Wednesday, April 05, 2023

More Mental Models: Applied Mathematics

 

Our brains are wired to have us believe what we see and hear as a matter of self-preservation. The noise in the brush may not be a dangerous animal, but it's safer to run away than risk the consequences. 

The power and danger of ideas lies in their use. The Dartmouth girls who told each other the Big Lie, "Today is an easy game" fell victim to overconfidence. 

Let's review a few mental models from mathematics. 

  • Multiplying by zero
  • Regression to the mean
  • Compounding 
  • Probabilistic thinking
Multiplying by zero. "Anything times zero equals zero." This translates into 'fatal mistakes' such as in the case of Len Bias who died of a cocaine overdose, "the greatest basketball player who never played professionally." It shows up in aphorisms like, "an army of asses led by a lion can defeat an army of lions led by an ass." And in the reality that "a rotten apple spoils the barrel." 

Leadership matters. Coaching matters. Effective coaches exert a multiplier effect. A bad teammate can ruin a group. Don't multiply by zero. 

Regression to the mean. Hot streaks and 'divergence from historical norms' end. This gets illustrated in many fields, especially investing. 

Stock prices can maintain divergences from the 40 week average (blue) for years during "bull markets" but invariably return like most lost puppies. 

Even the strongest programs have down periods. The bull market in Melrose volleyball has been ongoing for over twenty years, an exceptional run in high school sports.  

Compounding. Darren Hardy wrote The Compound Effect about the power of compounding. What is compounding? "Compound, to savers and investors, means the ability of a sum of money to grow exponentially over time by the repeated addition of earnings to the principal invested."

Work invested in skill, strategy, physical and psychological development grows over time. It's one reason that veteran teams have an advantage, an "in the long run" effect. 

Here are a few quotes: 

“A daily routine built on good habits and disciplines separates the most successful among us from everyone else.”

“Ask yourself each day: If I only did 3 things today, what are the actions that will produce the greatest results in moving me closer to my big goals?”

“Track every action that relates to the area of your life you want to improve. All winners are trackers.”

The work you invest in yourself defines you. "Champions do extra."

Probabilistic thinking. Seldom is there the 'sure thing'. Note the proliferation of ads for sports gambling. If it were that easy, everyone would be rich. In her book, Thinking in Bets, World Series of Poker champion Annie Duke explains that in poker and life, probability impacts risk and outcomes. She opines that Texas Hold 'Em at her level is 76 percent skill and 24 percent luck.  


"Overplaying your hand" can produce big wins or catastrophe such as the Space Shuttle Challenger disaster where the data suggested safety within certain launch temperature levels and uncertainty outside.

Lagniappe. The mental game.  

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