The Mathematics of Perseverance: The Formula to Help You Decide Whether to Strive or Settle

Say you’re unhappy about something in your life: your job, your health, your spouse, your skills. In all these cases you have many choices about what you can do, but they all largely fall into two different categories:

  1. Do something about it.
  2. Accept things as they are.

Doing something about it can take many forms. If you’re unhealthy you can start eating healthier and exercising more. If you’re unhappy in your relationship you could try to change the relationship you have or leave the person you’re with and find someone new. If you want a better job, you could quit yours or try to become better at it and negotiate better terms from within.

Accepting things as they are requires an attitude adjustment. It means accepting that you won’t have six-pack abs or be able to run a four-minute mile. It means learning to accept your partner’s faults instead of trying to change them. It means learning to appreciate your life instead of trying to improve it.

Accept or Try?

Most people tend to make the accept-or-try decision the same way for everything in their lives.

If you’re a die-hard striver, you may have looked at all of the examples I listed above and thought the answer was obvious: set goals and work harder. If you’re a settler of Zen proportions, you probably aren’t reading this blog, but you may have seen all those sources of dissatisfaction in life as coming from your own desires which you can eliminate.

Unfortunately, the world is rarely this simple.

Sometimes people who strive too much fail to accept things they can’t change, or try to chase a utopian version of their life making them always unhappy with the present. Sometimes people who accept too much become complacent about things of importance and end up being struck by entirely avoidable misfortune.

The question is, how do you separate instances when you should strive from when you should settle?

The Formula for Strive or Settle

The first thing you need to consider when deciding whether to strive or settle is: given the actions you plan to take, what is the probability of success? If success is trivial, it might be worth doing even if the expected benefits are low. If success is impossible, it might not be worth undertaking even if the expected benefits are high.

You can see this by considering some edge cases:

  • You want to become taller. Your plan of action is to stand straight and try to stretch yourself everyday. Probability of success: almost zero. Therefore this action is likely a waste of time, even if you’d really like to be taller.
  • You want to avoid tooth decay. Your plan of action is to brush and floss your teeth everyday. Probability of success: high. Therefore this action might be worthwhile even if tooth decay wasn’t your biggest priority.

The second thing to consider is how the outcomes of striving or acceptance impact your overall well-being. This is a tricky thing, but I’ll consider it in two ways: the happiness of your moment-to-moment experience and the “happiness” of your self-reflection on the status of your life. I’ve written before about the two types of happiness and why this can be complicated, but for now let’s lump them together to make things simpler.

Obviously if taking action will make you considerably happier (in a moment-to-moment sense, or even just in a self-reflective way) that gives points to taking action. If taking action won’t make you any happier, that seems to weigh more heavily on self-acceptance.

The third thing to consider is how much happiness you have to sacrifice by taking action. If pursuing your goal requires you to endure some unpleasantness in the meantime, you might consider it a trade-off between your current and future selves. (Of course, sometimes taking action actually makes you happier, I’ll discuss this case later.)

So, without further ado, here is the formula for striving versus settling. If this number is greater than zero—take action. If it’s less than zero—you’re better off just accepting things as they are:

p_success = probability of being successful with the action you take
h_success = happiness when you succeed
h_failure = happiness when you fail
h_accept = happiness of accepting things
c_action = cost (in terms of happiness) of taking action (note: may be negative)

render

This formula simplifies a few things (for instance, it assumes there is no time preference). It also assumes that these quantities are knowable, when you may have wildly inaccurate estimates for all of these numbers.

With this equation now, we can look at some possible cases where these numbers might make the decision obvious:

  • You regret the chances you didn’t take more than the chances you failed at. This corresponds to h_failure being greater than h_accept.
  • You’re happiest when you’re pursuing a goal that matters to you. This corresponds with c_action actually being negative. If taking action makes you happier, then the “sacrifice” you make by taking action is negative.
  • Being successful doesn’t make you any happier. This corresponds with h_success and h_accept being the same (and possibly also being equal to h_failure). In this case, the only relevant variable now becomes c_action—if you can’t change your happiness by changing the outcome, then it’s only the change in happiness from possibly making yourself miserable or inspired trying to achieve a goal.
  • You succeed, and now you’re miserable. This could happen in some instances where h_success is actually less than h_accept or possibly h_failure. You become famous, but now resent the constant attention. You earn more money, but now you have to work too many hours.

Obviously many of these truisms are now contradictory. Often we hear many pleasant-sounding aphorisms that turn out to be false once we actually try to make them concrete. That’s one of the reasons we use math in many domains–it forces you to be more consistent and rigorous in your thinking.

