# Problem Solving

Before we can address the complaints against Dan Mullen, we have to discuss problem solving.

## Most Humans Are Bad at Problem Solving

Most human beings are bad at problem solving. Typical standardized tests measure a person's ability to solve simple problems. Those that get nearly all the questions correct on a test like the logic portion of the SAT will have an IQ score of about 130. Only one person in 50 has an IQ of 130.

You may think that standardized tests are hard. 49 out of 50 people would agree with you. Yet, a standardized test, like the math portion of the SAT, gives you the answer. All you have to do is pick the right one out of 5 choices for a simple question. You may think the questions are hard. However, for someone who is good at these tests, the question only takes a minute to answer. How difficult can these problems be if a person can answer them correctly in a minute? If you cannot answer the question correctly in a minute, that does not mean the problem is hard. That means you are not good at this type of problem solving.

Take a chess grandmaster. A chess grandmaster is as expert in his field as anyone. A chess grandmaster's job is only to solve problems. Towards the end of the game, there may only be a few pieces on the board for each player. There are only 64 squares on the chessboard. The rules of what you can do are limited. Yet, when you analyze a chess game between two grandmasters with a computer, you find that the grandmasters made mistakes, sometimes blunders. Sometimes they miss the blunders the other grandmaster made. Worse, the grandmaster may be certain he made the best move. Bobby Fischer said that Jose Capablanca, one of the great chess geniuses of all time, often wrote about himself that the way he played the rest of a game could not be improved upon. Fischer said that was not true. Fischer said if you played over Capablanca's games, you could find mistakes.

Real life problems are infinitely more complex than SAT questions and chess games. Real life problems do give you the answer. Real life problems do not have simple sets of constraints. Real life problems cannot be solved in a minute. Compared to real life problems, the problems on the SAT and chessboards are trivial.

If chess grandmasters can make mistakes so often over problems that are so specifically described, and if 49 out of 50 people make mistakes on standardized logic tests, how many mistakes are people making in real life?

## Most Humans Are Bad at Knowing How Wrong They Are

Worse than being bad at solving problems is that people are far more confident that their answers are correct than they should be. Daniel Kahneman won a nobel prize in economics for the work he did with Amos Tversky on this subject. In The Undoing Project, Michael Lewis describes an experiment by Kahneman and Tversky. The experiment was something like this. The researches showed doctors images from medical imaging devices. The doctors made a diagnosis for each image. The doctors were asked to rate their level of certainty in the correctness of their diagnosis. Certainly doctors made the wrong diagnosis some of the time. Sometimes when shown the same image a second time, they made a different diagnosis. The more serious problem was that they far overestimated the likelihood of their being correct. In other words, not only are people wrong, but they are even more wrong about how right they think they are.

## Generalizing Answers to Specific Problems

Most people do not know how to analyze problems. One mistake people make is they try to find general answers to specific problems. People look for one overriding reason when there are a number of issues, each having their own individual solutions. For example, the problem is the Gators lost several games. The reason is the coach sucks. The solution is find a new coach. This is dumb problem solving. The proper analysis is to go through the film for each game to determine the reasons for each loss. This we will do later on.

## Unrealistic Expectations

People have unrealistic expectations, especially expectations of others. People overly value their own performance. People under value the performance of others. This is why we have a judicial system with an unbiased judge and jury. Two people go to court each thinking they are right and the other person is wrong. When they get in front of the judge, more time than not, the judge finds them both wrong. You must have reasonable expectations.

## Judging Based on Outcomes

Real life problems do not have guaranteed answers. The solutions to real life problems have probabilities of success. You try something you have reason to believe will improve your chances of success. You cannot control outcomes. The things you can control are limited. LeBron James was criticized for throwing the ball to an open teammate for a last second shot. His teammate missed. Critics said James was not clutch because he did not take the last shot. James insisted he made the right basketball play because his teammate had a higher percentage shot than James had. Michael Jordan did the same thing twice with Steve Kerr and John Paxson hitting game winning shots. No one thinks Michael Jordan made the wrong play. James and Jordan made the same play, the right play. Whether their teammate hit the shot was beyond their control. You judge someone's performance on the reasonableness of what they do, not on the outcome.

## The People that Are the Best at Solving a Problem Are the Most Knowelgeable Over the Details

The people that are best able to solve a problem are the ones who know the most about the intricacies of the details. The people managing the people solving the problems cause more harm than good when they start making decisions. Look at the Challenger space shuttle disaster. The engineers knew the O-ring would fail at the given temperature, but management went ahead with the launch anyway.

## People Do Not Understand Randomness

There are two big problems with randomness. The first is people do not understand how much randomness affects everything. In other words, you have to be lucky. Over enough time, luck evens out.

The second problem is people do not understand probablities. For example, which of these sequences of five heads and tails are more likely to happen?

A. H H H H H B. H T H T H C. H H T H T

Go ahead, commit to your answer. Test your knowledge before you read on.

If you know the answer, congratulations. Most people think C is the the most random. If you picked C you are wrong. Try again.

The Monty Hall Problem based on the TV show Let's Make a Deal goes like this. There are three doors. There is a prize behind one door. There is no prize behind the other two doors. Say you pick door #1. Monty opens door #3 to show you the prize is not behind door #3. Monty then asks you if you want to stay with door #1 or switch to door #2. What would you do?

For our first problem, did you pick choice B? If you did, you would be wrong again. Try one more time.

Back to the Monty Hall problem. Did you switch to door #2 or stay with door #1? Why did you pick which answer? What were your odds of being right the first time? What were your odds of being right the second time?

Returning to our first problem of heads and tails, if you picked choice A, you would be wrong again. Choices A, B, and C all have exactly the same odds of occurring. Each of those sequences have a 1 in 32 chance of occrring.

Let us rephrase the Monty Hall Problem to make the answer more obvious. There are 100 doors. You choose door #1. Monty opens all the other doors, #3 through #100, to show you there is nothing behind all those doors. Would you swich to door #2 now? Maybe not. Maybe they are gaming you. Maybe they always put the prize behind door #1.

You want to start over. You choose door #51. Monty opens all the other 98 doors except door #2 again. Do you stay with your original door #51 or switch to door #2? What are your odds now of picking the correct door?

If you stay with door #51, your odds of that being the right door is 1 in 100. What are your odds if you switch to door #2?

If you switch to door #2, your odds of that being the right door is 99 in 100.

## The Lesson

Here is the lesson. There are all these media people influencing the public on what is wrong with Gator football. The question is which of these media people would be willing and able to solve these two simple problems on randomness? If they are unwilling or unable to solve these problems, they do not have the analytical insight to know what is wrong with Gator football or to know what the solutions might be. We will go through the specific complaints raised against Dan Mullen's Gator football to see what we can understand about the problems and solutions.