Invasive species management requires allocation of limited resources towards the proactive mitigation of those species that could elicit the highest ecological impacts. However, we lack predictive capacity with respect to the identities and degree of ecological impacts of invasive species. Here, we combine the relative per capita effects and relative field abundances of invader as compared to native species into a new metric, ''Relative Impact Potential'' (RIP), and test whether this metric can reliably predict high impact invaders. This metric tests the impact of invaders relative to the baseline impacts of natives on the broader ecological community. We first derived the functional responses (i.e. per capita effects) of two ecologically damaging invasive fish species in Europe, the Ponto-Caspian round goby (Neogobius melanostomus) and Asian topmouth gudgeon (Pseudorasbora parva), and their native trophic analogues, the bullhead (Cottus gobio; also C. bairdi) and bitterling (Rhodeus amarus), towards several prey species. This establishes the existence and relative strengths of the predator-prey relationships. Then, we derived ecologically comparable field abundance estimates of the invader and native fish from surveys and literature. This establishes the multipliers for the above per capita effects. Despite both predators having known 123Biol Invasions (2017) 19:1653-1665 DOI 10.1007/s10530-017-1378 severe detrimental field impacts, their functional responses alone were of modest predictive power in this regard; however, incorporation of their abundances relative to natives into the RIP metric gave high predictive power. We present invader/native RIP biplots that provide an intuitive visualisation of comparisons among the invasive and native species, reflecting the known broad ecological impacts of the invaders. Thus, we provide a mechanistic understanding of invasive species impacts and a predictive tool for use by practitioners, for example, in risk assessments.