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).