Habits Productivity

The Procrastination Equation – The Mathematics of Getting Things Done

By Jon Rumens on 11 December 2018

The world is governed by universal laws…

When you let go of an object, the law of gravity will make sure it crashes to the floor. If said object is a balloon filled with helium, it will go the opposite direction and float to the heavens. If you add energy to a substance, it becomes hot. If it loses energy, it becomes colder.

All of these are laws of physics.

There are other laws as well. For example, let’s take the classical economic law of supply and demand. If demand for a certain good increases, the price of that good will tend to go up. A recent example is cryptocurrency, like bitcoin. Where only a few years ago, you could buy thousands of bitcoins for only a few dollars, at the end of 2017, just one bitcoin was worth about twenty thousand dollars. In the meanwhile, that price has lowered significantly again.

Did something inherently change about the nature of bitcoin to justify these changes? Not really. It was just that people suddenly didn’t want their bitcoin anymore, so when demand dropped, the price crashed as well.

Then you’ve got certain biological and psychological laws. For example, we tend to find people more physically attractive when their faces are symmetrical. If people are nice to us, we tend to like them more as well (unless they’re just sucking up and act like sycophants to get favors in return).

Do you know what else is governed by laws like these?

Your tendency to procrastinate.

That’s right. When you have difficulty keeping your attention to the task at hand, this is because there’s a mathematical formula at work in your brain that measures certain factors and compares them to one another.

The author and professor of economics, Piers Steel, PhD., calls this formula the ‘Procrastination Equation’. In a book that he wrote about this topic, he delves a bit deeper into these elements that determine whether you’re eager to do a certain activity as soon as possible, or whether you’ll tend to postpone it.

This formula, according to Steel, looks like this:

At the center of it all, there’s motivation. This one is obvious. It’s the drive you experience, the inner desire to do a certain thing. You’ll notice in your life that your motivation for watching TV or playing video games is probably a lot higher than your motivation to clean your room or go on a diet.

According to Piers Steel, this motivation is determined by four different quantifiable factors. These are: value, expectancy, impulsiveness and delay.

At the top of the equation are ‘expectancy’ and ‘value’. At the bottom, we find ‘impulsiveness’ and ‘delay’. If you’re not much into math, what the formula says is this: the higher the expectancy and value that are associated to a certain task, and the lower your impulsiveness, and the time you’ve got to finish this task, the higher your motivation will be, and vice versa.

It’s this motivation that is the central determinant of whether you will procrastinate or not.

So let’s go a bit deeper into all these elements and examine why you’re procrastinating.

Factor #1: Expectancy

Expectancy, at first sight, seems like a bit of a vague word. What it means in practice is the chance that a certain activity will yield positive results. It’s the chance of success.

As an example, let’s take investing money. You’ve got thousand dollars to invest. Let’s say there’s a certain stock that you think will perform well, and you expect a ten percent return on it. On the other hand, you could invest in triple A-bonds that yield about five percent. These types of bonds are very secure, so you’re certain to get your money’s worth.

The higher your expectancy that the stock will do well, the more likely that you’ll choose the stock over the bonds. On the other hand, when the stock is highly volatile, and the possibility that it will drop in value becomes higher, you’ll be more likely to choose the bonds instead.

Now, what if the financial markets are a complete mess? Stocks are doing poorly, bonds aren’t having a good time either, and all the banks are failing too. In this doomsday scenario, you’re probably not going to want to invest in either stocks, bonds or even a savings account, because the chance you’ll lose all your money is pretty high for all three investments.

When you expect to make a huge profit, you’ll probably be a lot more likely to invest

In this case, the expectancy of making a profit is close to zero. As a result, your motivation to invest will be non-existent too. Hiding your money under your mattress is the safer option here.

Now, maybe investing is a bit too abstract a concept to explain procrastination. When we procrastinate, sometimes money is involved. This often happens when we have to pay the bills, or we don’t put a part of our earnings in a savings account right away.

But it’s not the most common type. Most of the time, we have trouble with doing a school assignment, a project for work, cleaning the house, or something like that.

So let’s take another type of activity: a paper you have to write for school.

