The vast majority of plant and animal species reproduce sexually despite the costs associated with sexual reproduction. Genetic recombination might outweigh these costs if it helps the species escape parasite pressure by creating rare or novel genotypes, an idea known as the Red Queen hypothesis. Selection for recombination can be driven by short- and long-term effects, but the relative importance of these effects and their dependency on the parameters of an antagonistic species interaction remain unclear. We use computer simulations of a mathematical model of host-parasite coevolution to measure those effects under a wide range of parameters. We find that the real driving force underlying the Red Queen hypothesis is neither the immediate, next-generation, short-term effect nor the long-term effect but in fact a delayed short-term effect. Our results highlight the importance of differentiating clearly between immediate and delayed short-term effects when attempting to elucidate the mechanism underlying selection for recombination in the Red Queen hypothesis.