Numbers of observations in BLUP analyses and after adjustments for genetic parameter estimation are shown in Table 3, and the basic statistical characteristics of penalty points and their transformations are shown in Table 2. The records on jumping performance had a non- normal distribution. This was due to a high number of observations with 0, 4, 8 and 12 penalty points and a high number of unfinished jumping events and disqualifica- tions (e.g., originally more than 50 penalty points). Dis- tributions of dependent variables are shown in Fig. 1 for log APPs and PPs, and Fig. 2 for Blom-transformed PPs APPs. Defining the effect of event as both fixed and random was tested for all transformations, however differences of results were very small in favor of fixed (e.g., maximal difference in heritability was 0.005). Relative variances of random effects to total phenotypic variances in model with fixed event are shown in Table 4. Based upon the genetic parameters estimated from the single-trait model and criteria described in materials and methods, Blom-transformed penalty points were chosen as the most suitable dependent variable for the evaluation of horse show-jumping performance in the Czech Repub- lic. Blom-transformed PPs were therefore further exam- ined in multi-trait analyses, and the results are shown in Table 5. The Blom transformation was performed across the entire dataset at one time. However, an alternative