The person who is overconfident about his ability will choose the trickier task more often, as will the person who sticks to his belief in his ability in the face of conflicting evidence. Weinberg demonstrates that, under reasonable circumstances, such double irrationality will yield better outcomes:
an individual who underestimates the variance of his priors is more willing to choose the challenging task, which raises expected output and utility.
But on average, this overconfidence has served him well; the availability effect has caused his critics to overlook all the runs he has made by selecting extravagant shots.
And, compare his test record to that of men of comparable talent but lesser self-belief, such as Graeme Hick or Mark Ramprakash. Their under-confidence led them to scratch around defensively until they got out. Which corroborates Weinberg’s theory, that overconfidence can be a good thing.
This is not just a theory about cricket. It applies to less important matters. For example, moderately over-confident traders or chief executives, on average, might do better than ones with more accurate beliefs about their ability.
And it also raises a puzzle about the nature of rationality. Belief rationality - proportioning one’s perception of one’s ability to the evidence - can conflict with act-rationality, the choice of best (on average) actions.
* You might object that he is not moderately but extremely overconfident, but I‘m not sure; his ability is high, as well as his self-regard.