Showing posts with label Probabilities. Show all posts
Showing posts with label Probabilities. Show all posts

Tuesday, January 14, 2020

Luck; Skill, or both?

Do you need luck, skill, or both to become successful? You can find many answers to this question. Some people say others have luck and they have great skills. Some people say you need both. The answer to this question starts with words ”It depends on.” and continues with ”what you are doing. Michael Mauboussin has written a great book, ”The Success Equation” which gives more answers to this question than I can give to you in this text.

Let's start with the definition of luck. It can be defined as ”A single unrelated event that gives you an advantage or a disadvantage.” Some people may say that you can work hard to be lucky. They say you can develop yourself to become luckier. These phrases do not apply to the definition of luck. What happens is that when you have better skills in what you do, luck strengthens your success. Skill can be defined as: ”An ability to use your understanding to execute an action or a decision.” The more skilled you are the better ability you have to do this on average. The last two words are the most essential ones. Single actions or decisions that give you a great result do not mean you are skilled. Great executions that you can deliver on an average day by day are the best symptoms of great skills.

Luck-skill-continuum

Different types of actions or decisions can be put into luck-skill-continuum. On one side of the continuum are actions or decisions that need only luck and on the other side are actions or decisions that need only luck. You can find most actions and decisions from the middle of the continuum. They are based on luck and skill. In the middle are the actions that are based on both luck and skill and from this point to the left luck becomes more important and from this point to the right skill becomes more important. Lottery and most games like roulette at the casino are completely on the left side of the continuum and games like chess are on the right side of the continuum. Ask yourself: ”Can you lose on purpose?” if you want to know about the position on the continuum. If you can lose on purpose, you are on the right side of the continuum. If you cannot, you are on the left side of the continuum. In the middle, you can find an author that sells lots of books. Shitty authors cannot sell any books, but good ones can still not sell if they are not lucky.

Three things tell you more about the actions or decisions and whether to put them to the left or right side of the continuum. The first one is the sample size. When you are on the right side of the continuum, even the small sample size of the results can tell you much about skills. For example, the time for a hundred-meter run can tell you whether the runner is a good or a bad one. In the lottery, you can put hundreds of coupons and how much you win tells you nothing. In other endeavors like playing poker, small samples tell you nothing about the skills of the player, but when you play hundreds or thousands of hands, more skilled players win and worse players lose much more.

The second one is the form of feedback you get. When you need to be skilled, the feedback you get is based on clear cause-effect relationships not random or complicated like on the left side of the continuum. In this side, the feedback you get will lead you to problems. You may think that you are skilled even though you are just lucky. This does not happen on the right side of the continuum.

The third one is the return to the average or to mean if you want to use the statistical word. When the endeavor is based on skill, the return to the average happens slowly. When the endeavor is based on luck, the return to the average happens fast. In the middle of the continuum, the speed of the return to the average is somewhere in between.

There is an interesting paradox about the role of luck in the middle of the continuum. The better the relative skills of the performers are, the more luck you need to perform better than average. What I mean with this is that when the average performance is closer to the best one, the more luck you need to succeed and vice versa. The bigger the difference between the average performer and the best performer there is, the less luck the best performers need. When this is the case, you have to be sure you are better than your opposition.

I kept this text short. Sorry for not publishing anything for a long time. Hopefully, I will get something published in the next two weeks after this.

-TT

Tuesday, August 20, 2019

How to predict better?

Everybody makes predictions. Most predictions are irrelevant in the big picture, but everyone makes them. For example, you can predict tomorrow´s weather. Most of the time, it doesn´t matter whether you are right or wrong. But sometimes you have to be outside for the whole tomorrow and then it matters. You make these predictions without a systematic process. You need to have a systematic process to make better predictions. This text is about making them.

Commit to the truth

The first step for making better predictions is to commit to the truth. You have to recognize the influence of your beliefs, and psychological tendencies and you have to question them. You cannot make predictions that confirm your way of seeing the truth when the evidence does not confirm your beliefs or assumptions. You have to be willing to update your beliefs and assumptions when the objective facts tell you different stories than you would like to see. Your beliefs and assumptions have the power to modify your predictions in wrong directions unless you commit to find the truth no matter what that is. Your goal is to make the best prediction you can make with the facts you can gather. If you think you do not have enough facts, you have to commit to finding them. If you have too many facts, you have to commit to separating the relevant facts from noise.

The process of making good predictions

Most people have three different answers to predictions: ”Yes”, ”No”, and ”Maybe.” People who make good predictions live in an uncertain world. In this world, ”Maybe” is the only right answer. This means that you have to make predictions with probability estimates. Your prediction could look like this: ”There is a 70% chance of raining tomorrow.” You also have to second-guess all the people who make vague predictions like ”It may rain tomorrow” or ”The unemployment rate may be less than 5% in the next two years.” You cannot know whether these people have made the right predictions because their predictions can mean anything. If you want to make better predictions, you have to commit to making probability estimations.

