Base Rate Neglect and How to Fix It

## The Bias Toward the Specific Base rate neglect is the tendency to underweight statistical base rates in favour of specific case information. In betting, you know the specific details of the match (form, injuries, motivation) and may underweight the general statistical base rate (how often do teams in this position win?). ## The Classic Demonstration Kahneman's cab problem: A witness identifies a cab as blue in a city where 85% of cabs are green and 15% are blue. Witnesses correctly identify colours 80% of the time. What is the probability the cab is actually blue? Bayesian answer: P(blue|witness says blue) = (0.80 × 0.15) / (0.80 × 0.15 + 0.20 × 0.85) = 12% / 29% ≈ 41% Despite the witness saying "blue," the base rate (85% green) means it is still more likely to be green. Most people ignore this. ## Base Rate Neglect in Betting A punter analyses an away team's attack and concludes they will score 2+ goals. The analysis focuses on their attackers' quality, the home defence's weaknesses, and the match motivation. The base rate: away teams score 2+ goals in only 18% of top-division matches. If the analysis ignores the base rate, the probability estimate is likely too high. The correct approach: start with 18%, then adjust up or down based on specific case information. ## The Correct Integration Base rate + specific information adjustment: - Base rate: 18% (away teams score 2+) - Team quality adjustment: +4% (stronger than average away attack) - Match context adjustment: +2% (defensive injury to home team) - Adjusted estimate: 24% Compare to the implied probability in the market. The base rate discipline prevents overconfident estimates from specific case analysis.