How this Equation Can Help You

I don’t believe people will actually take this formula and make calculations to decide whether they should strive or settle. But I do think it can be useful as a way of thinking about under what assumptions you’re making your decision.

  • Are you taking action because you think success is likely or because you believe actually taking action will make you happier than doing nothing, even if success is unlikely? (p_success is high or c_action is negative)
  • Are you settling because you believe you’ll actually be less happy with success, or because you believe success is too difficult to achieve (h_success is lower than h_accept or c_action is high)?
  • Are you deciding to accept because you believe you can’t change your happiness (all h’s are equal)? Or because you believe success is too unlikely (p_success is low)?
  • Are you taking action because you believe you’ll be much happier when you’re successful (h_success is high)? Or because you believe settling will make you very unhappy (h_accept is low)?

You can use this formula and the variables to think about other people’s decisions and probe their own thinking. We all have friends or colleagues who make decisions which seemingly baffle us. But my guess is that, unconsciously, this person believes that the values for one of these variables is quite different from you, and that’s why they’re not taking the actions that seem most useful for their situation.

You can also use this formula to summarize certain life philosophies attitude to these questions (broadly speaking):

  • Buddhism – You can’t make yourself happier by striving (h_success, h_failure <= h_accept)
  • Zig Ziglar – “Happiness isn’t pleasure, but victory” (h_success > h_accept)
  • Protestantism – Happiness comes from hard work (c_action is negative)
  • Stereotypical motivational speaker – People underestimate what they can accomplish (p_success is higher than you think)

By breaking apart the components—chance of success, happiness of different outcomes, cost of striving—it’s easier to think more clearly about what matters to you.

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  • Chris

    Ow, after this article I really think I kind of love you, Scott! It is quite clear why I don’t take any action after reading personal development blogs. c_action is prohibitively large, p_succes is close to 0.5 and h_accept is probably somewhere in the middle of h_success and h_fail.

  • Chris

    Ow, after this article I really think I kind of love you, Scott! It is quite clear why I don’t take any action after reading personal development blogs. c_action is prohibitively large, p_succes is close to 0.5 and h_accept is probably somewhere in the middle of h_success and h_fail.

  • JOY

    I have no idea of how to use the formula but it’s fun!

  • JOY

    I have no idea of how to use the formula but it’s fun!

  • HI
  • HI
  • kipki

    I like the idea of the formula, but the problem with it is that most goals are not dichotomous but gradual: you do not end up as either a marathon man or a couch bag, a billionaire or broke, etc.. Most likely, in the case of a predefined action (having a fixed cost), you’ll end up in the middle with a partial success (lost 10 kg, doing sports a few time a week, an improved salary, …)

    Incorporating this in the formula is actually not so hard. The easiest way is to define total failure or p = 0 (e.g. no weight loss or income gain) and unimagined success or p = 1 (e.g. 30 kg weight loss or 500000 dollar income gain). Next, you draw two curves, one is the probability of occuring for p=0 to p=1, the other one is the happiness level for p=0 to p=1. Both can have any form: linear, logarithmic, exponential, quadratic, … Next, you look at the probability curve and determine the p value for which the area under the curve left of that value equals the area on the right hand side: this is expected outcome. The happiness level for that p- value is the expected happiness following from taking action. Then the formula reduces to h_expected – c_action – h_acceptance.

  • kipki

    I like the idea of the formula, but the problem with it is that most goals are not dichotomous but gradual: you do not end up as either a marathon man or a couch bag, a billionaire or broke, etc.. Most likely, in the case of a predefined action (having a fixed cost), you’ll end up in the middle with a partial success (lost 10 kg, doing sports a few time a week, an improved salary, …)

    Incorporating this in the formula is actually not so hard. The easiest way is to define total failure or p = 0 (e.g. no weight loss or income gain) and unimagined success or p = 1 (e.g. 30 kg weight loss or 500000 dollar income gain). Next, you draw two curves, one is the probability of occuring for p=0 to p=1, the other one is the happiness level for p=0 to p=1. Both can have any form: linear, logarithmic, exponential, quadratic, … Next, you look at the probability curve and determine the p value for which the area under the curve left of that value equals the area on the right hand side: this is expected outcome. The happiness level for that p- value is the expected happiness following from taking action. Then the formula reduces to h_expected – c_action – h_acceptance.

  • BABIMBA

    So, do you practice Chinese everyday?

  • BABIMBA

    So, do you practice Chinese everyday?

  • This applies to starting a business too:
    https://youtu.be/0CDXJ6bMkMY?t=6m38s

  • Guy Riese

    This applies to starting a business too:
    https://youtu.be/0CDXJ6bMkMY?t

  • Karen Chung

    Hi Scott –

    I enjoyed your post! It happens to connect with something I’ve been reading these days, and I thought you might be interested in it.

