Does Willpower Really Run Out — From the Radish Experiment to the Replication Crisis, with Publication Bias in Code

Opening — The Most Famous Muscle in Psychology

"Willpower is like a muscle: use it and it wears out. So make your important decisions in the morning, and do not blame yourself if your diet collapses on a day you spent resisting temptation."

Ego depletion theory was once the most popular gift psychology had given the public. There were hundreds of supporting papers, it produced a bestseller, and it became common sense — to the point that a president said he wore only the same suits to reduce decision fatigue.

Then, in 2016, this theory became the symbol of psychology's replication crisis. The fourth installment of Psychology Through Papers follows that dramatic arc. What makes this installment special within the series is that we will answer the perfectly reasonable question — "how can a theory with hundreds of papers behind it be wrong?" — by running code.

1998 — Chocolate, Radishes, and an Unsolvable Puzzle

The first experiment in the 1998 paper by Roy Baumeister's team is famous for its staging alone. Hungry undergraduates are seated in a room filled with the aroma of freshly baked chocolate cookies. One group is allowed to eat the cookies; the other group must eat only raw radishes instead. Afterwards, everyone receives a geometric puzzle that is in fact unsolvable, and the researchers time how long they keep trying.

The result: the cookie group persisted for about 19 minutes on average, while the radish group — the ones who had to resist the temptation — gave up after about 8 minutes. Each group had barely more than 20 people. The paper interprets it this way: resisting the lure of the cookies consumed some shared resource, which left too little persistence for the puzzle. That is the birth of the name "ego depletion".

Over the next 20 years the paradigm expanded explosively. Hundreds of studies piled up showing that after all kinds of "depletion tasks" — suppressing emotions, making choices, crossing out particular letters in a text — performance dropped on handgrip endurance, drinking a bitter beverage, or solving anagrams. A 2010 meta-analysis pooled 198 studies and reported a medium-sized effect (d around 0.6). There was even a theory that blood sugar (glucose) was the resource. It looked more than ready for the textbooks.

2016 — A Joint Replication by 23 Labs

From the early 2010s, however, ominous signals started to appear. Newly attempted large-sample replications kept failing, and in 2015 Carter and McCullough reported that once publication bias corrections were applied to the existing meta-analysis, the effect became indistinguishable from zero.

The decisive test was the 2016 Registered Replication Report. Coordinated by Martin Hagger and Nikos Chatzisarantis, this project shows what the standard design for replication research looks like.

• 23 labs and roughly 2,100 participants in total take part.
• The protocol is agreed upon and registered in advance, with advice from the original theory's camp: deplete with a letter-crossing task, measure with a standardized computer task.
• Publication is guaranteed regardless of the results. No null result gets buried in a drawer.

The result was shocking. The effect size pooled across the 23 labs was d = 0.04, with a confidence interval centered on zero. In effect, it means no effect at all. In 2021 a large-scale replication across 36 labs (Vohs et al.), with Baumeister's camp participating directly in the design, was carried out — and there too the effect was close to zero (around d 0.06, depending on the estimate). The glucose theory had collapsed even earlier.

Hundreds of papers versus two replications. So why does the latter win?

Understanding It in Code — The Mirage Built by the File Drawer

The key is publication bias. Even if the effect is truly zero, a single rule — "only significant results get published" — is enough to fill the literature with plausible-looking effects. Words alone do not make this intuitive, so let us confirm it with a simulation.

import random
import statistics

random.seed(42)

TRUE_EFFECT = 0.0   # the real effect size is zero
N_PER_GROUP = 20    # small samples, like the classic studies
N_STUDIES = 500     # labs around the world keep trying

published = []
drawer = 0

for _ in range(N_STUDIES):
    # two groups drawn from the SAME distribution (no real effect)
    control = [random.gauss(0, 1) for _ in range(N_PER_GROUP)]
    treated = [random.gauss(TRUE_EFFECT, 1) for _ in range(N_PER_GROUP)]

    # observed standardized effect (Cohen's d, pooled SD ~= 1)
    d = statistics.mean(treated) - statistics.mean(control)

    # crude significance rule for a two-sample test of this size:
    # |d| > ~0.64 corresponds to p < .05 with n=20 per group
    if abs(d) > 0.64:
        published.append(d)   # "exciting result!" -> journal
    else:
        drawer += 1           # null result -> file drawer

print(f"published studies : {len(published)}")
print(f"file drawer       : {drawer}")
print(f"mean published |d|: {statistics.mean(abs(d) for d in published):.2f}")

Run it and this is the picture you get. Even though the true effect is exactly 0, roughly 5% of the 500 attempts cross the significance line by pure chance, and if you collect only those "winning" studies and average them, you manufacture a literature worth d 0.7~0.8. The smaller the samples, the larger the amplitude of chance, so the winning effects look even more spectacular. Add researcher degrees of freedom (picking the best-looking of several measures, changing the outlier-exclusion criteria) and the winning probability climbs well past 5%.

This is the mechanism by which "hundreds of papers" can be wrong. The number of papers may measure not the amount of evidence but the number of samples that survived a selection process. That is why a handful of large-scale replications with preregistration and guaranteed publication carry more weight than hundreds of selected papers.

So What Remains of Willpower

It is important not to take the wrong lesson away from the fall of ego depletion.

What does not survive: the mechanical resource model — "resisting temptation drains a resource, so your next act of self-control must be weaker" — and using that model as an excuse ("I resisted earlier, so it is scientifically inevitable that I collapse now").

What survives, part 1 — fatigue itself is real. That sleep deprivation and long stretches of high-intensity focus break down judgment and emotional regulation is supported by a separate, robust literature (covered in the sleep debt installment). What collapsed is the precise claim that a 5-minute self-control task depletes a resource — not the common sense that you need rest.

What survives, part 2 — self-control is decided by design, not by will. Intriguingly, recent studies show that people who are good at self-control are not the ones who resist temptation heroically, but the ones who design their environment so they encounter temptation less in the first place. The friction design covered in Systems Beat Goals is exactly that strategy.

What survives, part 3 — evidence that science works. A famous theory collapsing is not psychology's disgrace but proof of its capacity for self-correction. Preregistration, registered replications, and multi-lab collaborations became the standard through these very events.

Guide to Reading the Originals

• Original paper: Baumeister, R. F., Bratslavsky, E., Muraven, M., & Tice, D. M. (1998). Ego depletion: Is the active self a limited resource? Journal of Personality and Social Psychology, 74(5), 1252-1265.
• Bias correction: Carter, E. C., & McCullough, M. E. (2014). Publication bias and the limited strength model of self-control. Frontiers in Psychology, 5, 823.
• Replication: Hagger, M. S., Chatzisarantis, N. L. D., et al. (2016). A multilab preregistered replication of the ego-depletion effect. Perspectives on Psychological Science, 11(4), 546-573.
• Second replication: Vohs, K. D., et al. (2021). A multisite preregistered paradigmatic test of the ego-depletion effect. Psychological Science, 32(10), 1566-1581.

Reading tips: in the 1998 paper, the method section of Experiment 1 is the highlight (down to the footnote on how many radish-condition participants touched the cookies). In the 2016 RRR, one forest plot (the per-lab effect figure) says more than the entire text. The next installment changes the mood — the most famous happiness study ever run on smartphones, A Wandering Mind and Happiness.