Substantial risk means a strong possibility, as contrasted with a remote or even a significant possibility, that a certain result may occur or that a certain circumstance may exist. It is risk of such a nature and degree that to disregard it constitutes a gross deviation from the standard of care that a reasonable person would exercise in such a situation.
The following are examples of case law defining substantial risk:
A substantial risk of serious harm means that the risk was so great that it was almost certain to materialize if nothing was done. [Miller v. Fisher, 2010 U.S. App. LEXIS 12932 (7th Cir. Ill. June 23, 2010)]
A substantial risk means a direct relationship between the offense and a risk of violence. [United States v. Bowers, 432 F.3d 518 (3d Cir. Del. 2005)]
In the context of prisoner cases, risks attributable to detainees with known 'propensities' of violence toward a particular individual or class of individuals; to 'highly probable' attacks; and to particular detainees who pose a 'heightened risk of assault to the plaintiff' are themselves sufficient to establish a 'substantial risk.'" [Brown v. Budz, 398 F.3d 904 (7th Cir. Ill. 2005)]