The arrival times at Earth of 166 flare-related shocks identified exiting the Sun (using metric radio drift data) during the maximum phase of Solar Cycle 23, were forecast in near-real time using the Shock Time of Arrival Model (STOA), the Interplanetary Shock Propagation Model (ISPM) and the Hakamada-Akasofu-Fry Model (version 2, HAFv.2). These predictions are compared with the arrival at L1 of shocks recorded in plasma and magnetic data aboard the ACE spacecraft. The resulting correspondences are graded following standard statistical methods. Among other parameters, a representative reference metric defined by {("hits" + "correct nulls") ¿ 100}/(total number of predictions) is used to describe the success rates of the predictions relative to the measurements. Resulting values for STOA, ISPM, and HAFv.2 were 50%, 57%, and 51%, respectively, for a hit window of ¿24 hours. On increasing the statistical sample by 173 events recorded during the rise phase of the same cycle, corresponding success rates of 54%, 60%, and 52%, respectively, were obtained. A χ2 test shows these results to be statistically significant at better than the 0.05 level. The effect of decreasing/increasing the size of the hit window is explored and the practical utility of shock predictions considered. Circumstances under which the models perform well/poorly are investigated through the formation, and statistical analysis, of various event subsets, within which the constituent shocks display common characteristics. The results thereby obtained are discussed in detail in the context of the limitations that affect some aspects of the data utilized in the models.