Hi Nablator,
indeed the two methods are different. As one can also see from Patrick's numbers, your method apparently results in fewer words in positions 5 and 10.
These are the total word counts I get for each position:
1 4809
2 3240
3 3503
4 3093
5 2659
6 3802
7 3456
8 3140
9 3603
10 1278
Of course, which method is best is debatable. If you normalize by the total number of words in each position (the totals listed above), instead of the sum of o+qo, you get something closer to Patrick's plot. Also, the numbers on the Y axis actually correspond to pattern frequency. The anomalies at 5 and 10 due to how positions are computed disappear.
Top is my attempt at writing in Python what you did with awk.
Middle is the same, but with the normalization I described above.
Bottom: my re-computation of Patrick's plot.
The plots are much closer with the normalization, but there still are differences, most notably at position 2. Unless I messed up something, these are likely due to how positions are computed. The normalized version of your method appear to produce the smoother results (these was already apparent from your ratio plots, which are not affected by the change in normalization).
indeed the two methods are different. As one can also see from Patrick's numbers, your method apparently results in fewer words in positions 5 and 10.
These are the total word counts I get for each position:
1 4809
2 3240
3 3503
4 3093
5 2659
6 3802
7 3456
8 3140
9 3603
10 1278
Of course, which method is best is debatable. If you normalize by the total number of words in each position (the totals listed above), instead of the sum of o+qo, you get something closer to Patrick's plot. Also, the numbers on the Y axis actually correspond to pattern frequency. The anomalies at 5 and 10 due to how positions are computed disappear.
Top is my attempt at writing in Python what you did with awk.
Middle is the same, but with the normalization I described above.
Bottom: my re-computation of Patrick's plot.
The plots are much closer with the normalization, but there still are differences, most notably at position 2. Unless I messed up something, these are likely due to how positions are computed. The normalized version of your method appear to produce the smoother results (these was already apparent from your ratio plots, which are not affected by the change in normalization).
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