UI design concept for a Kanban board.

Planning With Mathematics

How many times have I over scoped a project to throw away most of the work? How many times have I focused on a goal only to find out I need to pivot? Creative people want to build first, and ask questions later. Change is inevitable. But, with a little math, we can slow down the rate we throw our work away.

Updated 2019 Nov. 18, removed A* and Minimum Spanning Tree section and added Over Working And Experience Is Overrated.

Add And Subtract

To determine if a goal is worth it or not, assign a cost and benefit number to it. If the benefits are 2 times more than the costs, it is worth doing. Most people have experience estimating tasks on an hourly scale, so breaking big goals into tasks that can be done in 1 day will lead to accurate estimations.



Say we are working on a feature for our product that will take 1 month to complete. We have 3 employees working on it. The total cost is 3, or 1 point per person.

One person on the team has domain experience in the feature, +1 point. A competitor has implemented a similar feature, +1 point. The competitor's Amazon page has many reviews praising the feature and YouTube reviews also praise this feature, +1 point. We estimate the feature will pay for 3 months worth of salary for those 3 people, +3 points. In total, the feature has 6 benefit points.

Do Trial And Error

Is y = 28, and x = 10?

  1. y + 2 = 3x
  2. 28 + 2 = 3(10)
  3. 30 = 30

What if we got 60 = 10 on line 3? Either the original y = 28 or x = 10 was wrong, we did the math incorrectly, or the equation is wrong. In other words, we question the entire premise.

Likewise, if a plan is exceeding the costs, do not keep working on it for hours, question the entire premise. Were the goals too ambitious? Were the initial conditions off? Spend time gathering more information, read a book, go Wiki, check out competitors, watch YouTube tutorials, and find out what went wrong. Set aside one day a week to question the entire premise of the plan.

Compound Interest

Think of learning a skill as an investment. Even a little effort can pay off over time. We may start off dedicating 1 hour a week to learning a skill, but each week we get more productive than the previous week. Our productivity is increased, because we are getting better at using the tool for that skill.

In practice, it can be hard to figure out what goals or skills to invest in. Investments can crash, as shown by the stock market. We can lose knowledge too. If we don't consistently practice what we learned, we forget it.

Invest $100 at 10% interest

  1. 100 + 100*0.1 = 110
  2. 110 + 110*0.1 = 121
  3. 111 + 111*0.1 = 133
  4. 133 + 133*0.1 = 146
  5. 133 + 133*0.1 = 161

General Solutions

Have you ever done an activity with a friend to discover they seem to have a natural talent for it? They figured out a general solution that can work in many situations. Like compound interest, putting in a fixed amount of time into learning a skill will keep paying off over time. For example, we would expect a basketball player to learn another physical sport, like tennis, faster than they would to an unrelated skill. Their skills transfer over quickly to related domains.

Diminishing Returns

After a certain point, investments stop growing quickly, and it is less enticing to invest. From personal experience, when it comes to learning a skill, I slow down around 2 years. A simple way to detect when investments stop growing is to keep track of it, and observe it for long term trends. When learning skills, people typically keep a to do list, compare that from week to week to see the growth trends.

In Dota 2, the average rating of a player is 3000 MMR. Reaching 4200 MMR, puts the player in the top 10%. We went from being better than 50% of player to better than 90%, a 40% increase. It's not hard to imagine going from 3000 to 4200 in two years. After that, there is only 10% to climb, which could take another 2 years. That extra 2 years could be invested into gaining 40% in another skill.

Dota 2 matchmaking, MMR distribution for January 2018

What if we've been working on our business for 4 - 10 years?

If we've studied marketing for 1 - 2 years and the product is still not selling, then it is safe to give up or pivot. For video games, if the trailer or let's play gets 100 k views, then marketing did its job. If the game does not sell well at that point, then consider moving on.

Over Working And Experience Is Overrated

What is the best use of our time? Most of us know the answer is education. The value of education is beaten into us at an early age, but for some reason the workplace still overvalues working long hours.

First, consider the average person works 8 hours a day. If they work 16 hours a day, they only double their productivity. It is not worth it, because it cannot be sustained. More importantly, 2 times productivity is so small compared education, which has 10 times productivity.

Our pay is determined by a few factors:

We tend to avoid hazardous jobs and unusual work hours. We can't control the law, and moving may not be possible for various reasons. This leaves us with education, experience, and demand. Which is more productive?

Experienced people have practical knowledge that allows them to avoid pitfalls and save money. Experience is overrated, because it is limited by our physical abilities. The current record for the mile run (1.6 km) is 3 minutes and 43 seconds. The average man runs a mile in 9 minutes. The fastest runner in the world is only 2.4 times more productive than average, and they had to train for years. This is just as inefficient as working longer hours. Practice has diminishing returns. Notice that working long hours is also a physical limit.

The average reading speed is 200 words per minute. I've seen articles claim people can accurately read 800 words per minute. The fastest reader is only 4 times faster than average. With 1 year of training, I'm sure the average person can get up to 300 words per minute, so now the fastest reader is only 2.6 times more productive. The point is humans have around the same physical limits.

If a CEO worked 16 hour days at their physical limits, they would only be 10 times more productive than average. Say the average CEO makes 100 times more than the average person. How do they go from 10 to 100 productivity? The only factor left is education.

Skills That Combine Well

Why is education 10 times productive? Think of skills like chemical elements. Most of the time, combining them doesn't do anything, but sometimes they can cause lucrative reactions.

Most business-oriented people will quickly find out that storytelling and usability are important. What other skills have proven themselves for centuries? Visual art, sex, food, music, math, etc. Incorporating a little bit of each should lead to positive results.


Avoid plans that depend on two unrelated events. The odds of unrelated events are multiplied, so the odds to get two heads in two coin flips is 1/2 x 1/2 = 1/4. Jake dropped out of high school, and loves video games.

Which is more likely?

  1. Jake is unemployed
  2. Jake is unemployed and plays video games

Option 1 is more likely. The two events in option 2 are unrelated, but we pick it because of our bias. Let us pretend the odds of a high school drop out being unemployed is 1/5 or 20%. If the odds of boys being gamers is 3/4, the odds for option 2 is 3/4 * 1/5 = 3/20 or 15%.

Prefer plans that depend on either events, but neither event can happen at the same time in one attempt, because those probabilities are added. The chance of getting a tail or head in one coin flip is the probability of heads, plus the probability of tails, or 1/2 + 1/2 = 1. If we need people to invest in our start up, and know 1/33 people have a chance to become a millionaire, then making friends with 33 people now might give us access to 1 millionaire in the future.