Hybrid control arms, which supplement the control arm of a trial with either historical trial controls or historical/contemporaneous real-world cohorts, can reduce the amount of time and resources required to complete a trial. Methods have been proposed for designing hybrid control arm trials that adaptively change the randomization ratio at interim analyses based on how many control patients are effectively borrowed from external data. However, the standard statistic for measuring this quantity, referred to as the effective historical sample size (EHSS), can be misleading because it makes assumptions about the ratio of treated to control patients that do not hold if external controls are borrowed. This can lead to underestimating the number of patients borrowed. We propose an improved statistic for exponential survival outcomes based on inverting the variance, as well as potential extensions to other generating distributions. We show through simulations that our statistic can reduce the mean squared error by over 90% in estimating the number of events borrowed in exponential data compared to the standard statistic, and discuss implications for trial design.