Decision analysts are concerned with the relative benefits of alternative strategies that could be implemented in the future, yet they must rely on evidence from the past. The values given to every model parameter must therefore reflect assumptions about the relationship between what has happened in the past and what will happen in the future. The purpose of this study is to explore alternative interpretations of variation in previously observed parameter values. We focus in particular on the case where a parameter, for example a log odds ratio, has been summarised by a random effects meta-analysis. We ask the question: if the log odds ratio has varied in previous studies, what distribution best represents our beliefs about the values it might take in the future ? Our analysis suggests that the answer to this question depends on the reasons why the log odds ratio has varied. Sources of variation in meta-analysis include: random variation in outcome definition - amounting to a form of measurement error, variation in treatment efficacy between the patient groups in different trials, variation between protocols, and variation in the way a given protocol is implemented. Each of these alternatives leads to a different model for how the previously observed heterogeneity might relate to the log odds ratio, or ratios, that would be seen in a future implementation. We show that these alternative models require different computations in both deterministic and probabilistic modelling frameworks. Further, when the net benefits are non-linear in the efficacy parameters, the different models will result in different expected net benefits. Our analysis suggests that the mean treatment effect from a random effects meta-analysis will only seldom be an appropriate representation of the efficacy expected in a future implementation. Instead, modelers should consider either the predictive distribution of a future treatment effect, or should assume that the future implementation will result in a distribution of treatment effects. A worked example, in a probabilistic, Bayesian posterior framework, is used to illustrate the alternative computations, and show how parameter uncertainty, variation between individuals, heterogeneity in meta-analysis, and uncertainty regarding the degree of variation, can all be combined.