For disciples of rational choice theory the business of gambling presents a headache. Supposedly individuals always make rational decisions by trying to maximise their advantage whilst minimising their losses. You wouldn’t pay €1,000 for a holiday if you thought it was worth only €500. If a bet has an expected value of zero or lower, why do gamblers strike them? Read on to find out.
The psychology of betting is undoubtedly a complex subject but on the surface, there is a simple question; if gamblers, on average, lose money, why do they still find it desirable to gamble? In this article, we will explore the lack of understanding in terms of expected value as well as why mathematical expectation and utility (or desirability) don’t necessarily mean the same thing.
For most types of gambling, including casino games and lotteries, the expected value is negative. For the vast majority of sports bettors where outcome probabilities are not determined mathematically from first principles, expectation appears to be similarly unprofitable.
Once the costs of playing have been taken into account – the house edge, the poker rake, the bookmaker’s margin and so on – the typical gambler will lose money over a period of play. Granted, short term providence can see them make gains but ultimately the law of large numbers will conspire to defeat even the luckiest of players.
Our inability to judge probabilities correctly is but one of many cognitive biases that we experience and which lead us astray from rational decision making.
On this basis it might be reasonable to argue that gambling represents an irrational behaviour. Furthermore, there is abundant evidence to suggest that players do not understand the probabilities that accompany their decision making.
One specific example of the above involves the Possibility and Certainty Effects where decision makers overweigh and underweigh the probability of unlikely and near certain events respectively. In betting, this manifests itself as the favourite–longshot bias where longshots contain relatively poorer expected value with respect to favourites.
Our inability to judge probabilities correctly is but one of many cognitive biases that we experience and which lead us astray from rational decision making. In the context of gambling it arguably gives rise to perhaps an even more powerful bias: overconfidence.
Overconfidence or illusory superiority is a cognitive bias whereby individuals overestimate their own qualities and abilities relative to others. Given the competitive environment that exists in gambling and particularly sports betting where forecasters’ wits are pitted against each other, we should expect to see overconfidence commonplace.
Sometimes known as the Lake Wobegon (or above-average) effect, named after a fictional town in Minnesota, it describes the natural human self-serving tendency to overestimate one’s capabilities. In Lake Wobegon all the women are strong, all the men are good-looking and all the children are above average. The Lake Wobegon effect, where the majority of a group claims to be above average, has been observed in many domains including social popularity, intelligence and driving skill.
Odds just represent a public reflection of all privately held opinions about the likelihood of the outcome, expressed through money.
I have certainly observed the Lake Wobegon effect amongst the sports advisory service community. In the 1976/77 (US) College Board Student Descriptive Questionnaire, 60% of the 829,000 high-school seniors rated themselves as being above average in athletic ability compared to just 6% below. These figures diverged even more when rating for leadership qualities (70% versus 2%). For the ability to get along with others, none of them considered themselves to be below average at all!
In his best seller Thinking, Fast and Slow, cognitive psychologist Daniel Kahneman tells the story of an encounter with an investment manager at a Wall Street firm, and specifically a question he posed. “When you sell a stock, who buys it?” More generally, what makes one person buy and the other person sell? What do the sellers think they know that the buyers don’t?
Evidently, someone must be wrong, or at least more wrong than the other. The alternative is that every transaction takes place at the ‘true’ price implying no one ever makes a profit. Now that would be irrational. Given that both parties are happy to engage in a transaction, mutual overconfidence of their own abilities to assess a stock price accurately must account for why they are willing to do so.
Having knowledge of how much a bookmaker charges you or why we bet doesn’t detract from the enjoyment it can bring, it simply sets you on the right path to finding expected value.
The same is true in betting. In essence, the odds for an outcome broadly reflect the probability of it happening. After all, no one is going to bet 1.05 (or 1/20) for Sutton United to beat Arsenal FC, regardless of what they might think about Arsène Wenger. The odds just represent a public reflection of all privately held opinions about the likelihood of the outcome, expressed through money.
The value the odds settle at represents an implicit process of bartering and compromise. Both backer (buyer) and layer (seller) will intuitively have in their minds roughly what they think a suitable price would represent for them. Overconfidence then allows for both parties to mutually hold the perception that each of them has secured some sort of positive expected value at the expense of the other, which of course is a logical impossibility.
Without this overconfidence, the bet would not take place since both rationally self-interested parties are motivated by the expectation of making a profit based on information that is better than his opponent’s, not throwing away money for the sake of it.
While irrationality, overconfidence and other behavioural biases may explain why we bet, it doesn’t necessarily mean they can control how we bet. With an understanding of what these behavioural biases mean and that to some degree, they influence everyone; bettors can take an “outside looking in” view.
Knowing how behavioural biases influence betting decisions and being able to calculate betting margins doesn’t detract from the enjoyment it can bring, it simply sets you on the right path to finding expected value and taking a more educated approach to betting.
The obvious question that arises from this article is: what is it that breeds such overconfidence in a betting context? What makes bettors so sure that they are right?