The violin students of Berlin

In 1993 Ericsson, Krampe and Tesch-Römer published a paper that has since been cited well over ten thousand times (Ericsson et al. 1993). At a music academy in West Berlin they asked professors to sort violin students into three groups: the “best”, likely to have careers as international soloists; the “good”; and students preparing mainly to become music teachers (ten in each group). The students estimated, year by year, how many hours a week they had practised alone since they began, and kept a detailed diary for a week. By the age of 18, the “best” group had accumulated an estimated average of about 7,410 hours, the “good” group about 5,301, and the teachers’ group about 3,420 (Ericsson et al. 1993; Macnamara and Maitra 2019).

Their central concept was deliberate practice: not simply playing or performing, but activities designed by a teacher, with clear goals, aimed at current weaknesses, demanding full concentration and accompanied by feedback; activities that are often not enjoyable. The paper’s claim was strong: the differences between experts and others arise mainly from deliberate practice accumulated over many years, not from innate talent.

Where “10,000 hours” came from

The “10,000-hour rule” was popularised by Gladwell’s 2008 bestseller Outliers (Gladwell 2008). The figure comes from the 1993 study’s estimate of the average practice accumulated by the best violinists by the age of 20. Ericsson himself later criticised this popularisation explicitly (Ericsson and Pool 2016): 10,000 hours was an average, not a threshold, with some above and some below it; at 20 these students were still far from being masters; the time required differs greatly between fields; and Gladwell did not distinguish deliberate practice from all the other kinds of “time spent doing the thing”. “Practise for 10,000 hours and you will become an expert” was neither the conclusion of the 1993 paper nor the position of its authors.

Meta-analyses: how much of the difference does deliberate practice explain?

What “explains 12 % of the variance” means

These figures are often misread as “practice accounts for 12 %, talent for 88 %”. Neither reading is right. First, the remaining 88 % is not “talent” but all other factors plus measurement error: the quality of practice, the age at which it began, teachers, health, opportunity, luck, and genes and early abilities. Second, and more fundamentally, “how much of the difference between individuals is explained by the amount of practice” and “how much practice improves a person” are different questions.

Part 1 converts the meta-analytic correlations into shares of variance. Part 2 builds a synthetic population (illustrative weights, not estimates) in which every person’s performance rises markedly with the logarithm of practice, but in which people also differ in the quality of their practice, the age at which they started, prior ability and other factors.

# Part 1: meta-analytic r (Macnamara et al. 2014) as r^2. Part 2: synthetic population
# (illustrative weights) in which practice helps EVERY person, yet explains little BETWEEN them.
import math, random
from statistics import correlation, fmean, pvariance

print("Part 1  meta-analytic correlations (Macnamara et al. 2014)")
for dom, r in (("overall", .35), ("games", .51), ("music", .46), ("sports", .42),
               ("education", .21), ("professions", .05)):
    print(f"   {dom:11s} r = {r:.2f} -> r^2 = {r * r:5.1%} explained, {1 - r * r:5.1%} not")

rng = random.Random(23)
people = []
for _ in range(5000):
    hours = math.exp(rng.gauss(math.log(3000), 0.6))       # accumulated practice, log-normal
    quality = rng.gauss(0, 1)                                # how well the hours are used
    start = rng.gauss(0, 1)                                  # earlier start (standardised)
    ability = rng.gauss(0, 1)                                # prior ability, aptitude
    other = rng.gauss(0, 1)                                  # teaching, health, luck, ...
    gain = 1.0 + 0.4 * quality                               # each person's return per log-hour
    perf = gain * (math.log(hours) - math.log(300)) + 0.35 * start + 0.8 * ability + 0.9 * other
    people.append((math.log(hours), quality, start, ability, other, perf, gain))

perf = [p[5] for p in people]
def r2(i):
    return correlation([p[i] for p in people], perf) ** 2

print("\nPart 2  synthetic population of 5,000 learners (illustrative)")
print(f"   within a person: +1 log-unit of practice (x2.7 hours) adds on average "
      f"{fmean(p[6] for p in people):.2f} performance units")
sd = math.sqrt(pvariance(perf))
print(f"   between people: SD of performance {sd:.2f} units")
print(f"   so going from 300 to 3,000 hours moves a typical person {math.log(10) / sd:.2f} SD")
for name, i in (("log practice hours", 0), ("practice quality", 1), ("starting age", 2),
                ("prior ability", 3), ("everything else", 4)):
    print(f"   share explained by {name:18s} alone: {r2(i):5.1%}")
qp = [p[0] * p[6] for p in people]                           # hours weighted by quality
print(f"   share explained by quality-weighted hours:  "
      f"{correlation(qp, perf) ** 2:5.1%}")
# Part 1  meta-analytic correlations (Macnamara et al. 2014)
#    overall     r = 0.35 -> r^2 = 12.2% explained, 87.8% not
#    games       r = 0.51 -> r^2 = 26.0% explained, 74.0% not
#    music       r = 0.46 -> r^2 = 21.2% explained, 78.8% not
#    sports      r = 0.42 -> r^2 = 17.6% explained, 82.4% not
#    education   r = 0.21 -> r^2 =  4.4% explained, 95.6% not
#    professions r = 0.05 -> r^2 =  0.3% explained, 99.8% not
#
# Part 2  synthetic population of 5,000 learners (illustrative)
#    within a person: +1 log-unit of practice (x2.7 hours) adds on average 1.00 performance units
#    between people: SD of performance 1.69 units
#    so going from 300 to 3,000 hours moves a typical person 1.36 SD
#    share explained by log practice hours alone: 12.1%
#    share explained by practice quality   alone: 29.6%
#    share explained by starting age       alone:  4.1%
#    share explained by prior ability      alone: 22.6%
#    share explained by everything else    alone: 28.5%
#    share explained by quality-weighted hours:  37.0%

