Modeling Motivation Weights

Where does motivation come from and how can we get more of it?

A boy falls in love with a girl.  There’s just one problem: this girl is currently dating the captain of the football team.  So, our boy hatches a plan to steal her from his competition by becoming the captain himself.  Surely then she will notice him and reciprocate his love.

To achieve this goal, there’s a lot of work to do.  Our hero isn’t really much of a hero.  He’s out of shape and doesn’t really play football.  There are many practices, training sessions, sprints to run, and weights to lift.

So how do we determine if our hero will be motivated enough to do all this work?  We can use mathematical modeling to predict how motivated our hero will be, and we can use those models to discover how we can find our own motivation.

First we start with an older, but simple model developed by Victor Vroom.

Expectancy theory

Expectancy theory treats motivation as the desirability of an outcome.  It has three components:  expectancy, instrumentality, and valence.

I.  Expectancy:  Will our effort result in the performance we desire?

This expectancy is based on our past experiences and our self-efficacy.  When we try hard, do we perform well?  Do we have a past filled with trying hard, yet failing to perform, or do we have a past where we tried hard and succeeded?  Do we get better when we practice?

Expectancy is also based on the difficulty of the goal.  If our opponent is highly skilled and we are not, our expectancy is lower.  Trying to get into the NFL is much more difficult than becoming a good high school player, so our expectancy for getting into the NFL would be lower.

Perceived control:  do we have control over the outcome of our efforts?  Can we train whenever we want, or are we stuck with whatever our coach tells us to do for example?  This also affects expectancy.

II.  Instrumentality:  Does our performance determine the outcome?

This is tricky.  We may put in the effort to train and become a great wide receiver, but if no one throws us the ball, we can’t catch it.  If the rest of the team doesn’t play well, we can’t score.  If no one blocks for us, we get tackled.

Without a strong connection between our individual performance and the likelihood of our outcome, we won’t be motivated.

So our hero becomes the greatest player of all time.  However, the current captain of the football team just so happens to be the son of the coach.  Burn.  Now our performance may not matter because no matter how good we are, perhaps the coach will sabotage us.

Worse yet, maybe our Waifu doesn’t care about football as we expected.  Instead she just actually likes the guy who happens to be the captain of the football team.  No amount of sprinting and footballing will result in her falling in love with our hero.

The more our hero’s performance doesn’t tie directly to the reward he wants — getting the girl — the less motivated he will be to show up to practice or to the gym.

Most important about instrumentality’s impact on our motivation is that it’s about perception.  Do we BELIEVE that our performance will result in the reward we desire?  We can be wrong about reality, but still be motivated based on what we believe.

III.  Valence

Valence is the final component of expectancy theory.  Valence is simply the expected value of the outcome and whether it is positive (reward) or negative (punishment).

So in our example, the more our hero likes this girl, the greater the valence she has as a reward.  It’s also important to note that this value is an expected value.  So our fair maiden could be missing an eye, but if our hero really likes eye patches, then her valence remains high.  She could be a terrible girlfriend in reality, but if he expects her to be amazing, valence is high as well.   It’s only the value he places on achieving the goal that matters.

Mathematically, valence is assigned a negative one to positive one value.  Outcomes we want to avoid are negative.  Neutral rewards, or things we don’t care about either way are zero.  Positive rewards are positive.

Getting burned might have  -0.75 value (negative).  This means we don’t want to get burned so we aren’t motivated to grab hot pans for example.

Getting a new car might be a 0.25 value (positive) because we want the reward of a new car.

In expectancy theory, motivation is expressed as

Expectancy * Instrumentality * Valence

Very simple.

Where expectancy theory falls short is that it doesn’t account for time.

Hyperbolic Discounting

Would you rather have $1 today or $1 a year from now?  Today.
Would you rather have $1 today or $1000 a year from now?  Probably the $1000.

We value rewards differently depending on how soon we expect to receive them.  The further away we are from the reward, the less motivated that reward makes us.  So our motivation is not only a function of how large the reward is, we also care about when we’ll get it, and how likely we are to get it.

Generally the “discount” we apply to future rewards follows a nice curve, hence “hyperbolic discounting.” The value of a reward drops very quickly when we add a small delay, but as the delay grows larger there is less drop in the reward.

The difference between receiving a reward today versus tomorrow is much larger than the difference between receiving a reward 100 days from now versus 101 days from now.  That extra day is much less important in our minds, when we already have to wait 100 days.


