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Budgets in organisational units are considered to be traditional management support tools. On the other hand, budgetary control is the essence of control measures, allowing for the increase in the efficiency of an enterprise through appropriate allocation of resources. The methodology used in the analysis of budget variances (obtained as a result of applying budgetary control) undoubtedly influences the management efficiency of almost every organizational unit. The authors indicate a research gap of methodological and application nature in the area of risk measurement in the analysis of budget variances. Therefore, the aim of the article is to create universal and flexible models enabling probabilistic quantification of the risk of budget variance regardless of the nature of the cost, the person budgeting and the budgeting unit. Extreme value theory was used to develop the model. The results of the work are models allowing for the estimation of the limit level of deviation for assumed probabilities and models determining the level of deviation for a given probability level. The application of these models in budgetary control will allow for a synthetic assessment of the degree of budget execution in the company, comparing the quality of budget execution over time as well as between units, defining the limits of materiality of budget variances. For the purpose of model verification, the authors have used budget variances of cost energy consumption, which have been determined on the basis of empirical distributions obtained from data coming from the system of budgetary control implemented at a university located in a larger European city. Full article