Lady Luck

There is a reason I am far more impressed by a top poker player than a top trader in a bull market. There is a reason I admire a golfer who has a fantastic season more than a football manager fighting off relegation against all odds. There is a reason one-off star performances are far less exciting than a record of above average and why I would prefer to use maths to predict the future rather than a good understanding of history. That reason is luck.

Probability is the key intersection between disciplines from finance and economics to philosophy. Yet the human mind is not equipped to fully understand and use probability. Most people, even with fantastic understanding of odds, still approach probabilistic problems from an emotional point of view. This blog looks at how people tend to massively underestimate the role of luck in their lives and attribute far too much of their success to talent.

Intro

Nassim Taleb’s Fooled by Randomness (strongly recommended) defines the concept of alternative realities. Everybody understands that when you throw a dice you have a 1-in -6 chance of rolling a particular number. However, few people think of past outcomes from a probabilistic point of view. What has happened has happened and that’s that. But just like throwing a dice, every real world outcome is one reality path chosen amongst a long list, if not infinite, number of alternative realities. 

The key to understanding Taleb’s book and what follows is to focus on the idea that the reality we live is simply a realisation of many possible realities. It seems odd to think about “paths that never happened,” so I provide some examples. Most simply, you roll a dice and it lands on a three. There are five other equally probable alternative realities even though the observed outcome is a three. Roll again and you are unlikely to throw a three again. Pushing beyond this, we must understand that we live in a stochastic world and that when there is uncertainty, there are alternative realities (with different probabilities of occurring). We wake up in the morning and decide to take the M25 to work rather than the train. Even though there was no traffic in the observed outcome, this is not necessarily a good choice for the future since the probability of heavy traffic at 8am on the M25 is extremely high; we just observed a low probability event. The guy that gets hit by lightning in a storm appears extremely silly for choosing to be outside, but there are a million more alternative realities where he doesn’t get struck.

From the Big Bang to the present day we have observed an individual realisation from an infinite pool of alternative realties. If we turned back the clocks to the start of the 1900s, we would see an entirely different realisation of the century. Some events with high probabilities may very well still occur, but just like in the movie Butterfly Effect, the new observed reality would certainly be different as probability at every decision node reshapes history.

Of course talent can affect the probability of random outcomes. However, apart from the sun rising in the morning, there are very few predetermined outcomes in the world we live in. Hence thinking without the benefit of hindsight rather than focusing on results is a good way to analyse performance, choices and outcomes.

Finance

The main feature of Taleb’s book is trading on the financial markets. Star traders earning mega returns tend to have short-lived careers and “blow up”. The most successful guys over a long period are more methodical, less extravagant risk takers. The guys that understand and use probability tend to do better if given the opportunity over a long period of time. That is because they shield themselves from risk according to that risk’s probability of occurring. There is of course a lower variance of returns for these more methodical guys. Sometimes protecting themselves against risks when those risks do not happen gets them fired. Hence these are not the guys you see all over the front of the FT and Time. These are the guys that make consistent returns over a long sample of time.

Efficient markets describe an environment where all information publically available is already priced into the market. This means there are no profit opportunities for investors and hence asset managers and traders are no more than monkeys throwing darts at a dartboard. If you believe in efficient markets then you should never admire a trader that has a good year. Although somebody made stellar returns betting against the consensus or “predicting a black swan”, given that markets are efficient, you are simply admiring the luck of his choice rather than talent.

If you do not believe in efficient markets then there opportunities to exploit the markets and make profits. That said, all future returns have a sampling distribution and hence you are always playing a game of probability.

It does seem immensely impressive when somebody predicts a recession but for one correct prediction there are always many more that are incorrect. Good performance does not necessarily reveal skill. In fact if the outcome was a low probability event, then the trader has to thank Lady Luck rather than his own ability. After all, you do not admire a lottery winner for his talent of picking numbers.

Hence a good trader is wrong when he is unlucky whereas a bad trader is right when he is lucky. A good trader who gets a decision wrong in highsight may be a victim of a low probability outcome path rather than a misjudgement. There are of course another group traders who understand and focus on probabilities of alternative realties and are simply not very good at it.

