Bias does not lead to random errors. Error in which measured values depart from true values in a consistent, predictable way. The measurements are biased and inaccurate. You're pretty sure that the smokers will be slower, and this bias is reflected in your readings of their running times. Bias leads to systematic errors.
Systematic errors lead to bias.
For example, you're comparing amoxicillin to placebo for treatment of otitis media, but most of the kids in your placebo group have more severe ear infections than most of the kids in your amoxicillin group. For example, you expect kids receiving amoxicillin to get better faster than those receiving placebo, and this causes you unintentionally to exaggerate the improvement in the kids receiving amoxicillin and to over-rate the continuation of symptoms in the kids receiving placebo.