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The degree of human cooperation among strangers is a major evolutionary puzzle. A prominent explanation is that cooperation maintained because many individuals have a predisposition to punish those violating group-beneficial norms. A critical condition for cooperation to evolve in evolutionary models is that punishment increases with the severity of the violation. Here we present evidence from a field experiment with real-life interactions that, unlike in lab experiments, altruistic punishment does not increase with the severity of the violation, regardless of whether it is direct (confronting a violator) or indirect (withholding help). We also document growing concerns for counter-punishment as the severity of the violation increases, indicating that the marginal cost of direct punishment increases with the severity of violations. The evidence suggests that altruistic punishment may not provide appropriate incentives to deter large violations. Our findings thus offer a rationale for the emergence of formal institutions for prompting large-scale cooperation among strangers.