Carbon dioxide emissions impose a social cost on economies, owing to the damages they will cause in the future. In particular, climate change may trigger tipping points in the climate or economic system. Tipping points induce higher expected damages and risk that damages may be catastrophic, both of which increase the Social Cost of Carbon. However, the respective contributions of higher expected damages and risk have not been disentangled. In this article, we develop a methodology to compare how much expected damages explain the Social Cost of Carbon, compared to the risky nature of a stochastic tipping point. We analyze the conditions under which approaches relying on expected damages underestimate the Social Cost of Carbon in the presence of tipping points. We find that it takes productivity shocks higher than 10\%, for risk aversion to play a role, which is on the high end of the range of damages commonly assumed in Integrated Assessment Models. Deterministic approaches are suitable to estimate SCC for lower shocks.