A choice positively contributes to a player's sense of agency when it leads to meaningfully different content. We shed light on what a player may consider meaningfully different by developing a formalism for interactive stories in terms of the change in situational content across choices. We hypothesized that a player will feel a higher sense of agency when making a choice if they foresee the available actions lead to meaningfully different states. We experimentally tested our formalism's ability to characterize choices that elicit a higher sense of agency and present evidence that supports our claim. Study participants (n=88) played a choose-your-own-adventure game and reported a higher sense of agency when faced with choices that differed in situational content over choices that didn't, despite these choices differing in non-situational ways. We contend our findings are a step toward principled approaches to the design of interactive stories that target specific cognitive and affective states.