I must note at his point that going against a consensus opinion does not necessarily make you a bad trader. First of all the consensus may be agreeing (irrationally) on a low-probability event in the eyes of the trader betting against them. Furthermore, a good trader will trade according to risk and return. He may make a modest bet on a small but under-priced low probability event either to hedge himself against a potentially rising risk or as a way of making large profits in this unlikely state of the world.  Furthermore it must be noted that all alternative realities have an associated probability although these probabilities are never observed. A good trader will be trying to assess the true probability of each event occurring and trade accordingly. A fantastic trader will tend to get the true probabilities correct more often that he does not (even if the observed outcomes are the unlikely ones).

Poker

Poker is a game of luck, which is why it is truly an amazing feat to have “successful” poker players. The concept is very similar to finance. Poker is about decision-making given incomplete information and probabilities. Those that choose on emotions and superstition do not get very far in the game. The best poker players tend to be patient, playing the hands where the payoff odds exceed the odds of winning. Of course, the best poker players lose as well. (Two aces can lose to a 7,2 offsuit and often does in my experience)!

The point is that no poker game is predetermined and you of course need luck to win. The reason some poker players are famous is because they understand odds and positions themselves to win more hands than they lose. A bad beat is a low probability event and those that only lose to bad beats tend to be the best players over time. In any one game, these players may very well be the first to lose, but over a large sample of games, they tend to perform the best. This is because they bet on hands and in situations where they have a higher probability of winning.

As for bluffing, poker is also about observing player reactions and strategies. Some great poker players play the person rather than his cards. This is still a probabilistic strategy. Nobody can be certain the opposition is playing nothing or that he will fold a good hand. The best poker players read others around the table with higher accuracy and play their estimated probabilities accordingly.

Football Managers

Football managers often get far too much blame (or sometimes credit) far too quickly. There is no doubt that there are top football managers. Alex Ferguson and Arsene Wenger are clearly talented and are proof that there is skill in football management. But once again football results are stochastic outcomes. A great manager can be the victim of a low probability event that reshapes his entire observed outcome. Injuries and referee decisions can determine outcomes crucial to a manager’s career. Of course we can only rate managers on observed performances but it fascinates me how quickly decisions can be made given the stochastic nature of sport.

It is hard to attribute blame on a manager for any individual match. Of course managers can increase the probability of their team winning any given match with tactics and man management. However a low probability event can still occur. Swansea beating Man Utd on the weekend was a shock result, which will already beg questions of Van Gaal’s formation. However, to truly observe Van Gaal’s talent we would need to know what would happen if the match were replayed many times over. What would be an acceptable number of wins for Man Utd fans? How many wins define a good manager given the two squads?

A truly good manager increases the odds of winning a match over and above anybody else. That is why managers who have failed miserably are not necessarily bad managers. A manager that sends their team to relegation may have failed on their results but may have outperformed any other manager probabilistically. For example, a great manager of Cardiff may have increased their odds of beating a top four team from 10% to 20%. However, the likelihood is he will still lose. Furthermore, Man City’s 86 points last season seems fantastic at first look but is this a result of Pelligrini increasing the odds of his team winning or is it in line with your initial probability estimates given their squad?

It may be the case that Man City won the league in spite of Pelligrini. Two examples exist. The first is the simple case that Pelligrini was the success of a series of low probability events. The second is that Pelligrini reduced the odds of Man City winning any given match but their initial odds were so high that they were still strong favourites in most games.

History

To conclude, I want to talk about using history to predict the future as is constantly done in finance, sports and many other professions.

As constantly mentioned throughout this blog, history is a specific realisation of many different realities. You cannot therefore use this as a basis for the future just like a mathematician would not choose a sample size of 1. You may be using an extremely low probability event for your predictions.

Very rarely does the same situation occur again and again in same circumstances. Only in these cases, where you have a Monte Carlo type experiment, can you use history to help predict identical problems in the future.

This blog is not intended to downplay talents. If anything, this blog can be used to argue that you have more talents than your results suggest (or vice versa). The idea is that we should be sceptical of using short-term results, in a stochastic world, to indicate talent. Unfortunately therefore, talent is hard to judge. We do not know the underlying probabilities of these abstract alternative realities. However, give somebody a large enough sample size (enough time) and consistently above average performances will tend to indicate talent (unless of course he is just really really lucky).