Is willpower a tank of fuel that runs dry?

Every model in the previous chapters needs a “push”: a steady outside force, random disturbance, the energy to cross a barrier. A popular view holds that a person’s push comes from a limited inner resource that, like muscular strength, runs out with use: resist temptation in the morning and you will find it harder to persist in the afternoon. This is the theory of ego depletion. This chapter checks its evidence, because it bears directly on how to design action: if willpower really is a tank that empties, it should be rationed; if not, the strategy is different.

The classic study and the large replications

Where does the gap between 0.62 and nearly zero come from? One important reason is publication bias: there are many small studies, and significant results are easier to publish.

# How a near-zero effect can look large in the published record.
# Suppose the true ego-depletion effect is d = 0.05. Many small labs run studies with 20 people per group;
# only studies with a positive, significant result (p < .05, one-tailed direction) reach print.
import math, random
from statistics import NormalDist, mean, stdev
random.seed(4)
TRUE_D, N, STUDIES = 0.05, 20, 4000
z_crit = NormalDist().inv_cdf(0.975)

all_d, published = [], []
for _ in range(STUDIES):
    a = [random.gauss(TRUE_D, 1) for _ in range(N)]
    b = [random.gauss(0, 1) for _ in range(N)]
    sp = math.sqrt((stdev(a) ** 2 + stdev(b) ** 2) / 2)
    d = (mean(a) - mean(b)) / sp
    se = math.sqrt(2 / N + d * d / (4 * N))
    all_d.append(d)
    if d / se > z_crit:
        published.append(d)
print(f"true effect d = {TRUE_D}; {STUDIES} studies with {N} per group")
print(f"mean d of all studies run:      {mean(all_d):5.2f}")
print(f"share reaching significance:    {100 * len(published) / STUDIES:4.1f} %")
print(f"mean d of the published ones:   {mean(published):5.2f}")
print("for comparison: 2010 meta-analysis d = 0.62; 2016 23-lab replication d = 0.04; 2021 36-lab test d = 0.06")
# true effect d = 0.05; 4000 studies with 20 per group
# mean d of all studies run:       0.05
# share reaching significance:     3.9 %
# mean d of the published ones:    0.79
# for comparison: 2010 meta-analysis d = 0.62; 2016 23-lab replication d = 0.04; 2021 36-lab test d = 0.06

In this simulation the average effect over all studies correctly sits near 0.05, but only about 4 % of studies reach significance, and those published studies show an average effect of 0.79 — higher even than the 2010 meta-analytic estimate. Small samples plus selective publication are enough to create a “robust” literature out of an effect that barely exists. This does not prove that such selection happened in ego-depletion research, but it shows why large pre-registered replications are more credible than the pooled results of many small studies.

Fuel arithmetic

Ego-depletion theory once proposed that self-control uses up blood glucose. The claim can be checked by simple arithmetic on orders of magnitude.

# Could half an hour of self-control use up the brain's fuel? Order-of-magnitude arithmetic.
BRAIN_W = 20.0           # W: the adult brain uses roughly 20 % of resting metabolism, about 20 W
TASK_RISE = 0.05         # focused tasks raise whole-brain energy use by a few per cent at most (upper bound)
MINUTES = 30
KJ_PER_G_GLUCOSE = 15.6  # kJ released per gram of glucose fully oxidised
extra_kj = BRAIN_W * TASK_RISE * MINUTES * 60 / 1000
grams = extra_kj / KJ_PER_G_GLUCOSE
BLOOD_GLUCOSE_G = 4.5    # grams of glucose circulating in an adult's blood (about 5 L at 5 mmol/L)
LIVER_GLYCOGEN_G = 80.0  # a typical fed-state liver glycogen store
print(f"extra energy for {MINUTES} min of hard thinking: {extra_kj:.1f} kJ = {extra_kj / 4.184:.2f} kcal")
print(f"glucose needed: {grams:.2f} g, i.e. {100 * grams / BLOOD_GLUCOSE_G:.1f} % of the glucose in the blood "
      f"and {100 * grams / LIVER_GLYCOGEN_G:.2f} % of liver glycogen")
print(f"a 250 mL sugary drink (about 27 g sugar) carries {27 / grams:.0f} times this amount")
# extra energy for 30 min of hard thinking: 1.8 kJ = 0.43 kcal
# glucose needed: 0.12 g, i.e. 2.6 % of the glucose in the blood and 0.14 % of liver glycogen
# a 250 mL sugary drink (about 27 g sugar) carries 234 times this amount

Even taking the task-related increase as 5 % of the brain’s energy use (a generous upper bound), half an hour of hard thinking costs about 0.43 kcal extra, about 0.12 g of glucose — roughly 3 % of the glucose in the blood and 0.14 % of the liver’s glycogen store. A sugary drink carries more than two hundred times as much. Half an hour of self-control “running out of fuel” does not add up by orders of magnitude. This agrees with the argument of Kurzban and colleagues that the brain’s total energy use hardly changes with the task, so “running out of fuel” is the wrong explanation for subjective fatigue and giving up (Kurzban et al. 2013).

Reallocating motivation

If it is not fuel, what makes people more likely to give up after a stretch of effort?

Both explanations share one feature with the models of this book: what matters is not a stock that runs out but a comparison of values. In the language of Chapter 3, how high a task’s “barrier” is depends on what alternatives are available at the moment and how tempting they look. This suggests a different strategy from “rationing willpower”: instead of storing willpower, lower the barriers to be overcome (Chapters 2 and 3) and change how attractive the alternatives are (for example, by putting the phone in another room), so that continuing the current task becomes the higher-value choice.

“Cognitive energy budget” as a metaphor

The “cognitive energy budget” in this chapter’s title is a metaphor. Attention and motivation really are limited: they can go to only a few things at a time. But their limit is more like the limit of time than the limit of a fuel tank. An hour can be spent only once, and how much one is willing to put into it depends on how one weighs this task against others. The point returns in Chapter 8’s four-step barrier audit, which checks not how much “willpower” you have left but whether the outside structures that get you started and keep you going are in place.

Summary

Ego depletion is one of the most closely watched cases of psychology’s replication crisis: an effect supported by hundreds of studies all but vanished in large pre-registered replications. The blood-glucose fuel story fails on orders of magnitude too. More credible explanations involve the reallocation of motivation and attention and the weighing of opportunity costs. For the design of action this means relying less on “gritting your teeth” and more on lowering barriers, borrowing outside structure and reducing tempting alternatives in the moment.