I hope you have enjoyed the first part of the series “Thinking, Fast and Slow: Lessons for Punters” in which I covered the issue of overconfidence and how to deal with it in a betting context. Today I will continue with the second part of my review of Daniel Kahneman’s bestseller “Thinking, Fast and Slow” in which I will talk about extreme events in betting.
When analysing the historical results of a series of bets, be it from a tipster record or from a betting strategy, we will often encounter figures that are hard to believe. Any experienced punter knows that a long-term yield of 1% is more than most could hope for and yet we often encounter two-figure positive yields. Below you will find out what is causing such results and how you should read them.
And while on the long term things tend to even out, in the short term the variance is huge and you are bound to see some pretty extreme series of bets. You will learn why this is part of the game and why such occurrences should not bother you nearly as much as they do.
In short, today we will deal with extremes in betting – what do they mean and what should we do about them. Let’s dive in.
Collect small samples – get extreme results
A study on the incidence of kidney cancer in the 3141 counties in the USA found out that the counties with the lowest kidney cancer incidence are mostly rural, sparsely populated and located in traditionally Republican states.
What do you make of it? Perhaps the lack of air and water pollution and the access to fresh food contribute to the healthy lifestyles of the people living in these counties. But here is the kicker:
The same study also found out that the counties with the highest incidence of kidney cancer are mostly rural, sparsely populated and located in traditionally Republican states.
What is going on here? The study is the perfect example that small samples tend to deliver extreme results – both in the positive and in the negative domain. In fact living in a rural county has no proven connection to the risk of kidney cancer. Those counties simply have a small average amount of people living in them so they tend to deviate from the average quite a bit – not the case for densely populated counties.
This is a powerful example of the well-known (but not so well intuitively understood) fact that if your sample is not big enough the conclusions you draw from it probably don’t mean much. In betting you have the additional issue that until your sample grows to a sufficient size, any trend that you might have benefited from will probably be already gone. You must account for both facts and make a reasonable trade-off when deciding on a betting strategy to follow. In any case, approaching any statistics drawn from small samples with caution is a useful habit which can save you a lot of time and money when it comes to betting.
Regression to the Mean – in the long term things even out
This one has been covered in virtually every betting blog out there and yet people just continue to forget it – such is the nature of behavioural biases.
Daniel Kahneman has worked as an adviser to Israeli Air Forces and has spoken to a few flight instructors. The flight instructors seemed to have deduced from their experience with pilots that if you encourage a pilot after a good maneuver, their performance will always deteriorate for the next one. On the contrary, if you scream into their earphone after a bad maneuver they will always improve afterwards.
It turns out that, as it often happens to punters, those instructors have forgotten about the regression to the mean. A pilot executing an extremely good or bad maneuver will, statistically speaking, always tend to move to the average with his next one. Therefore performance will deteriorate after a good move and improve after a bad one, regardless of the reaction of the instructor to it.
The same happens in football when a new coach arrives at a team –the losing streak is over which is often incorrectly interpreted as a positive influence from the new coach. In fact, the old coach was probably fired a little too soon as a result of a few unlucky games. It is only natural that when a team has performed sub-par for a little while it will probably improve afterwards regardless of who is coaching them.
Ignorance of regression to the mean has been observed time and time again and yet it is one of the most difficult biases to cope with. It is simply in our nature to look for trends everywhere, including where they don’t exist. Learning to deal with this bias would surely be beneficial to any punter.
Cause and Chance – in the short term, expect the unexpected
We are predisposed to see patterns everywhere. As a consequence, we find it hard to believe that certain patterns are not the result of a trend but a pure coincidence. Imagine you have a football team that either beats the spread (W) or loses against it (L) in 6 consecutive games. Which of the following series is least likely?
If you are like most people you would have gone for the second option. The right answer is that they are all equally likely. Long winning and losing streaks are not only possible in a betting strategy, they are bound to happen – regardless of whether the strategy has an edge or not.
