Piers Steel's Procrastination Equation and the Snooze Button

Piers Steel’s Temporal Motivation Theory says the pull toward any action equals its expectancy times its value, divided by your sensitivity to delay times the delay itself. For waking up, that implies the bed wins every morning for a simple reason: its payoff is warm and arrives in seconds, while the payoff for rising is hours away, and of the four terms in the formula an alarm can only change the delay.

What did Steel’s 2007 paper actually find?

Steel (2007, Psychological Bulletin 133(1): 65-94) reviewed the procrastination literature and ran a meta-analysis of 691 correlations. The abstract names the strong and consistent predictors: task aversiveness, task delay, self-efficacy, impulsiveness, and conscientiousness with its facets of self-control, distractibility, organization and achievement motivation. Neuroticism, rebelliousness and sensation seeking showed only weak connections.

The numbers in the paper’s tables, as uncorrected average correlations with procrastination:

Predictor	Average r	Studies (K)
Conscientiousness	-.62	20
Self-control	-.58	21
Distractibility	.45	13
Impulsiveness	.41	22
Task aversiveness (task procrastination)	.40	8
Self-efficacy	-.38	39
Organization	-.36	25
Neuroticism	.24	59

Corrected for unreliability, the conscientiousness figure rises to about -.75, which Steel says is comparable to the correlations among conscientiousness measures themselves. His reading is that procrastination is close to a measure of low conscientiousness, and that it accounts for a large share, though not all, of conscientiousness’s link to job performance.

These are correlations between questionnaire scores, mostly from students and workers describing tasks like term papers. None of them is a measurement of someone lying in bed at 6:00.

How common is procrastination, by Steel’s wording?

Steel opens with the prevalence claim: “Estimates indicate that 80% to 95% of college students engage in procrastination,” citing Ellis and Knaus (1977) and O’Brien (2002). He adds that approximately 75% consider themselves procrastinators and almost 50% procrastinate consistently and problematically, and that among adults some 15% to 20% are chronic procrastinators.

Steel did not measure these figures. They are secondhand estimates, they concern students, and the 80% to 95% band describes engaging in procrastination at all, which is a low bar. The one-in-two and one-in-five figures are the ones that describe a problem.

What is the equation, and what do its four terms mean?

In the paper’s simplest form, utility equals expectancy (E) times value (V), divided by a delay-sensitivity parameter (gamma) times delay (D). By Steel’s definition, “we pursue whatever behavior has the highest utility.” Each term has stand-ins in the data:

• Expectancy is represented mainly by self-efficacy (r = -.38 with procrastination).
• Value is represented by task aversiveness, need for achievement and boredom proneness.
• Sensitivity to delay is linked to impulsiveness, distractibility and self-control.
• Delay is the timing of rewards and punishments.

Steel’s worked illustration is a student, “Thomas Delay,” assigned an essay on September 15 and due December 15. Socializing pays off in the present, so its utility stays high all semester. Writing pays off at the deadline, so it starts low. In his figure the two lines cross on December 3rd, leaving 12 days of concentrated effort. Nothing about the task changed in September or November. Only the distance to the payoff shrank.

For why the curve is steep near the present and flat far from it, the shape comes from hyperbolic discounting, which Steel combined with expectancy theory.

What does the equation say about the first ten minutes after an alarm?

Take the two options at 6:00 a.m.: stay in bed, or stand up. The figures below are invented for illustration, in arbitrary units, with delay in minutes and the same sensitivity (set to 1) for both options.

	Expectancy	Value	Delay	Pull
Five more minutes	1.0	6	1 min	6.0
Get up (meeting at 9:00)	0.9	10	180 min	0.05

Getting up is worth more in this sketch, 10 against 6, and still loses by a factor of about 120, because the one pays off now and the other in three hours. Steel’s prediction for the Thomas Delay case is the same shape: the thing with the later payoff loses until the payoff is close.

Now go through the terms and ask which one a morning routine can touch.

Expectancy. Self-efficacy is the strongest-supported stand-in, so the credibility of “I can do this” matters. But an alarm cannot raise it much in the moment. A plan made the night before might, and the sleeper rarely doubts they can stand up. The doubt is about wanting to.

Value. The bed’s value, warmth and unconsciousness, is not something a routine edits. The reward for rising is also fixed by the day’s content. What a routine can add is a negative value on the staying option, which is the delay question again, since a penalty only counts if it is near.

Sensitivity to delay. In the paper this tracks impulsiveness, distractibility and self-control, all trait-like measures. A person cannot rewrite them between 5:59 and 6:00. The paper does not test whether sleepiness inflates them, so that remains a guess, though research on how long grogginess lasts, such as Burke et al. (2015), points to a body that is at its least deliberate in exactly this window.

Delay. The delay on the rising reward cannot shrink: the meeting is at 9:00 whatever the alarm does. The delay on the cost of staying can. If skipping has no consequence until the late arrival at 9:00, it carries a delay of 180 minutes and a probability below one. If skipping has a consequence in half a minute, the cost arrives before the covers have warmed up.

What changes when the penalty lands in 30 seconds?

Steel says to apply punishments by taking the reciprocal of the equation, because “we prefer our punishers to be distant, unlikely, and small.” The sketch below simplifies this to a signed sum, so read it as a cartoon of his point rather than his algebra.

Suppose being late has a cost of -8 at 9:00 with a 30% chance of anyone caring: 0.3 times -8 over 180 minutes is about -0.013. It does not register against the +6 pull of the bed. Now suppose the cost of not responding is also -8 but certain and 30 seconds (0.5 minutes) away: -8 over 0.5 is -16. Staying in bed now nets 6 - 16 = -10, and the 0.05 pull of getting up is the best option on the page. The cost did not get bigger. Its address in time moved, from 9:00 to 6:00:30.

The same logic underlies the pigeon results Steel reviews: in Mazur’s experiments, pigeons put off a small amount of work now in favor of much more work later for the same result. Ainslie’s 1974 pigeons are the related case, where some birds learned to cut off the near option in advance. And a deadline is only a delay term in disguise, as the Thomas Delay curve shows, which is also why goals with no deadline tend to stay unstarted.

Where the argument stops

This is a thought experiment built on a correlational literature. Steel’s evidence supports the claim that delay, aversiveness, self-efficacy and impulsiveness predict procrastination in tasks that people report about. It does not show that shortening a penalty’s delay makes people leave bed, and the arithmetic above uses numbers chosen to make the contrast readable. Steel himself closes by calling for further research.

One more limit comes from the formula’s structure. If the penalty is large and certain but still hours away, the model says it will lose to the bed, and if it is certain and immediate but trivial, it will lose too. Both size and nearness have to be there.

DontSnooze applies this to the delay term directly: when the alarm fires there are 30 seconds to record a short video proving you are up, and if there is none, a random photo from your camera roll goes to your friends. The consequence of skipping stops being something that might happen at 9:00 and becomes something that happens before the room has warmed up.

Shrinking the delay works at larger scale too: closing the smallest debts first shortens the time between effort and a visible result.

At 6:00:29, the bed’s score and the penalty’s score are being compared in the same minute for the first time, which is the one place in the morning where Steel’s denominator can be shortened on purpose.