    It’s chapter four, entitled “A Dangerous Lecture to a Young Woman”, from a book called Self and Self-management: Essays about Existing, by Arnold Bennett (1867-1931). I listened to it as an audio book on Librivox:

    https://librivox.org/self-and-self-management-essays-about-existing-by-arnold-bennett/

    The text is also available from Gutenberg:

    https://archive.org/details/selfandselfmana00benngoog

    Hope you can make it to Taiwan again sometime! 🙂

    Karen Chung
    karchung@ntu.edu.tw
    (we chatted one evening in a Taipei Starbucks on your last visit to Taiwan!)

  • Karen Chung

    Hi Scott –

    I enjoyed your post! It happens to connect with something I’ve been reading these days, and I thought you might be interested in it.

    It’s chapter four, entitled “A Dangerous Lecture to a Young Woman”, from a book called Self and Self-management: Essays about Existing, by Arnold Bennett (1867-1931). I listened to it as an audio book on Librivox:

    https://librivox.org/self-and-

    The text is also available from Gutenberg:

    https://archive.org/details/se

    Hope you can make it to Taiwan again sometime! 🙂

    Karen Chung
    karchung@ntu.edu.tw
    (we chatted one evening in a Taipei Starbucks on your last visit to Taiwan!)

  • Hi Scott, well articulated piece. Nice how you break the elements apart which would make it easier identify which element of a decision might be our of whack! Thank you

  • Boldore

    How much value do you accertain to each component in the formulae. Even based on the level of happiness or any other basis. Wouldn’t zero be too small a value to compare with it’s counterpart for acceptance?

  • Boldore

    How much value do you accertain to each component in the formulae. Even based on the level of happiness or any other basis. Wouldn’t zero be too small a value to compare with it’s counterpart for acceptance?

  • Scott Young

    Well the idea is that if the value is zero then your expected happiness in both situations is equal.

  • Scott Young

    Most days.

  • Scott Young

    Well the idea is that if the value is zero then your expected happiness in both situations is equal.

  • Scott Young

    Most days.

  • Scott Young

    Obviously the formula fails to encapsulate all the complexities and nebulousness of real life. I think it provides a useful starting point to think about these issues without introducing so many variables as to become unweildly.

    An obvious improvement would be to include some kind of discount rate based on time. With happiness of success, failure, effort and acceptance being measured in their suspected duration.

  • Scott Young

    Obviously the formula fails to encapsulate all the complexities and nebulousness of real life. I think it provides a useful starting point to think about these issues without introducing so many variables as to become unweildly.

    An obvious improvement would be to include some kind of discount rate based on time. With happiness of success, failure, effort and acceptance being measured in their suspected duration.

  • Scott Young

    c_action is the cost, in terms of happiness, of pursuing said action. So I think a restatement would be that it appears you don’t enjoy taking action very much. I’m somewhat of an opposite personality, so I think many goals may be positive for me even if they don’t affect net happiness as an outcome.

  • Scott Young

    c_action is the cost, in terms of happiness, of pursuing said action. So I think a restatement would be that it appears you don’t enjoy taking action very much. I’m somewhat of an opposite personality, so I think many goals may be positive for me even if they don’t affect net happiness as an outcome.

  • George

    i liked the article. with regards to Buddhism, i think the interpretation of the formula is inaccurate. One of the strands of the eightfold path is Right Effort. The Buddha allegedly once used a metaphor this: if a musician plays a string instrument and the strings are too tight, the sound will not be good. if the strings are too loose, the sound wont be good either. this is how it should be with effort too. i guess we need to understand the instrument (ourselves) and using questions like the ones Scott raises in the article helps us finetune it. Thank you.

  • Jude Miller

    What’s the numerical scale of these? Is p_success between 0 and 1, and the other values on some arbitrary scale, say, 1 to 10 or 1 to 100?

  • Jude Miller

    What’s the numerical scale of these? Is p_success between 0 and 1, and the other values on some arbitrary scale, say, 1 to 10 or 1 to 100?

  • Kevin Griffin

    Loved the post! It’s very interesting. I always feel borderline Buddhism but something holds me back. For example, I am learning Chinese. I’m an intermediate and always struggle with the idea of should I doing something I don’t enjoy to get better i.e. subtracting from present happiness. For example, writing and listening to podcasts I don’t enjoy but they make me substantially better at Chinese. However I question why I strive for this? To better connect with Chinese people and make deeper relationships in China? Why would I value this experience over one where I know less Chinese. For example learning how to order off the menu my first week in China was a great time. Why is that valued over talking to someone about politics in Chinese. This is where I get stuck between Buddhism and improvement. It seems like being better at the cost now would be worth it build better and interesting relationships… But then I think hey, it just provides me with a different experience. I think I will never know the answer. I also think each situation is so different to evaluate using your goal equation! Thanks for making me think! Would love input if you have it.