It is more of a roller coaster than a smooth ride
Famously, a professor has had his students write what they feel were random series of two different elements (like the ones above) and then compute series of the same length with a random number generator. The professor then managed to guess which series are human-made and which are the truly random ones. How did he do it? The samples written by his students didn’t have long enough series of repeating elements.
If you follow a betting strategy you should expect relatively long winning and losing series. If you test the self-published records of a tipster it would be reasonable to look for losing runs of certain length in order to verify that the record was not falsified. Or if you don’t thrust your intuition on that one, you can try the Wald–Wolfowitz runs test instead. If you don’t manage to find the inevitable losing streak, even though the series is long enough, it’s probably better to stay out.
The Halo Effect – extreme performances don’t last
We tent to think in clusters. If you like a person based on certain positive qualities you know in him/her, you are much more likely to guess that that same person holds other favourable qualities even if you have no evidence for that and those qualities are completely unrelated to the ones you know.
In sports, teams with strong charisma can create this effect. You might be fooled into thinking that the most unlikely Premier League winner, Leicester, has world-class players and would remain in the English top 6 in the years to come. You can be forgiven for that as you would not be the only one, however if you have bet on your conviction you would have lost quite a lot of money in the seasons thereafter.
In general, it pays to put your sympathy or dislike for certain teams or players on the side when you are betting. Furthermore, it is important to recognize the cases in which a team has won a game or even a whole tournament thanks to some portion of luck on their side. In terms of games your anchor could be expected goals. It terms of tournaments – expected points. In any case, such lucky streaks don’t tend to last. Instead of expecting the extreme the next season as well, bet against it and you could be among the few winners.
Hindsight Bias – the outcome is less important than the process
We know by now that in a short series of bets you will inevitably see very little signal and a lot of noise. Even though we know this in theory, it remains hard not to look back after a series of extremely unlucky outcomes and think how life would have been had we not placed those bets. All too often we fall victim of the hindsight bias.
The hindsight bias is prevalent in almost every area of life and is covered extensively in “Thinking, Fast and Slow”. It refers to the situations in which we look back at a surprising event, falsely believing that we were expecting it all along. Inevitably, this illusion leads us to focus on the outcome of a process, more than on the process behind it. This is the case especially when our decision lead to an undesirable outcome even though we did everything right.
We try to make sense of the past and make up stories that fit our retrospective view of things. Often times when you win a bet you will remember feeling an almost absolute certainty about the outcome of the game before placing it. Similarly, when you lose a bet you remember how you were very unsure about placing it on the first place and you already knew back then that it might not have been a very good idea. Of course in both cases you approached the bet similarly but in the one case luck was on your side and in the other one not, which later significantly altered your perception.
The very same thing happens in many different areas of life. For example today many experts would be able to explain to you the allegedly obvious hints to the previous financial crisis, while next to no one was able to predict it at the time. As Kahneman puts it:
Your inability to reconstruct past beliefs will inevitably cause you to underestimate the extent to which you were surprised by past events.
The “I-knew-it all-along” effect can significantly deteriorate your decision making process. It forces us to punish good decisions leading to bad outcomes and to reward bad decisions leading to good outcomes. Extreme outcomes can trick you into judging the process that let to them unfairly. You can turn down a bet with an edge based on a few unlucky outcomes from previous bets or similarly, pursue an unprofitable strategy just because you got lucky with the first few bets of it. The moral of the story here is to focus on the process and not to fixate on single bets. Betting is incredibly volatile activity and a good bet can go wrong in many ways – this cannot be the anchor in your betting activity. Focus on improve the way you pick your bets and the bets will pay you back later.
That was all to the second part of the series and the topic of extreme events in betting. Hopefully it has helped you gain new insights into the statistical side of sports that you can apply to your betting activity. In the next article I will continue the review of David Kahneman’s “Thinking, Fast and Slow” by covering the topic of risk aversion. You will learn what are the common mistakes we do when trying to manage risk and how to approach risk in a more rational way. Until then, I wish you a solid edge in your bets and good luck with everything else!