The Probability of Manufacturing Success

I came across a short clip recently discussing the difference between being lucky and getting lucky. It got me thinking about whether people can make themselves luckier by repeatedly creating opportunities for good things to happen.

At first glance, it sounded like standard social media fluff. But there is a useful question underneath it: how much can repeated attempts improve our chances of success, and what does that imply about how we should act?

The probability of at least one success

Suppose each attempt at something has a 10% chance of succeeding, and the attempts are independent. Failing twice does not improve your odds on the third attempt. It is still 10%; the previous failures do not make a success due.

The chance of succeeding at least once across several attempts is a different question. To calculate it, we first work out the probability that every attempt fails. If the probability of success is p and we make n independent attempts with the same odds:

Subtracting this from one gives the probability of at least one success:

With a 10% chance on each attempt, the results are:

• 1 attempt: 10.0%
• 5 attempts: 41.0%
• 10 attempts: 65.1%
• 20 attempts: 87.8%

No individual attempt has become more likely to succeed. Making 20 attempts has simply provided more opportunities for a success to occur. In this limited sense, the idea of “manufacturing luck” has a reasonable mathematical basis.

The difficulty is deciding how well this describes the opportunities we encounter in life.

The cost of reaching the next attempt

The calculation tells us the probability of at least one success, but says nothing about whether we can afford the failures along the way. Sending another job application is very different from starting another business with our remaining savings. An attractive chance of succeeding over 20 attempts offers little comfort if five failures would exhaust our resources.

Nor does surviving a failure make it costless. Time spent pursuing one opportunity cannot be spent pursuing another. We therefore need to consider whether the potential reward justifies the resources we may use before reaching it.

Learning and dependence between attempts

Real attempts rarely have fixed, independent odds. We might improve a pitch after a rejection or discover why customers do not want a product. If we use that information well, our next attempt may have a better chance of succeeding. This is an additional benefit of trying, although it depends on our willingness to learn rather than simply repeat ourselves.

Dependence can also work against us. Applying to 20 companies during a hiring freeze gives us less variety in our opportunities than the number suggests. The same economic conditions may affect all of them. Equally, sending an unchanged, weak application to more employers may keep producing the same result.

This limits what we can infer from the formula. We usually do not know our probability of success, and a larger number of attempts does not necessarily represent the same number of independent opportunities.

The value of a success

There is a further distinction between succeeding and doing well overall. The calculation treats success as a yes-or-no outcome, regardless of its size. In some businesses and investments, one large success can cover many failures. In others, a win earns too little to recover what the earlier attempts cost.

We therefore need to consider the size of the possible gains and losses as well as their probabilities. A high chance of eventually recording a success is insufficient if the process is likely to leave us worse off.

I still find the idea of manufacturing luck useful. Where the reward is worthwhile and failure is affordable, making more attempts can improve our chances. Learning from those attempts may improve them further. But persistence only makes sense while we continue to examine the opportunity, the cost, and what the results are telling us.

The formula gives us a reason to look beyond a single failure. It does not relieve us of the judgement required to decide whether to try again.

Disclaimer: The ideas presented in this post are solely my personal perspective and have not been substantiated by any verifiable evidence. Please form your own opinions on such matters.