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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

The basic formula for determining if something is worth doing is reward minus cost. We prioritize positive results over negative ones.

Cost is time to complete task * hourly salary. If someone is paid $20 an hour, then having them complete a 40 hour task costs $800. The task has to earn $800 or more to be useful. Similarly, tools have predictable rewards. Reward = time saved per employee * hourly wage.

We also have to factor the chances of success.

The formula becomes (reward - cost)*chance of success. Estimating the reward of a long-term goal can be difficult.

Costs are easier to calculate. Say we get paid $50 k a year, and get 10% raises by switching jobs. We quit our job to work on a game for 4 years. In those 4 years, we could of been working and earned: $55 k + $60.5 k + $66.55+ 73.2 k = $255 k. Our game needs to make $255 k to break even.

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, stop making the same mistakes. 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

Start ups cannot compete with big companies in terms of money and workers. They have to out think the competition. Learning a skill has similar gains to compound interest. The more we learn a skill, the more productive we become. Our productivity is increased, because we are reusing what we learned previously.

Compound interest example: $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

Once we learn a skill, learning a related skill is quicker, because we can skip the fundamental theory stage. A pro basketball player wants to switch to playing tennis. Most athletes probably spend their first 4 k hours learning fundamental athletic skills. A pro basketball player can skip the first 4 k hours, and spend 6 k hours on tennis specific skills.

Diminishing Returns

After a certain point, investments stop growing quickly, and it is less enticing to invest. When it comes to learning a skill, I slow down around 2 years. We can estimate our growth by comparing our previous work to our current work. My art work in year 1 is dramatically different from year 2. My art work from year 3 is similar to year 4.

In Dota 2, the average rating of a player is 3000. Reaching 4200, puts the player in the top 10%. Going from 3000 to 4200 is a 40% increase. We went from being better than 50% of players to better than 90%. 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

Over Working And Experience Is Overrated

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, hours worked and demand. Which of the 4 is most productive?

If the average person works 8 hours, then at most they can achieve is 16 hours or 2 times productivity. Practice or experience has diminishing returns, because our body has physical limits. The current record for the mile (1.6 km) run 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 leaves us with education. The reason a founder is paid 10 to 100 times is because they have knowledge no one else has. Knowledge leads to 10 to 100 times productivity. In comparison, working longer hours and experience is around 2 times productivity.

Probability

The more requirements we have the less likely we will be able to achieve it. If 1/100 people are good at writing, and 1/100 are good at art, then 1/10 k people are good at art and writing

This is why designers like simplicity. There are less requirements, or features, so it is easier to understand, maintain, and fix.

References