — 100,000 Lichess games, Stockfish's space term: more space was an advantage at every rating tier, and the advantage did not grow with rating. Publishes a chart rather than numbers, and it contradicts the author's own hypothesis, which is why Strategy marks its caution about grabbing space as coaching judgement standing against the data rather than resting on it.
The Puzzle Rush / Puzzle Storm community challenge — 89 participants, 56% finishing, self-reported, improvement measured on the drill itself. Reported both ways on Tactics, because it is not one-sided.
The blindfold-tactics pilot (2023) — 27 players against 11 controls, FIDE 1650–2100; solving times fell ~31%. The same paper reports a "26% increase in FIDE rapid Elo," which read literally is 400+ Elo in three months. This site declines to repeat that figure. Its standard-rating result was null.
Chabris & Hearst (2003, Cognitive Science) — the exception: peer-reviewed. 1,188 games, 23 grandmasters, Fritz 5 at a 1.5-pawn threshold. The rapid and blindfold games are from Monaco 1993–98; the 396 classical games were drawn from regular tournaments worldwide and deliberately matched in count. Blunders per 1,000 moves 5.02 classical / 6.85 rapid / 7.63 blindfold rapid, the last two not significantly different. A 2010 comment disputed parts of the analysis; the headline pattern survived.
Gee, Seese, Curley & Ward (2025) and Chowdhary, Iacopini & Battiston (2023, Scientific Reports) — the two tilt datasets. 145 very high-volume players versus 123 million games from ~0.98M players. Neither touches rapid or classical.
The move-15 "fragility" result (arXiv 2410.02333, later Physical Review E) — a graph-theoretic average across a game database, not a landmark inside any one game. Noted on Calculation precisely so it is not turned into a time budget.
Tablebases are not in this category. Lichess's 7-piece Syzygy set (complete since 19 August 2018) is ground truth, and the endgame verdicts on Endgames were checked against it rather than taken from books. It gives results and never reasons.

Coaching and practice

Dan Heisman — "Real Chess" vs "Hope Chess," the checks-captures-threats scan, and Counting as the primary beginner skill. His original Novice Nook columns are no longer reachable online; the collected volume is A Guide to Chess Improvement (Gambit, 2010).
Nate Solon — the engine-off analysis protocol, and the argument that standard puzzles train you to find your tactics while blunders come from missing theirs. He notes candidly that he has no silver bullet for blundering.
ChessDojo (Kraai, Pruess, Kavutskiy) — classical-only training philosophy and the case for own-game annotation as the central activity.
Dissent worth hearing — Kevin Lincoln, Make Good Moves (~1650 USCF): the full engine-off ritual has real opportunity cost, perfectionism about analysis makes people skip it entirely, and a fast engine-first pipeline on a rapid game beats doing nothing. Solon concedes the same ground for blitz, and adds a wider limit — that below a fairly high level you may not draw correct conclusions unaided however long you spend. Both concessions are quoted in full on Analyse, and Principle Ⅱ is scoped to match.
Dan Heisman, further — Hope Chess and Passive Hope Chess (the latter placed at 1200–1700, pool unspecified), the "1700 barrier" (a 2014 Q&A remark, one coach's impression, no published rating histogram shows a bump there), the resting-position stopping rule, and Is Your Move Safe? (Mongoose Press, 2016).
The Steps Method (Stappenmethode) — the second curriculum tradition that puts piece safety before mating patterns, and the ordering the motif tiers track. Convergence between two curriculum designers, not evidence.
The candidate-moves literature — Kotov (Think Like a Grandmaster, Batsford 1971) and the authors who reject his single-pass rule: Nunn (Secrets of Practical Chess, also DAUT and LPDO), Dvoretsky, Aagaard, Hendriks, Soltis, Tisdall. Two weak citations, flagged in place on Calculation: the Tisdall row traces to a blog comment thread, and the Soltis quotation reaches us through a quotation database rather than the book.
Chessable (2024) — candidate-moves experiment, 207 players, ten tactical positions, five minutes each; no significant difference between the instructed and uninstructed groups. One null result on ten puzzles, and the only direct test of a structured thinking method this site could find.
Silman, Complete Endgame Course — the rating-gated structure, and the instruction almost nobody follows. His Part Four places Lucena and Philidor at 1400 USCF; Endgames wants them at about 1200 and says plainly that this is a disagreement with a titled coach, not a correction of one.
Endgame authorities used sparingly: Tarrasch on the rook behind the passed pawn (with his own "except when it is incorrect to do so"); Shereshevsky's "do not hurry," given in quotation marks as received Soviet doctrine rather than his coinage; de la Villa and Dvoretsky as Tier 4 references only.
Strategy authorities: Flores Rios, Chess Structures (28 structures, 140 games); Watson, Secrets of Modern Chess Strategy on rule-independence; Hendriks's 110-game test of the wing-attack/centre-counterattack maxim (at most 10% support it) and Silman's reply that imbalances were "a shortcut to pattern recognition" — both reached us through one review, neither checked against the original. Outpost definitions from Nimzowitsch, Hooper & Whyld and Romanovsky come from a single secondary compilation with page numbers we have not verified.
Kaufman's piece values — statistical study of ~300,000 master games at 2300+, drawn from a larger set of about 925,000, published with methodology stated: knight = bishop at 3¼, bishop pair ≈ ½ pawn, the exchange ≈ 1¾ and rising as pieces come off. Averages over a database, not evaluations of your position.

