Result of a specfic plot
Just read the graph carefully. With a low value threshold, you have a very high log probability of false detection. You want to minimize this detection rate. If your goal is to minimize the false alarm rate with a lower threshold, then the yellow curve is preferable. The false alarm rate drops off at a lower threshold in that case, and more rapidly too. Stated another way, you will get fewer false detections over a wider range of thresholds with yellow.