An engine control system includes a dosing control module and an offset determination module. The dosing control module actuates an injector to inject a first amount of reducing agent into exhaust gas produced by an engine during a period when a temperature of the exhaust gas is greater than a predetermined temperature threshold. The offset determination module determines an efficiency of a selective catalytic reduction (SCR) material based on measured amounts of nitrogen oxide (NOx) during the period and expected NOx amounts, wherein the measured amounts of NOx are measured at locations upstream and downstream from the SCR material, and wherein the expected NOx amounts are based on the temperature of the exhaust gas and the first amount of reducing agent.