In this synthetic population practice has a large effect on every individual: going from 300 to 3,000 hours raises a typical person by about 1.36 standard deviations. Yet across the population practice hours alone explain only about 12.1 % of the differences in performance, close to the meta-analytic average. The reason is that people practise differently: in the model, the same hours bring more to those whose practice is of higher quality, and weighting hours by quality raises the share explained to about 37 %. This is only an illustration, but it makes two points. A figure of 12 % is entirely compatible with “practice is very useful for the individual”; and counting hours without asking how they were spent throws away much of the information, which is one of Ericsson’s objections to the meta-analyses.

Why the figures differ so much between studies

One true relation (synthetic data, a correlation of 0.45 between log practice and performance) seen through different samples and measures.

# One true relation (log practice vs performance, r = 0.45, synthetic data) seen through
# (1) range restriction: only the top performers are studied; (2) measurement: practice
# estimated with large error, or recalled in a way that tracks present performance.
import math, random
from statistics import correlation

rng = random.Random(7)
pop = [(lp, 0.45 * lp + math.sqrt(1 - 0.45 ** 2) * rng.gauss(0, 1))
       for lp in (rng.gauss(0, 1) for _ in range(20000))]
r2 = lambda rows: correlation([a for a, _ in rows], [b for _, b in rows]) ** 2
print(f"whole population: practice explains {r2(pop):.1%}")
ranked = sorted(pop, key=lambda r: r[1])
for top in (0.10, 0.02):
    print(f"   top {top:.0%} performers only: {r2(ranked[int(len(ranked) * (1 - top)):]):.1%}")
for label, err, bias in (("large recall error", 1.0, 0.0), ("recall tracks performance", 1.0, 0.5)):
    obs = [(lp + err * rng.gauss(0, 1) + bias * pf, pf) for lp, pf in pop]
    print(f"   {label}: {r2(obs):.1%}")
# whole population: practice explains 20.0%
#    top 10% performers only: 3.4%
#    top 2% performers only: 1.3%
#    large recall error: 9.8%
#    recall tracks performance: 33.8%

In the whole synthetic population practice explains about 20 % of the differences; among the top 10 % of performers, about 3.4 %; among the top 2 %, about 1.3 %. This is range restriction: in an elite sample everyone has practised a great deal and has been selected on performance, so differences in practice naturally explain less; the figure of about 1 % in elite sports samples does not mean that elite athletes’ practice is “useless”. Measurement matters too: retrospective estimates with large error weaken the correlation (about 9.8 %); if recall of practice is coloured by present level, the correlation is inflated instead (about 33.8 %). That retrospective interviews explained more (about 20 %) than diaries (about 5 %) in the meta-analysis may be related to this, but this is only one possible explanation.

Four elements of high-quality practice: a synthesis

Taking this chapter together with the research of the chapters that follow, four elements of high-quality practice can be distinguished. This is the author’s synthesis, not the conclusion of any single study; each item notes the strength of the evidence behind it.

1. A clear, small goal. Each stretch of practice targets one specific sub-skill, rather than “play the whole piece through” or “go over the chapter again”. This is central to the original definition of deliberate practice (Ericsson et al. 1993); but “the more specific the goal the better” has itself seldom been tested in direct comparisons. Evidence: mainly theoretical and descriptive.
2. At the edge of the sweet spot. Difficulty is set so that most items are answered correctly, but not all: the model of Chapter 1 gives a reference band of roughly 80–90 %. Evidence: strong in mathematical models and simulations; few direct tests in complex human skills.
3. Prompt, high-fidelity feedback. The learner finds out quickly whether they were right and, if not, where they went wrong. Evidence: supportive overall, but Chapter 6 shows that the effects of the timing, frequency and type of feedback vary greatly, and that more than a third of feedback interventions make performance worse.
4. Correct the error and try again. Once an error has been pointed out, the learner does another item of the same kind until it is right. Evidence: consistent with experiments on retrieval practice and on learning from errors, but few studies compare “correct and redo” directly with “just look at the answer”.

Chapter summary

Ericsson and colleagues introduced deliberate practice in 1993, stressing goal-directed practice with feedback aimed at weaknesses; “10,000 hours” is Gladwell’s popularisation, which Ericsson himself criticised. Meta-analyses find that deliberate practice explains on average about 12 % of individual differences (games 26 %, music 21 %, sports 18 %, education 4 %, professions under 1 %), and about 1 % in elite sports samples; the replication of the 1993 study found no difference between the “best” and the “good”; and the dispute between the two sides is largely about definitions. “Explains little variance” does not mean “practice does not work”: synthetic data show the two are fully compatible, and range restriction and the way practice is measured can move the figures a great deal. The next chapter turns to the brain: what does practice change in the nervous system?