A metric for improvement

In your first analysis, you will investigate how times of swimmers in 50 m events change as they move between low numbered lanes (1-3) to high numbered lanes (6-8) in the semifinals and finals. We showed in the previous chapter that there is little difference between semifinal and final performance, so you will neglect any differences due to it being the final versus the semifinal.

You want to use as much data as you can, so use all four strokes for both the men's and women's competitions. As such, what would be a good metric for improvement from one round to the next for an individual swimmer, where t_a is the swim time in a low numbered lane and t_b is the swim time in a high numbered lane?