The analysis of games and sports as complex systems can give insights into the dynamics of human competition and has been proven useful in soccer, basketball, and other professional sports. In this paper, we present a model for dodgeball, a popular sport in U.S. schools, and analyze it using an ordinary differential equation (ODE) compartmental model and stochastic agent-based game simulations. The ODE model reveals a rich landscape with different game dynamics occurring depending on the strategies used by the teams, which can in some cases be mapped to scenarios in competitive species models. Stochastic agent-based game simulations confirm and complement the predictions of the deterministic ODE models. In some scenarios, game victory can be interpreted as a noise-driven escape from the basin of attraction of a stable fixed point, resulting in extremely long games when the number of players is large. Using the ODE and agent-based models, we construct a strategy to increase the probability of winning.