- Quantitative measures vs. emotional impressions
- Vividness - thinking the ball into the net
- Phraseology - the importance of wording
- Underweighting rare events
Probability
Do you understand why wagering on your preferred team might not be wise? It's akin to why lotteries capture so much attention and why the odds of rare occurrences, such as making a hole-in-one, are often misjudged. This all boils down to our skewed perceptions, a result of what's known as the possibility and certainty effects.
Many gamblers don't evaluate a bet's worth through its Expected Value (EV). Instead, they lean on their sentiments regarding the potential gains. Take, for instance, assessing the significance of these enhancements in your chance to secure €1 million:
Although each scenario presents an identical quantitative change (a 5% increase), they evoke distinct qualitative feelings – that is, each scenario triggers a unique emotional response. Observe the following chart:
Scenario (a) shifts you from a zero chance to a slim chance of claiming the €1million prize, with a likelihood of 0.05. This leap into the realm of possibility serves as a pivotal moment for positive feelings. Known as the possibility effect, this sensation often causes gamblers to overestimate long shots, fueling lottery participation where a modest investment can lead to substantial winnings.
Scenarios (b) and (c) usually leave less of an impression. While your chances technically double in (b), it fails to deliver a significant qualitative impact—it doesn't hit the same psychological triggers.
In scenario (d), the outcome becomes a certainty (100%), showcasing the certainty effect's inverse. Without EV calculations, results nearing certainty are frequently undervalued relative to their actual likelihood.
Vividness – thinking the ball into the net
Even with the advantages of accurately assessing odds, punters often prefer betting on Team A over Team B, believing it's more probable, not due to a calculation of value but intuition.
Moreover, research indicates that the objective application of odds in determining outcomes diminishes when the subject matter elicits a strong emotional image of a result or when a wager's phrasing demands concentrated attention.
Regarding our lottery example, consider the common daydream: "what would you do if you won the lottery?" This conjures a vivid fantasy about an improbable win, leading to an overestimation of winning the jackpot.
For similar reasons, placing bets on a favored team or athlete is ill-advised as your emotional connection creates more intense visions of winning scenarios—like imagining the ball in the net—thus overstating the chances.
Phraseology – the importance of wording
Clear wording in a bet facilitates more accurate Expected Value calculations, ensuring weightings are aligned with or close to actual probabilities. However, subtle differences in phrasing can alter perceptions.
"One of the cardinal betting principles is evaluating any wager by its Expected Value."For instance, head-to-head markets might be described either as 'Player A versus the field', or by listing all competitors, including Player A (e.g., Player A: 3.201, Player B: 9.454, Player C: 11.232, etc.).
The first approach simplifies Player A's challenge, leading to a cognitive bias towards his likelihood of success. The latter, despite representing the same odds, appears more intimidating simply because it enumerates the rivals Player A needs to defeat, causing an undervaluation of his chances.
Focus is as important as emotion
Likewise, the emphasis is crucial in misestimating odds. Common bets include:
“Will Team A score?”
Odds Yes/Odds No
“Will Team B score?”
Odds Yes/Odds No
Bettor's assessments are biased when focusing on single options rather than considering both questions together:
“Will both Team A & Team B score”
Odds Yes/Odds No
A 1999 study by Craig Fox and the late psychologist Amos Tversky illustrates this. They queried a group of American basketball enthusiasts about the individual odds of the eight quarter-finalists in the NBA Playoffs.
Judging without accurate calculations leads to the underestimation of likelihoods.
Focusing solely on one team at a time, coupled with their vivid impressions as fans, led them to overestimate the combined odds for the eight teams to an unrealistic 240%. Logically, it should have been 100%.
However, when estimating the chances for a winner from either the Eastern or Western Conference, the probabilities were much closer to 100%. This occurred because both options elicited less emotional reaction and were similarly specific.
Rare events & underweighting – the hole in one gang
The notorious bet by two individuals in 1991, dubbed the Hole In One Gang, exemplifies how difficulty in visualizing uncommon occurrences and judgments without proper calculations result in the underestimation of odds.
After thorough statistical analysis, they determined the chances of an ace during a European Golf Tour event were around 2.25. With this insight, they traveled the country, proposing wagers on aces occurring in televised golf tournaments to independent bookies, who lacked advanced risk assessment and thus relied on gut feeling.
Bookmakers deemed aces rare, having little personal experience or televised evidence to count on. Consequently, they offered odds ranging from 4.00 to 101.00, starkly underestimating the event's likelihood.
A fundamental betting axiom is that every wager should be gauged on Expected Value – the mean of possible outcomes, each weighted by its probability.
Regrettably, bettors often assign significance to bet options based on their feelings about the chances, leading to the possibility and certainty effects, which can be quite detrimental.
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