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)


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.