Here is my two cents worth.
Lets say I have a total of 3000 putts. Based on Nivlac's example.
Putt Distance Conversion #putts
0-5ft 48.51% 1455
5-10 ft 15.98% 479
10-25 ft 8.50% 255
25-50ft 0.64% 19
The above example represents an overall putting average based on the total number of putts. Hence 792 putts out of 3000 were not converted at the specified distances.
Now if we knew how many putts one had the opportunity at each distance then you can examine putting percentages at each distance. These values will be significantly different. For example lets segregate out of the 792 putts that were not converted, 265 of those putts were in the 0-5ft range and 300 putts were in the 5-10 foot range.
Putt distance Conversion Percentage
0-5ft 1455/1720 84.59%
5-10ft 479/779 61.48%
Hence, the first table gives you an overall view and the second table gives you a per distance view. Each are valuable. The second table can give you a better indication of what you need to work on.
However, if you following your game and keeping notes like I do, (spreadsheet form) you already know what areas you are improving on and what areas you need to improve.
Thus resetting the putting stats from time to time or using the last 200 rounds in the calculation will provide more information to a player which is statistically sufficient. Hence the improvement one may see is entirely dependent on the total number of putts.