def get_binary_target_scale_label_id(score, display_names, proba=None):
    """
    Return (target_name, scale, label_id) tuple for a binary classifier.

    >>> get_binary_target_scale_label_id(+5.0, get_target_display_names([False, True]))
    (True, 1, 1)
    >>> get_binary_target_scale_label_id(-5.0, get_target_display_names([False, True]))
    (False, -1, 0)
    >>> get_binary_target_scale_label_id(-5.0, get_target_display_names([False, True], targets=[True]))
    (True, 1, 1)
    >>> get_binary_target_scale_label_id(-5.0, get_target_display_names([False, True], targets=[False]))
    (False, -1, 0)
    """
    if score is not None:
        label_id = 1 if score >= 0 else 0
        scale = -1 if label_id == 0 else 1
    else:
        label_id = 1 if proba[1] >= 0.5 else 0
        scale = 1
    if len(display_names) == 1:
        predicted_label_id = label_id
        label_id, target = display_names[0]
        scale *= -1 if label_id != predicted_label_id else 1
    else:
        target = display_names[label_id][1]
    return target, scale, label_id
