Our startup is constantly focused on improving our SERP position for key, transactional terms. However, measuring progress on a weekly basis across thousands of terms can be a challenge. Moving from SERP position 45 to 40 is way easier than moving from 6 to 1, and this makes it challenging to determine holistically how much we are improving on a weekly basis across thousands of terms.

One can imagine that the SERP position vs. difficulty graph looks like 1/x where the y-axis is difficulty and the x-axis is SERP position. Thus, measuring improvement would involve summing 1/$current_serp_position - 1/$previous_serp_position for each term. This is obviously very crude, has anyone come up with a more refined and accurate way to measure this?