We use computational modelling to examine the ability of evidence accumulation models to produce the reaction time distributions and attentional biases found in behavioural and eye-tracking research. We focus upon simulating reaction times and attention in binary choice with particular emphasis upon whether different models can predict the late onset bias (LOB), commonly found in eye movements during choice (sometimes called the gaze cascade). The first finding is that this bias is predicted by models even when attention is entirely random and independent of the choice process. This shows that the LOB is not evidence of a feedback loop between evidence accumulation and attention. Second, we examine models with a relative evidence decision rule and an absolute evidence rule. In the relative models a decision is made once the difference in evidence accumulated for two items reaches a threshold. In the absolute models, a decision is made once one item accumulates a certain amount of evidence, independently of how much is accumulated for a competitor. Our core result is simple – the existence of the late onset gaze bias to the option ultimately chosen, together with a positively skewed reaction time distribution means that the stopping rule must be relative not absolute. A large scale grid search of parameter space shows that absolute threshold models struggle to predict these phenomena even when incorporating evidence decay and assumptions of either mutual inhibition or feed forward inhibition.