We ask how the offense-defense balance scales, meaning how it changes as investments into a conflict increase. To do so we offer a general formalization of the offense-defense balance in terms of contest success functions. Simple models of ground invasions and cyberattacks that exploit software vulnerabilities suggest that, in both cases, growth in investments will favor offense when investment levels are sufficiently low and favor defense when they are sufficiently high. We refer to this phenomenon as offensive-then-defensive scaling or OD-scaling. Such scaling effects may help us understand the security implications of applications of artificial intelligence that in essence scale up existing capabilities.