The starting point for making a probability estimation is to find a base rate for the thing you are predicting. For example, if you have to predict what is the probability that your football team will win the next home game, you have to start by looking at how many wins they have won in their home games this season. Your sample size should be enough. If the season has just started, you have to look for last season´s statistics, too. Let´s say they won 7 out of their last 10 home games, then the base rate is 70%. This is your starting point. Then you have to use other data to adjust your probability estimate. Why should you start with a base rate? Because your first estimation is just your hunch and the probability of it being right is smaller than using the base rate. The figure you find first will be the most available for your brains. It will be your anchor during your prediction process. Do not forget to define the time frame for your prediction if necessary.

After you have figured out the base rate, you can start forming your view. Break your question to smaller questions like ”What would have to be true for this not to happen?”, ”What kind of information helps me to answer this question?” or ”What I do not know about this question?” You have to figure out what you don´t know and what you do know. After many questions, you should make your probability estimate and write it down and the reasons behind it.

Then, it is time to find out some outsider view about the same question. Consult people who have made predictions about the same question. Find out what the experts think and their reasons. Focus on the differences in reasons between your view and other people. Consult prediction markets, like stock markets, or betting offices that give odds to a thing you predict. You can use polls if you predict the elections, etc. After you have found out the base rate, made your probability estimate, and found out about the outside views, you have to synthesize and make another probability estimate.

Let the time pass and then you can scrutinize your own prediction and make another estimation. You can do it by assuming your first estimate is wrong. Consider why it is wrong and write down the second estimate and reasons for it. And then find out about other outside views again. Then, synthesize again and update your prediction when new important information arrives. This process ends when the time frame closes. This process can feel frustrating. If you want to predict better, you have to update your estimates often and make gradual adjustments to your predictions.

Prepare to be wrong. Even the best predicting professionals are occasionally wrong. Do not mix up the outcome of the prediction and the quality of the process. When you have 80/20 predictions, you are rt only 4 out of 5 predictions when your probability estimates have good accuracy. No matter whether you are right or wrong, have a postmortem. Think about the process and the reasons behind your estimate. Did your process have high quality? Did you find out the right base rate? Did you update your estimate often enough? Did you find out the outside views of the best professionals and prediction markets? How many times you synthesized these views? All these questions help you to predict better next time.

Sources:


-TT

Tuesday, January 22, 2019

Backcasting and Premortem

A normal way of making decisions about the future is to imagine where you want to be and how will you get there by thinking about the goal and the objectives you need to achieve. You start doing it from the beginning. This is not the way to maximize the probability of getting there. What you should do instead, is to invert. Backcasting and premortem are better ways of doing things. They start from the future and move backward until you get to the beginning.

Backcasting

Backcasting means a process in which you move back from the positive outcome. You have an availability bias. One way it represents itself is that you focus more on the here and now and for the immediate future. Longer timeframes are more problematic for keeping the focus on the most important things. When you focus on the present, you consider only things that are in your mind right now. You can probably design a few next steps. This is not enough for successful planning. The better way to think is to start from the point in which you have already success. From this point, you start going backward. Ask questions like:

  • Why did I get here?
  • What events occurred?
  • What decisions you had to make to get here?
  • How I must have changed to get here?

You can probably understand the probability of accomplishing a goal better. Sometimes you can decide not to pursue the goal by seeing that it is too improbable related to the expected value of the success. You can also identify responses to developments that can cause interference in reaching your goals. For example, what you should do to get back on track when you move away from your goals. These slumps are facts of life. You cannot move straight toward a successful future. Progress has some fast movements and some slow points. Boredom and excitement have variations.

Premortem

Premortem is the exact opposite of backcasting. You start from the negative outcome and move backward toward the present. Premortem helps you to anticipate problems along your way. You can ask yourself the same questions about the future as you did in backcasting, but with a negative twist. For example, instead of asking ”Why did I get here” you can ask ”Why didn´t I get here?” You have better chances for success when you have thought about the negative scenarios. You can also imagine how some obstacles can become too hard to overcome. Dreaming about achieving a goal is not as efficient as doing the premortem. You can have positive goals, but it is better to think about the negative outcomes while having them.

Both have equal importance

Since backcasting and premortem are two sides of the same coin, you have to do both. Positive and negative outcomes have a combined probability of 100%. By doing both, you get a better view of the future. You reduce the probabilities of negative outcomes and increase the probabilities of positive outcomes. Failures and obstacles become less surprising and you have better chances to cope with them. It is easy to lie to yourself by focusing on backcasting and forgetting premortem. You cannot put your head into the sand and forget the negative outcomes. You will make better decisions by doing both.

