People have a common-sense notion of intelligence and use it to evaluate decisions and decision-makers. One can attribute intelligence by evaluating the strategy or the outcome of a goal-directed agent. We propose a model of intelligence attribution, based on inverse planning in Partially Observable Markov Decision Processes (POMDPs) in a probabilistic environment, inferring the most likely planning parameters given observed actions. The model explains the agent’s decisions by a combination of probabilistic planning, a softmax decision noise, prior knowledge about the world and forgetting, estimating the agent’s intelligence by a proxy measure of efficiently optimising costs and rewards. Behavioural evidence from two experiments shows that people cluster into those who attribute intelligence to the strategy and those who attribute intelligence to the outcome of the observed actions. People in the strategy cluster attribute more intelligence to decisions that minimise the agent’s overall cost, even if the outcome is unlucky. People in the outcome cluster attribute intelligence to the outcome, judging low-cost outcomes as a sign of intelligence even if the outcome is accidental and make neutral judgements before they observe the result. Our model explains human intelligence judgements better than perceptual cues such as the number of revisits or moves.