Social robots have become increasingly prominent in the realm of physical activity promotion. However, the technological complexity and primarily anthropomorphic designs of these robots pose challenges for their application in everyday settings. This study positions spherical robots as an emerging subtype of social robots and explores their potential to promote physical activity at home by identifying useful behavioral design patterns. To this end, we engaged theater professionals and human-robot interaction researchers in a 4-day workshop, leveraging a speculative design methodology. A puppeteer controlling a robotic ball and two actors improvised human-robot encounters in a staged home setting. These encounters were analyzed to identify instances where the ball triggered physical activity. From this analysis, we extracted nine design patterns that articulate robot behaviors for initiating physical interaction. Additionally, our findings revealed that these patterns could be combined into complex sequences to sustain physical activities, which are experienced as meaningful when framed within a narrative. We discuss the contents of these patterns and their potential value for home-based healthcare applications. Our contribution lies in articulating the potential of spherical robots for promoting physical activity at home through design patterns informed by a performative approach to human-robot interaction.