This is all for now, until next week,

-TT

Tuesday, March 6, 2018

Risks

Definitions

A risk can be defined as ”A potential of gaining or losing something of value.” or ”An exposure to the chance of injury or loss.”

Personal risks

First I would like to say that risks affect on you in many different levels. For example, they affect on you through corporations, nations and global events like wars. I will keep things in personal level. Humans are very good in understanding risks related to their survival. Especially, when their intuitive decision-making systems are on. You can avoid an imminent threat to your survival without even noticing it. For example, changing your direction from the normal route, because of something is not feeling right. Survival in these cases means not hurting yourself physically in an imminent danger. You are not good in avoiding long-term risks. Modern world has less imminent threats than your brain thinks. This creates many problems that even the risk management experts do not understand.

You have many personal risks other than risks of physiological harm. Financial risk is maybe the most common risk you think about. Losing your job, or inability to pay your debt can cause you harm. You may lose your reputation if you do something really stupid or someone spreads rumours about you. You also have a risk of not being able to adapt to the changing world. Doing what you have always done before is your path of least resistance. Changing things is hard, even when it is necessary. People are also increasing their technology risks, because their dependence on technology is rising. Personal risks can compound in a long-term. Taking small, but unnecessary risks without suffering the consequences fast may lead to severe problems later on. For example, eating crappy food may not cause you any harm for decades, until one day you get a heart attack without any warnings.

Risk Management

Risk management is about probabilities. You need to understand them to understand risk. Repeatable events with fixed probabilities are easier to understand. For example, risks at the roulette table and lottery are fairly easily quantifiable. When you cannot calculate a probability of something happening, you cannot really understand risks. Uncertainty is not well understood. Managing risks without understanding power laws is one of the most common causes of financial destruction for institutions and in a personal level. The other common cause is not understanding complex systems and the second order effects in them.

You have to consider your risk appetite too. Some people cannot sleep well with moderate risks in their lives and some people cannot sleep well without them. Risks are not all bad things. Progress comes from taking risks. Some of them are managed and some of them are not. Humans have developed as a race by avoiding risks concerning on survival. Risk-seeking is about functioning against your basic instincts. It is hard, but many times worth all the effort. When you understand the risks you are taking, it is easier to get better results. You have to ask yourself some questions to understand risks better:

  • What are the consequences of not doing it? What will it cost you? What are the unwanted outcomes that can come true? How will you react if they happen to you?
  • What are the positive consequences? What will you benefit? How will you react? How do you feel about the outcoming benefits now?

Risks can also be quantified in terms of impact of their consequences. You should use a simple scale in how you want to rate the impact of the risks. Make it reasonable. For example, you can use a three-level scale of impact for risks. Risks with high, medium or low impact. Think about high risks all the time. Risks with medium impact are not that important, but you should check them regularly. Low risks are not that relevant. You should still check them occasionally. You should also remember that low and medium impact risks can become high risks through compounding. In this case, it means taking many small risks many times.

Asymmetric risk

There are two kinds of asymmetric risk. Good ones and the bad ones. An asymmetric risk means that the reward is a lot bigger than the risk taken, or the reward is a lot smaller than the risk taken. In other words, the expected payoff is high or low, depending on the risk taken. Nobody wants to take an asymmetric risk where the expected payoff is crappy. Most often, this happens because the risk taker do not understand what he/she is doing. This happens to the most respected experts too. Especially, financial market participants do not understand risks. One reason is that they haven´t noticed the power laws in the markets or understand them. Many assumptions about the returns in the financial markets are made by thinking through a normal distribution. The problem is that returns in financial markets do not really realize through them. Most of the profits are made with a small number of stocks or during the small number of days, etc. In other words, extreme outcomes in financial markets have higher probabilities than using normal distribution tells you.

It is easy to make a statement that you should avoid all the asymmetric risks, where the downside is enormous compared to the expected payoff. For example, not going to see a doctor, when you have a severe chest pain. Not going to a doctor can cause a death and going to the doctor can save you. You can also take lots of asymmetric risks where the probabilities are against you. When expected payoff is high, you need smaller amounts of successes. This doesn´t mean that all the risks come true and payoff is always high. You should be ready for many losses with these kinds of risks. Overall, the expected payoff will be good in the long run.


-TT

Wednesday, February 21, 2018

Probabilities and statistics

First, I would like to say that I am no mathematician and I am only to some extent familiar with probabilities and statistics. I will keep this introduction in a very basic level. There are many better texts about probabilities and statistics. You should probably try to find better sources for these things.

Definitions

You can define probability as ”The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible”. Probability can also be defined as ”The likelihood of given event´s occurrence”.