  • Kevin Griffin

    Loved the post! It’s very interesting. I always feel borderline Buddhism but something holds me back. For example, I am learning Chinese. I’m an intermediate and always struggle with the idea of should I doing something I don’t enjoy to get better i.e. subtracting from present happiness. For example, writing and listening to podcasts I don’t enjoy but they make me substantially better at Chinese. However I question why I strive for this? To better connect with Chinese people and make deeper relationships in China? Why would I value this experience over one where I know less Chinese. For example learning how to order off the menu my first week in China was a great time. Why is that valued over talking to someone about politics in Chinese. This is where I get stuck between Buddhism and improvement. It seems like being better at the cost now would be worth it build better and interesting relationships… But then I think hey, it just provides me with a different experience. I think I will never know the answer. I also think each situation is so different to evaluate using your goal equation! Thanks for making me think! Would love input if you have it.

  • Vineet Kumar Singh

    Hi Scott!
    I really liked this article.

    Inspired by your article, I tried to devise a formula for calculating personal productivity for one day. I looked all over the internet and didn’t find anything similar to this. It’s a really simple one. It assumes two things:
    1) A realistic to-do list has already been made for the day and sorted according to the priority of each task.
    2) It is more or less known what the goals are for that day for each task. (for example, you might want to study the first 3 topics out of a chemistry book.)

    Here is the formula:

    SUM[W(i)*C(i)]
    divided by
    10*SUM[W(i)]

    All the factors- W(i),C(i) etc. – are given a number from 1 to 10.

    Here W(i) is the weight of the i(th) task. W(i)=U(i) + I(i) ,where U(i) is its urgency and I(i) is its importance.
    C(i) is the amount of task completed, a 0 being not started at all, and a 10 being finished.
    This formula can also be extended to a week or month.

    Although I think this will work well for most people, I found some inconsistencies with the formula:
    1) This formula may not work well for highly creative tasks and tasks which require deep work (As C(i) may not be known beforehand. But still, a value can be given based on whether the person used her full potential or not)
    2) It does not take into account unavoidable circumstances which may hinder progress (Although in this case suitable adjustments can be made in the variable C(i)).
    3) There are serious problems with W(i)=U(i)+I(i).It gives equal significance to urgency, U(i) and importance, I(i) of a task. This can be inappropriate in many cases. If so, either these two variables may be ignored and an intuitive value may be assigned to W(i), or unequal weightage can be given to the two variables.

    I am trying to make the formula more accurate by including other variables and expanding on current variables (Although this will make the formula complicated and time-consuming to calculate).

    I have attached an example.

    Scott, I would really like to hear from you on this.

  • Vineet Kumar Singh

    Hi Scott!
    I really liked this article.

    Inspired by your article, I tried to devise a formula for calculating personal productivity for one day. I looked all over the internet and didn’t find anything similar to this. It’s a really simple one. It assumes two things:
    1) A realistic to-do list has already been made for the day and sorted according to the priority of each task.
    2) It is more or less known what the goals are for that day for each task. (for example, you might want to study the first 3 topics out of a chemistry book.)

    Here is the formula:

    SUM[W(i)*C(i)]
    divided by
    10*SUM[W(i)]

    All the factors- W(i),C(i) etc. – are given a number from 1 to 10.

    Here W(i) is the weight of the i(th) task. W(i)=U(i) + I(i) ,where U(i) is its urgency and I(i) is its importance.
    C(i) is the amount of task completed, a 0 being not started at all, and a 10 being finished.
    This formula can also be extended to a week or month.

    Although I think this will work well for most people, I found some inconsistencies with the formula:
    1) This formula may not work well for highly creative tasks and tasks which require deep work (As C(i) may not be known beforehand. But still, a value can be given based on whether the person used her full potential or not)
    2) It does not take into account unavoidable circumstances which may hinder progress (Although in this case suitable adjustments can be made in the variable C(i)).
    3) There are serious problems with W(i)=U(i)+I(i).It gives equal significance to urgency, U(i) and importance, I(i) of a task. This can be inappropriate in many cases. If so, either these two variables may be ignored and an intuitive value may be assigned to W(i), or unequal weightage can be given to the two variables.

    I am trying to make the formula more accurate by including other variables and expanding on current variables (Although this will make the formula complicated and time-consuming to calculate).

    I have attached an example.

    Scott, I would really like to hear from you on this.

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