The ability to innovate, i.e., to exhibit new or modified learned behaviours, can facilitate adaptation to environmental changes or exploiting novel resources. We hereby introduce a comparative approach for studying innovation rate, the 'Innovation Arena' (IA), featuring the simultaneous presentation of 20 interchangeable tasks, which subjects encounter repeatedly. The new design allows for the experimental study of innovation per time unit and for uncovering group-specific problem-solving abilities - an important feature for comparing animals with different predispositions and life histories. We applied the IA for the first time to investigate how long-term captivity affects innovative capacities in the Goffin's cockatoo, an avian model species for animal innovation. We found that fewer temporarily-captive wild birds are inclined to consistently interact with the apparatus in comparison to laboratory-raised birds. However, those that are interested solve a similar number of tasks at a similar rate, indicating no difference in the cognitive ability to solve technical problems. Our findings thus provide a contrast to previous literature, which suggested enhanced cognitive abilities and technical problem-solving skills in long-term captive animals. We discuss the impact and discrepancy between motivation and cognitive ability on innovation rate. Our findings contribute to the debate on how captivity affects innovation in animals.