This discount varies from individual to individual.  People with less self-control want things sooner and are willing to give up future rewards in order to get smaller, but more immediate rewards.

We call this impulsiveness.  The more impulsive you are, the less you will value rewards far in the future.  You’re also more likely to procrastinate where you avoid painful tasks now, to put them off into the future.

In simple terms, highly impulsive people care much more about what happens now than in the future.

Temporal Motivation Theory

When we combine these concepts with expectancy theory, we get Temporal Motivation Theory.
Motivation =

Expectancy * Value
1 + Impulsiveness * Delay

So the more impulsive we are, the less motivated we are when there is a delay in our reward.  Similarly the longer it takes to earn that reward, the less motivated we are to earn it.

If our footballer has little discipline, he may like the idea of becoming captain of the football team and may believe his is capable and in control of the process to get there. However, if he knows it will take him 4 years to do it, he may not be motivated enough to put in the work.

This also explains why we might be quick to start a behavior change but then get bogged down and give up when we realize it will take much longer than we had planned.

Similarly, if our hero is number two on the football team and only needs a small improvement to become captain, he can achieve his goal sooner and, therefore, there is less delay and greater motivation.

Manipulating motivation

Once we understand this model, we can begin attacking each of these variables to help us get what we want.


At the core of expectancy is self-efficacy.  This gets a lot of attention, but I don’t believe enough of it is focused on how you build true self-efficacy.  We can’t just think positive thoughts and tell ourselves we’re wonderful to get self-efficacy.

Self-efficacy or confidence comes from COMPETENCE.  Competence comes from trying things, coping, success, and to some degree, from failure.  Only when we get good at things and learn that we are capable, do we get that confidence.

This is why behavior change comes first.

Without behavior change we can’t build experience to draw upon.  We must see that we are in control over our future rewards, and this comes through accruing evidence of that control via behavior change.

This happens by doing things we aren’t good at, things that we don’t feel confident in.  We have to fail for a while, learn, get better, and then eventually succeed to build confidence.

This may mean our hero has to go to football practice even if he’s terrible.  His motivation may be low at the start, because he is relying on valence alone, but as he gets better, and is rewarded, his expectancy will rise.  He will build confidence as his competence improves.

When we are successful, we like to believe that we made some magic shift in thinking that made all the difference.  Most often we simply tried something because we wanted some reward.  That action propelled us forward, got us small immediate rewards, and then those rewards changed how we saw ourselves.  The real shift in thinking comes after the change, rarely before.

Behavior change drives internal change, which reinforces our behavior.

Value (valence):

We can manipulate the value of our rewards by how we see them in our minds.  In many ways we subconsciously manipulate this value, sometimes to our detriment.

One way we lower valence is to soften the value of our rewards in order to not feel so bad about not getting them.  This can be counter productive.

Often our rewards are as simple as avoiding punishment or pain.  Rather than thinking of becoming healthy as a reward, we think of not being fat as avoiding punishment.  Not being fat may actually be a stronger motivator even though they are essentially the same idea.

So in order to soften the pain we feel now, we say…heavy or curvy instead of fat.  This is manipulating the reward of losing weight, making it seems less important and, therefore, reducing our motivation to achieve fat loss.

We do this hoping that feeling better about ourselves right now will increase our self-confidence, but we do so at the cost of valence.

So rather than downplaying our rewards, we want to intensify the value of our rewards.

Our footballer may not be good at football.  He has no confidence.  All he has to rely upon is that reward of getting the girl, so that reward must be as big as possible in his mind in order to overcome his lack of expectancy (confidence).

We can do this three ways:  Focusing more intensely on rewards, creating artificial rewards, and manipulating our environment to reinforce those rewards.

Remember valence is the perceived value of a reward.  By manipulating perception we manipulate valence.


One of the ways people get motivated is to decide more precisely what it is we want.  The more vague our rewards, the less motivating they are.  We need to spell out exactly what we want, make decisions about what we want our lives to be like.  Imagine these in detail.  Find reasons and support for our decisions to change.

What would it be like for our hero to be captain of the football team?  He may imagine others respecting him more, he may no longer be made fun of for being fat.  Maybe he gets the girl.  He can imagine how his day would go differently, what would people say, what would he do.  What would it look and feel like?  These details are more compelling than the more vague idea of being the best footballer.

Creating artificial rewards

As much as we like to think we’re really in control, much of our actions are based on simple behaviorism.  We experience a trigger, we perform an action, we get a reward.  We feel hungry, we eat, we feel good.

