Luck vs Hard Word

Is your status in life determined by the whims of fate and your current position? Or do you only have yourself to blame/credit for your failures/successes? I often think about this whenever I hear some billionaire talk about how they pulled themselves up by their bootstraps. I also think about this whenever I hear someone making excuses for themselves. Tonight, this topic once again came into my mind while watching this clip from the Joe Rogan podcast:

I thought, "I wonder if Joe Rogan realizes the tremendous luck that it took to become the world's largest podcaster." I really enjoy much of Joe Rogan's content and think that he is refreshingly willing to disagree with his guests. He seems to lean conservative when talking to his liberal guests and seems to lean liberal when talking to his conservative guests. This is what I want to see from a podcast! I believe that his hard work is very important to his success. In fact, I would even go as far to say that his success would be nearly impossible without hard work. That being said, his level of success is also nearly impossible without tremendous luck.

Following the theme of hard work, I put together this cool plot to illustrate what I mean ;). I'd like to propose the following model of success that admittedly is very simplistic, but which demonstrates some true dynamics of success.

  1. Each person, \(p_n\) individually has some amount of hard work \(w(p_n)\) and some amount of luck \(l(p_n)\)
  2. The success of a person, \(s(p_n) = l(p_n) + w(p_n)\)
  3. Hard work and luck are Gaussian random variables from which individual people are sampled.
In the following plot, hard work and luck contribute equally to success (their standard deviations are equal). The luck Gaussian has a zero mean, but the hard work Gaussian has a positive mean because most people don't try to actively sabotage themselves. Each circle represents one person and the amount of blue and red in a circle correspond to how much work and luck respectively that person has.

Note: You can zoom along the X-axis specifically by scrolling with your mouse hovered above the X-axis.

Notice that, although the most successful people (circles) have put in a lot of hard work (blue), they have also been very lucky (red). This results in the most successful people being pinkish (both working hard and lucky).