Statistics can be defined as ”A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data”. It can also be defined as ”A fact or piece of data obtained from a study of a large quantity of numerical data.

Basic things about probabilities

  1. The probability that two events will both occur can never be greater than each probability occurring independently. For example, a likelihood of you meeting a person who is a woman and likes ice-cream is never greater than you meeting a woman.
  2. If two possible events A and B are independent, then the probability that both A and B occur is equal to the product of their independent probabilities. For example, the probability of two consecutive heads in two coin flips is 0.5*0.5=0.25. Sometimes you need to calculate a conditional probability. For example, an event B occurs only if an event A has happened before. The probability of an event A happening will differ from the probability that A will happen if B occurs.
  3. If an event can have many different and distinct outcomes A, B and so on, then the probability that either A or B will occur is equal to the sum of the individual probabilities of A and B, and the sum of the probabilities of all the possible outcomes (A, B, and so on) is 100%. For example, you are throwing a dice with 6 numbers and you want to know what is the probability of you getting either a 1 or 2? The probability of either one happening is 1/6+1/6=1/3.
These three basic laws of probability form much of the basis of the probability theory. You should also remember that you can use inversion many times to make easier calculations for probabilities. For example, to get a probability for throwing the dice and getting 1,2,3,4, or 5 is easier by calculating a probability of not getting 6. The probability of an occurring event is always dependent on the number of ways it can occur. To calculate the ways an event can occur is easier, when you understand combinations and permutations. When you hear someone saying ”an outcome is probable, you really hear that an outcome is probable under some set of hypotheses he or she has about the way the world works. Maybe the most important way to use probabilities into one´s advantage is getting an an expected payoff. You get it by:

Multiplying the probability of each possible outcome by its payoff and add them all up

For example, you flip a coin with a friend and you bet 100$ for tails. The expected payoff is 0.5*100$=50$. You should always try to maximize the expected payoff in whatever you are doing.
Statistics

We have a saying in Finland: A lie, a big lie, and statistics. When there are two different parties like employee or employer organizations, they often interpret the same statistics differently. When this is the case, the truth is found from the middle. You should never take any interpretations of statistics at face value. Different incentives give different interpretations. There are so many ways of misinterpreting statistics that I will not get into them now. I will keep things short.

First, you need to understand a sample space which is the set of all possible outcomes. For example, when you are throwing a dice once your sample space is 1,2,3,4,5, and 6. When you work with the large sample space, you can help yourself by using a one value that describes the average value of the entire sample space.This is called the central tendency. Mean median and mode are ways to describe it. Lets keep this simple and think about the mean only. If you want to find a mean, you have to add up all the values at the data set and then divide them by the number of values you added to sample space. A sample space is an important feature in statistics. This applies especially to things that go with the normal distribution.

Normal distributions are often used to represent random variables whose distributions are not completely known. These distributions do not tell much about individuals. When the data represents bigger groups they work better. A bell curve describes the variation in normal distribution. Most of the observations are close to the mean. Curve slopes symmetrically downward in both sides of the mean. First, the number of observations diminishes fast and then slower, until it is hard to see any changes.

The bigger the sample size compared to the population, the more it reflects the underlying population of being sampled. These choices for the sample should be taken randomly. Otherwise the results are useless. A sample size of 100 in the poll or survey gives a margin of error that is too big for most of the purposes. A sample size of 1000 usually have a margin of error around 3%. Often this is enough. Repeating a survey with the same sample size do not give the same results. You should expect some variation in the results.

There is a difference between statistics and probability. Statistics concerns the inference of probabilities based on observed data. Probability concerns predictions based on fixed probabilities.

Shortly about randomness

A large number of independent random variables should be distributed according to the normal distribution. This is called the central limit theorem. For example, you want to manufacture 1000 screws that weigh 10 grams. You want to add enough metal that leaves each screw weighing 10 grams, when the screws are manufactured. According to the central limit theorem, the weight of your screws should vary according to the normal distribution. Unless this is happening, somebody is probably fabricating the results. There are many random processes in which the results look like a bell curve. For example, people´s heights, how long will they live, etc. There are also some processes in which the normal distribution is useless like damages from natural disasters, etc.

You can be fooled by randomness. Sometimes, random processes look like patterns of data. For example, so called hot hand, in which there is a shooting streak for a basketball player is actually mostly a random pattern. It doesn´t mean there is no skill involved. You just have to concentrate on the long term statistics, instead of short term patterns. It is not easy to separate random streaks from patterns. Among a large group of people, there are always random streaks that look like patterns. Our brains do not understand randomness well. It is better for acknowledging patterns, even when there isn´t any. Humans have a need to be in control of events. Random events do not confirm this need which creates a clash between reality and the need to feel in control.


Have a nice end of the week!

-TT