The Nuclear Regulatory Commission`s (NRC`s) ongoing Accident Sequence Precursor (ASP) program uses probabilistic risk assessment (PRA) techniques to assess the potential for severe core damage (henceforth referred to simply as core damage) based on operating events. The types of operating events considered include accident sequence initiators, safety equipment failures, and degradation of plant conditions that could increase the probability that various postulated accident sequences occur. Such operating events potentially reduce the margin of safety available for prevention of core damage an thus can be considered as precursors to core damage. The current process for identifying, analyzing, and documenting ASP events is described in detail in Vanden Heuval et al. The significance of a Licensee Event Report (LER) event (or events) is measured by means of the conditional probability that the event leads to core damage, the so-called conditional core damage probability or, simply, CCDP. When the first ASP study results were published in 1982, it covered the period 1969--1979. In addition to identification and ranking of precursors, the original study attempted to estimate core damage frequency (CDF) based on the precursor events. The purpose of this paper is to compare the average annual CDF estimates calculated using the CCDP sum, Cooke-Goossens, Bier, and Abramson estimators for various reactor classes using the combined ASP data for the four years, 1990--1993. An important outcome of this comparison is an answer to the persistent question regarding the degree and effect of the positive bias of the CCDP sum method in practice. Note that this paper only compares the estimators with each other. Because the true average CDF is unknown, the estimation error is also unknown. Therefore, any observations or characterizations of bias are based on purely theoretical considerations.