Classical texts

Analects — checked against ctext.org and Zhu Xi's 四書章句集註. Translations: Legge, Slingerland, Watson. Passages used: 1.1, 2.11, 2.15, 2.17, 6.3, 7.8, 7.22, 9.19, 13.17.
Doctrine of the Mean 20 — the five steps and the 弗措也 stopping rule (Legge; Muller).
Doctrine of the Mean 14 — 射有似乎君子，失諸正鵠，反求諸其身, the archer who seeks the cause of the miss in himself, used on the Analyse page (Legge; chapter number confirmed against Muller).
Xunzi 勸學 "Encouraging Learning" — the half-step, the nag and the thoroughbred (Watson; Knoblock; Hutton).
Numbering caveat: Legge's edition numbers Book 7 one lower than modern editions — 三人行 appears as VII.xxi in Legge but 7.22 in Slingerland and Watson. Both are correct within their own scheme.
Textual variants: Xunzi's 勸學 has minor recension differences (跬步/蹞步; presence or absence of 至 in 無以至千里). These are edition differences, not errors.
Reading caveat: Analects 9.19's 吾止也 has an older commentarial reading as "I stop [helping him]" rather than "the stopping is mine." This site uses the standard modern reading.

The repertoire

Every move sequence on the Openings page was replayed through a chess engine for legality and cross-checked against published theory. Four errors were found and corrected in that pass: an illegal move in the Caro-Kann Fantasy line, a refutation in the Italian that gave up a bishop in a position where the queen simply hangs, a mislabelled Milner-Barry Gambit presented as a blunder, and an impossible bishop retreat described as a mistake to avoid. Lines that are playable but not clearly main theory, and the one genuine gap in the repertoire, are flagged in place on that page rather than here.

The same pass was run over the newer pages. Every line on Endgames and Strategy was replayed for legality, and the endgame verdicts were checked against the 7-piece tablebase rather than a book. The worked game on Analyse is constructed rather than a real player's game — it says so on the page — and every evaluation quoted there is actual Stockfish output, with the depth-sensitivity of the near-equal moves stated in place, because that instability is part of the lesson.

If you find an error

Assume there are some. A site that publishes this many specific numbers will have got a few wrong, and the correct response to that is correction rather than vagueness. The claims most likely to need revising are the ones resting on a single unreplicated source — flagged as such above — and the projection model's exponent, which is a reasoned choice rather than a measured constant.