That reward doesn’t have to actually be caused by the action (this is where the term “artificial”comes into play –a reward not directly resulting from the behavior/action preceding it).  It just needs to happen around the same time so that we can build that association.

So if our footballer wants to increase his motivation to practice he can reward himself with chocolate for example.  Assuming chocolate reasonably fits within his diet, he can use this as a post-workout reward.  This reward has nothing to do with throwing footballs, but it reinforces the behavior of training and going to practice.

Eventually the end game is to have practice itself become the reward.  Early on, he may not enjoy it.  But as we see strength increases or body fat loss, those benefits are enough to sustain him.  He no longer needs chocolate as an artificial reward because he has real rewards.

Changing our environment

We can change our perception of rewards by manipulating our environment.  One way we can do that is to change who we spend time with.

When we spend time with people who share our goals, we intensify those rewards by making them more salient in our minds.  If you hang out with the football team, you’re going to talk about football.  When we spend time with people who value certain things very highly, we begin to take on those values ourselves.

Changing our environment can also improve expectancy.  We see others as models because they have achieved what we want to achieve.  We hang out with the captain of the football team and we see that he isn’t so different.  We learn how he made it to where he is.  We have a model to follow.


By manipulating the timing of our rewards, or reducing delay, we can become more motivated.  This is one of the most effective ways to change our behavior.

By breaking down our goal into smaller incremental goals, we gain small rewards.  These small immediate rewards have a disproportionately high value because the perceived value of a reward increases hyperbolically as it becomes more immediate.

Thus, in addition to achieving our overall goal of getting the girl, we should make smaller, intermediate goals.  We need to learn to throw a football to the left while running to the right.  We need to sprint 2% faster this week.  We need to score a touchdown in this game.  We need to make one good pass on this play.  We want to hit 5 sets of 8 reps on this exercise.

These small goals give us the satisfaction of getting us closer to our big goal, but they happen immediately.

Perceived control

We increase our perceived control by breaking down goals into concrete and very small steps.  If I do this one thing, I am closer to the big goal.  These small steps are very achievable individually, even though the large goal may seem very daunting.  If I can finish this workout, I can finish all the others.  If I finish all the others, I will achieve my goal.

  • What resources do I have that will help me get closer to my goal?
  • Who can help me achieve my goal?
  • What are the immediate steps I can take to get closer to my goal?

The same can be said for instrumentality.  As we look at the specific behaviors we can take on, we can also look at obstacles to our success and formulate plans to burn through those obstacles.  Then we begin to feel that nothing will stop us and that the rewards will come from our performance.  We gain an internal locus of control and strengthen self-efficacy by seeing the path to our goal and knowing that we can achieve it, if we execute this plan.


Impulsiveness is often thought of as a partly genetic trait.  However, our ability to control our own behavior is very complex.  While genetics may play a part in as much as half of our tendency to highly favor immediate rewards over long-term rewards, there are several ways we can combat this natural tendency towards impulse.

This is so important because it is the long-term goals, the things far off in the future, that require the most work.  These are the goals that have the largest impact on the quality of our lives over the long-term.  The ability to hit long-term goals is how we live a more fulfilling life.

So what influences impulsiveness?

Largely our response to stress.

When we are under stress we tend to become reactive, impulsive.  We sacrifice tomorrow for today. These same factors lead to procrastination where we are unable to do things we know we should do.  Stress hormones shut down activity in the prefrontal cortex and thus goal-directed behavior.

We can alter our sensitivity to stress, ability to regulate our emotions, and therefore our impulsiveness, via physical training (aerobic capacity), performing breathing drills, meditation, etc. making it easier to resist temptation and, ultimately, make us less impulsive.

We can also reduce our stress response by adopting behaviors that relax us.  We can go for walks, meditate, create art, listen to music, etc.

Anything that improves our recovery can also reduce impulsiveness.  Getting better sleep, eating right, getting time off from work, etc.

All these behaviors feed upon each other.  Working out lowers your stress over the long-term, which makes it easier not only to work out, but to take on other positive or goal directed behaviors.

Making that initial behavior change will help you find the motivation and reinforcement you need as you go along.

Putting it all together

This is kind of a lot to digest.  However, when you think through the actual model there are really only four questions to focus on:

  • How can I increase my expectancy (confidence and control)?
  • How can I increase the valence or value of my reward?
  • How can I lower my stress response and, therefore, impulsiveness and procrastination?
  • How can I get some reward sooner?

These questions may have an infinite number of answers, but if you can remember these four questions, you have model to find the motivation you need.

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