The following ratios measure to some degree the similiary between two paragraphs:
1) average length of the two paragraphs / length of lcs
2) average length / length of longest common substring
3) squared average length/ sum of squares of common substrings
Choosing the best among them as well as a reference constant required a bit of statistics which I, unable to find it online, did on my own.
I used paragraphs of various lengths (6 to 2268 characters), and various edit distances (0.29% to 56% contents changed - between couples of paragraphs meant to be matched)
I computed the above ratios for each pair of paragraphs (blue are the pairs of similar paragraphs, red are the different ones)
Here is the data; the second row histograms are zoomed-in views only including the leftmost 8% of the different paragraphs.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwViK5_hMpdwwIG3PciawoAU1wTEHbnN5SCFc3G7Bg_b4EYSEgAVy2dcgNL4HVC1cgmVcF0Hf6hxFtzHNNGLd5MSfpuv1h4eWwdn3WASPp08zdCvDTa6SZ-TcenkF2EIT0zQQ2XzyMhtc/s400/asd.jpg)
23% of the similar paragraphs are less than 25% under the limit
41% of the different paragraphs are less than 25% above the limit
2) if we choose border value 8:
8% of the similar paragraphs are less than 25% under the limit
1% of the different paragraphs are less than 25% above the limit
3) if we choose border value 30:
0% of the similar paragraphs are less than 25% under the limit
0% of the different paragraphs are less than 25% above the limit
The conclusion is:
1) inaccurate and slower
2) quite accurate and fastest
3) most accurate but slower
So a good trade off between time and accuracy is to use 2) for step 2 and 3) for step 3 (see previous post for the "steps")