Vincentizing (quantile averaging) is a popular means of pooling response time distributions across individuals to produce a group average. The benefit of Vincentizing is that the resulting histogram "looks like" an average of the individuals. In this article, we competitively test Vincentizing against the more mundane approach of averaging parameter estimates from fits to individuals. We simulate data from three distributions: the ex-Gaussian, the Weibull, and the shifted-Wald. For the ex-Gaussian and the shifted-Wald, parameter averaging outperforms Vincentizing. There is only an advantage of Vincentizing for the Weibull and only when there are few observations per participant. Overall, we recommend that researchers use Vincentizing only in select circumstances and with the knowledge that Vincentized estimates are often inconsistent estimators of averaged parameters.