Now, imagine that this is a very easy paper. You don’t have to do a lot of research, the topic you have to write about is pretty simple too. The chances of getting good grades are pretty high. The chances of failing are more or less non-existent, provided you put in a minimum amount of effort. You’ll probably be eager to start this task, because hey, easy top grades.

In other words: the expectancy of success is high.

In another scenario, you have to write a PhD dissertation. Apparently, procrastination is rampant amongst people who are working on their PhD degree. And why is that?

Simple: it’s hard, the chance of failure is real, and your degree won’t be served to you on a silver platter. You really have to put in some serious work to get good results. The chances of success are a lot lower than when writing an easy 5000-word paper. If it was easy, everyone would do it.

In this case, expectancy is much lower, and as a result, motivation will drop as well.

Factor #2: Value

The second element that will decrease the risk of procrastination is a high value.

When talking about value, the first thing you might think about is how much something costs. For example, that diamond ring you bought for your fiancée is pretty valuable. A Porsche or a Mercedes are valuable cars, compared to say, a Fiat or a Volkswagen.

Value isn’t necessarily limited to the monetary cost you place on something. Some things can have great emotional or personal value. You might treasure a friendship with someone. You might place great value on your free time, or your ability to speak and think freely.

Value, in the sense that Piers Steel talks about it, is simply the reward that a certain activity brings. This can be both a material reward or a non-material reward.

To go back to our example on investing, let’s say you’ve got two banks that offer different savings accounts. With Bank A, you get an interest rate of two percent. With Bank B, you get an interest rate of three percent. Since these are normally very safe investments, it’s more or less guaranteed that you’ll get your money’s worth. So high versus low expectancy is out of the picture here.

In this case, the reward, or the value, is higher when you give your money to Bank B. That means that your motivation to put your money in Bank B will be higher than the motivation to put your money in a savings account with Bank A.

Let’s give another example, for example, your diet.

In this example, you’re a few pounds overweight. You’re not super obese, but you could lose a few inches and look a little better. So you decide to cut the Snickers bars and the ice cream and replace them with fruit and vegetables.

Problem is: salads and tomatoes just don’t taste as good as Ben and Jerry’s. Whereas ice cream lights up the reward center in our brains like a Christmas tree, the reward value when eating an apple is more akin to a small candle. So, in principle, your motivation to eat crappy, but highly rewarding food, is going to be much, much higher than your motivation to eat healthy, yet not-so-rewarding food. This is all the more insidious when you know that food companies actively try to engineer food to make it as rewarding as possible, so that you’ll eat (and therefore buy) more of it.

I doubt there are many people who procrastinate when it comes to eating hotdogs

On the other hand, since we humans are beings that can look ahead and forego instant rewards for future rewards, there are other factors at work.

For example, even though the instant reward of crappy food is higher, you still might forego it in favor of the healthier food. This is because you know that if you eat healthy food, you’re going to look better in the future, which will increase the chances of that guy or girl you fancy to notice you, which in turn will increase your chances of procreational activities (which are, let’s face it, much more rewarding than eating pizza). When you take in account this kind of reward, postponing your diet and exercise regime will become much less likely.

Different kinds of rewards can be weighed against each other to determine the motivation of doing one thing versus another.

So that’s more or less what value is all about.

Factor #3: Impulsiveness

Next stop: impulsiveness. Here, we’ve come to the factors that detract from motivation.

Our ability to stop and think about the consequences of our actions plays a HUGE role in whether we procrastinate or not.

Say for example, that someone wants to give you five thousand dollars. But, he says, I’ll give you double the amount in a year if you don’t accept it now. Now, let’s assume two different scenarios.

In the first, you only get five seconds to think about it. In the second, you get half an hour. Research has shown that we tend to go for the immediate reward if we only get a very limited time to think about such an offer, and are more likely to go for the postponed reward if we get more time. In a similar fashion, impulsive people, which are people that tend to make quick decisions without thoroughly thinking them through, tend to go for immediate rewards, whereas people who aren’t impulsive at all will see things in a long term perspective.

Imagine, for example, that you have the choice between going out for beers with your buds or finishing that school assignment. Impulsive people will tend to put off on doing that school assignment and will say yes to the booze. Someone who is a lot less impulsive will be more likely to stop and think: ‘hey, if I go out to drink beer and don’t make my assignment now, that might get me in trouble’. An impulsive person will therefore tend to have a lower motivation to do the assignment, and procrastinate more.

