The Possibility and Certainty Effects give rise to a twisted perception that judging the likelihood of rare events is so difficult. The example of this is the lottery. However, betting on the team that you are attached to is extremely bad idea.
In general, bettors instead of measuring the value of a bet by its Expected Value (EV), they consider what they feel about the potential returns. Let’s try rating the importance of the increases below in our chance to win $1 million:
Every option stands for equal quantitative change (a 5% improvement). However, they produce different qualitative impressions, or so to say, every single option creates a different emotional reaction.
In option (a), one moves from no chance of winning the $1 million to having a chance. The positive emotion is present because this chance, no matter how small is, there is still a probability of 0.05 and this feeling is called the Possibility Effect. This leads bettors to overweight long shots and it is the incentive which makes gamblers participate in a lottery because for small money, it offers the possibility of a huge return.
In option (b) and (c) there is less dramatic impressions. Option (b) offers even double of what option (a) does. However, the qualitative impact is absent since it doesn’t have the same mental effects and it doesn’t cause significant mental reactions.
Option (d) provides a 100 % certainty and is opposite to the Possibility Effect. Thus is called the Certainty Effect, which means that when EV calculations are not present, and outcomes which are almost certain are in general underweighted compared to their probability.
Although weighing the probabilities is very beneficial, bettors will usually bet on one team over the other simply because the think it is a more likely occurrence, without calculating a superior value. According to studies, when a subject matter stimulates emotional representation of an outcome, one has a declined ability to assess the probability of outcomes in an unbiased way.
Therefore, your emotional attachment to your favourite team will create your biased projections of the desired outcome – thinking the ball into the net – and thus your will overweight the probability of that team winning. All of this makes placing a bet on your favourite team a really bad idea.
Why the phrasing is important
An Expected Value calculation is easier to make when a bet has a clear wording because in that way weighting will be close to or match probability. If a bet is worded in a slightly different way, then this could make a huge difference to how it is interpreted.
For example, outright markets can be phrased as either, ‘Player A vs. the field’, or as a long list of all participants including Player A (e.g. Player A: 3.201, Player B: 9.454, Player C: 11.232, etc.).
What this means is that the first option gives a simple presentation of the task for Player A and this stimulates cognitive overweighting of his probability of success. The second option seems to have more frightening prospect. The truth here is that the probability of success is the same as in the first option, but in the second option the opponents of Player A are known and listed. Thus, this results in underweighted assessment.
Never lose focus over emotion
| “Will Team A score?” Odds Yes/Odds No |
“Will Team B score?” Odds Yes/Odds No |
This is a very common bet to see. However, it is important to focus here in order to prevent misjudgment of probability.
If you focus on only one bet in isolation, i.e. not properly considering the other one as a whole, then your judgment may be overweighted. Thus, the following combination of both questions gives a better perspective:
“Will both Team A & Team B score”
Odds Yes/Odds No
There was one study in 1999 by Craig Fox and psychologist Amos Tversky. This study included a group of US basketball fans to assess the individual chances of the eight quarter-finalists in the NBA Playoffs. The aggregated probability for the outcomes was significantly overweighted at 240 % for the eight teams. This was because the focus was exclusively on assessing the chances of just one team at a time and because they were all NBA fans who had vivid impressions of each team.
On the other hand, later they were asked to assess the chances of winning of Eastern Conference as opposed to Western Conference and these probabilities turned to be close to 100 %. This was a result of the fact that the two options generated less emotional response and they were equally specific.
How are rare events related to underweighting?
The inability to visualise a rare event and the lack of proper calculation leads to underweighting of probability. This is illustrated by a betting coup in 1991, who became known as the Hole in One Gang.
The two bettors calculated that the odds of a hole-in-one occurring at a European Golf Tour event were approximately 2.25, after they analysed statistics. They targeted various independent bookmakers and requested odds for a hole-in-one, but as risk assessment in that time was not so sophisticated, they only relied on their intuition. With little or no experience with a hole-in-one events for bookmakers, the quotes offered ranged from 4.00 to 101.1 and this was a great example of how one rare event can be overweighted.
Sadly, as bettors rely on their feelings and place bets based on how they feel about the probabilities, which results in the Possibility and Certainty Effects, these kinds of mistakes can turn out to be very costly.
Again, the golden rule in betting is to assess every bet in terms of Expected Value – the average of outcomes each weighted by probability.