A bat and ball together cost $1.10. The bat costs $1 more than the ball. How much does ball cost? Intuition says 10¢, but it’s not. The answer’s in the long description…
Neys, Rossi & Houd (2013) Bats, balls, and substitution sensitivity: cognitive misers are no happy fools. Psychonomic Bulletin & Review
Our judgment is often biased because we minimize cognitive effort and intuitively substitute the harder questions for the easier ones. A key question is whether or not people realize that they are doing this and notice their mistake.
Above, this claim is tested with the bat-and-ball problem, one of the most publicized examples of what is also called the ‘substitution bias’. The study is designed so that subjects feel no intuitive need to substitute, given the assumed simplicity of the numbers involved.
But contrary to what psychologists previously believed, we are aware that we occasionally take the lazy rather than the more complex (and appropriate) route when asked a question, and we are also less confident about our answers when we do.
The correct answer to the bat & ball question is 5¢. With the total cost of bat & ball at $1.10, and the difference between the two being $1, the ball couldn’t cost 10¢ because that’d make the bat cost $1.10, which would bring the combined price to $1.20.
Most people struggle with this question, but it’s just a natural bias!
Takeaways for decision-makers
A rather naughty one, this, but retailers would be well-placed to take advantage of our laziness with offer pricing structures like this.
That said, this recent research shows that we are indeed mindfully-aware of the fact that we’re perhaps not allocating enough brainpower over these decisions, which may harm consumer sentiment and trust.
Also note that the effect seems to be most effective when we assume the maths to be so absurdly simple that no slow, thoughtful calculations are needed. Use this with complex pricing at your peril!