By the way, this is the book. You can act impulsive for a change and buy it RIGHT NOW!

Impulsiveness plays a key role in your ability to adhere to a diet as well. If you’re an impulsive person by nature, you’ll be less likely to resist when someone offers you a cookie. If you’re less impulsive, you’ll be able to see things in a long-term perspective: a cookie might act as an instant reward now, but it will harm you in the future, as you’ll be more likely to get fat.

The big problem with impulsiveness, compared to all the other factors, is that it’s not something you can do much about. That’s because it’s mostly an inherent character trait, linked to your biology. Some people are just naturally impulsive, while others are more able to stop and think about their actions.

Factor #4: Delay

Finally, we have what’s called ‘delay’. This simply means the amount of time that we have to complete a task.

Even when you procrastinate, you’ll probably not postpone the activity indefinitely. You might delay working on your paper today. You can say you don’t feel like working on it tomorrow. You feel a bit ill on Saturday, so it’s not happening then either. But it’s due to be turned in on Monday morning, so you’re definitely going to write it Sunday. Any further delay is simply impossible (unless you don’t care that much about your academic results).

The more days you’ve got left on your calendar, the less likely you’ll do anything

You probably notice this during exam periods as well. When your exam is still ten days away, you’ll say to yourself: ‘I’ve got some time, let’s watch some more Netflix’. Five days later, you’ll be like: ‘I’ve still got a reasonable amount of time left, but I should start getting to work now’. But even though you’re doing some actual work done, you’re still taking way too much breaks. Then you suddenly realize that the exam is tomorrow, you’ve still got two hundred pages to study. So you start cramming like mad until deep into the night.

A similar thing happens with people who want to diet and exercise. Oftentimes, they’ll wait until summer, is around the corner to start working out and start watching their diet. By which time, it’s usually too late to get completely lean and toned.

And this is more or less what delay is all about.

So let’s do some math, shall we?

Now that we’ve talked about all the different pieces of the puzzle, it’s time to put everything together. So why don’t we create a few example equations to show what we have learned and put it into practice?

Let’s take an example of one of each of the above elements and give it a rating from 1 to 10, 1 being lowest, 10 being highest.

As we talked a bit about investing above, it seems like a good concept to explain the Procrastination Equation.

Say, you’ve got five hundred dollars. And you can either choose to invest that, or buy a new game console with a few video games. (in this example, you’re an avid gamer, so playing the newest video games is very rewarding).

On the other hand, you’ve got your eye on a stock that has produced a return of 8 percent in the last year. Let’s give this stock a reward value of 8, while the new video game console has a reward value of 9.

Then, there’s expectancy. The stock market is a bit shaky, and chances are the company will do less well in the future, even though it made a decent profit in the last years. So expectancy is about a 4.

Yay. Math.

The video games you can buy get average review scores of 80 out of 100. The expectancy, (the chance that you’ll enjoy playing them) is 8.

In this scenario, you’re also a rather impulsive person, so you’ll be likely to choose instant rewards of long term ones. Impulsitivity is rated 8. It’s lower for video games since it has the short term reward, so let’s give that a 4 compared to other activities. (for example you could buy lots of drugs for even more instant rewards, which would then be counted as a 1)

Delay: you’ve got lots of time to buy the stock. You can still buy it next week, for about the same price. Let’s give delay a score of 8 here.

The video game console is on sale today and you won’t be able to afford it next week.You have to buy it right now. Delay gets a 2 out of 10.

If we put in the numbers, we get two different equations with two different results

Motivation to buy stock:


Motivation to buy video games:


The result – your motivation to buy video games is 18 times higher than it is for investing money. You will therefore be much more likely to buy the video game console than buy stock.

Putting it all together

So this is what procrastination is: comparing activities versus one another and choosing one of them based on the value they bring, the expectancy of success, your tendency towards impulsive behaviour, and the delay you’re allowed for doing them.

And this is what procrastination is all about.

Next time, we’ll give you some tips on how you can influence these factors to make the procrastination equation work in your advantage.

Signing off,