I have a set of data giving the finishing place of 10 people in a number of races. Each race starts with the racers in single file with a set distance between each racer. I want to evaluate how the starting place impacts the finishing place over time. Specifically, I want to find an average "rating" for each finishing position relative to starting position.
Let me interrupt myself here and apologize for my difficulty in stating my problem. I've been wracking my brain over this for some time now and I'm unable to get my brain around it... Anyway, I digress...
In a basic analysis, I can take the finishing position relative to the starting position which would give me a positive or negative number (Starting 5th and finishing 4th would give me a -1 place). Once I average out these results over a number of races I get the average +/- place rating for each starting position. (The 5th starting position averages -2.5 places).
This gives me a basic overview, but there are some flaws. The biggest comes at the end of the spectrum. The 1st starting position can NEVER do better than 1st and therefore can never get a negative finish relative to starting position and the 10th can likewise never do WORSE than 10th and can never get a positive finish relative to starting position. Therefore, this analysis technique is inadequate.
In the end, I want to be able to apply the final historical analysis and apply it to future races to give me an expected result of a future race.
What would be a better formula for evaluating these race results to give a more accurate overview? Or am I severely overthinking this?