In tasks as diverse as stock market predictions and jury deliberations, a person's feelings of confidence in the appropriateness of different choices often impact that person's final choice. The current study examines the mathematical modeling of confidence calibration in a simple dual-choice task. Experiments are motivated by an accumulator model, which proposes that information supporting each alternative accrues on separate counters. The observer responds in favor of whichever alternative's counter first hits a designated threshold. Confidence can then be scaled from the difference between the counters at the time that the observer makes a response. The authors examine the overconfidence result in general and present new findings dealing with the effect of response bias on confidence calibration.